These Studies on Security contain only the results of my scientific views, research, analyses and models. In other words, they provide a SUMMARY of my MAJOR contributions to the Science of Security.
  A systematization is given – including from the Security point of view – of a number of effects (inherent properties) that manifest themselves in most organizations and structures having a network character, i.e. representing one or another type of networks and being the architectural and functional basis of the Network Society that has taken place and is increasingly widespread and increasingly important.
  The following monograph of mine is devoted to a detailed analysis of these effects, common to most of the existing networks:
  Николай Слатински. Сигурността – животът на Мрежата. София: Военно издателство, 2014.
   [Nikolay Slatinski. Sigurnostta – zhivotut na Mrezhata. Sofia: Voenno iztadelstvo, 2014].
  Nikolay Slatinski. Security – the Life of the Network. Sofia: Military publishing house, 2014 (in Bulgarian)
  The gradual entry into the Network Society; the rise and spread of the network organization of processes – both in their very genesis and in their evolution; the associated generation and growth of non-traditional sources of uncertainty, insecurity and instability; the escalation of old and the emergence of new risks necessitate urgent and inevitable, undoubtedly radical and possibly dramatic changes. And this must be comprehensive changes – in the systemic dimensions of society and the complex nature of the institutional tools, in missions and visions, in goals and strategies; in the thinking and planning of actors and agents in global, continental, regional and national processes, in the overall way in which we relate to the world and construct the meaning and purpose of our behavior in it.
  The need for these changes brings to the fore one of the most difficult issues in the transfer of the civilizational baton from receding hierarchization to advancing networkization – about the interaction of hierarchical and network structures in a period of systemic, mental and behavioral transformation. This complex interaction reflects all the processes in which we , as states, peoples, societies and citizens, are interested observers and direct participants – both as causes of these processes and as their consequences.
  In the interplay between receding hierarchical and advancing network structures are also reflected those reasonable goals that we, as autonomous individuals, community beings, socially connected individuals and state-building citizens, set for ourselves in our original aspiration for greater security, controllability, order, predictability. and meaning.
  Networking, network challenges, network structures, the Network Society are extremely interesting objects of study in themselves, but their study would as well help us to know even better our world, its history and the prospects for its development. Since networks as a form of organization and mode of behavior do not arise today, they were one of the characteristics of the world in which human existence has taken place, is taking place and will take place. The changes consist in the fact that networking from a minor feature is becoming one of the leading features of the present world. And such changes cannot but change the arsenal of models and tools with which we study and manage societies, they cannot but also change the guidelines, attitudes and habits of our thinking about processes and trends.
  The web should not be seen as something predominantly technological. For the American researcher of new technologies Kevin Kelly (1952), the network is „organic behavior in a technological matrix“ [1]. We must think like one of the heroes of the American film director and actor Woody Allen (1935): „Life is all networking” [2].
  Yes, the network is also something technological, i.e. a means, a tool, an auxiliary resource, but it is much more than that. The network is multifaceted and diverse (and very strange!), always different, never the same, with a variable and fuzzy structure; with ambiguous and unfolding dynamics. It is the happening of things and the things that happens. The network is in everything and everything is in the network. The network spills and develops in time and, as it were, out of time.
  The great Bulgarian revolutionary Vasil Levski (1837 – 1873) once said: „Time is in us, and we are in time; it transforms us, and we transform it.“
  We can rephrase this thought as follows:
  "The Network is in us and we are in the Network; it transforms us, and we transform it.“
  Models and approaches from both social and natural sciences are increasingly used to study network structures. This is a quite logical association of efforts, because these sciences study one and the same world – ours, but the „sociologists“ from the social sciences, do this with more words (signs, symbols, metaphors), and the „mathematicians“ from the natural sciences, do it with more formulas. But the world is one and it obeys the general laws. This allows knowledge to be transferred from the social sciences to the natural sciences and vice versa.
  The network consists of nodes and links. The nodes are called vertices. The individual vertex in the specific networks has a different name: node, actor, author, site, etc. Connections are called edges. The individual edges in specific networks have a different name: tie, relation, bond, link, reaction, citation, etc. [3]
  In mathematical approaches, networks are considered as systems of elements, whose structure is woven mainly from horizontal connections, and vertically they are weakly structured – with no more than 2-3 levels. The study of networks, the features of their structure and their reproduction in time and space is mainly done by means of higher mathematics and physics. This allows not only to achieve a high degree of abstraction, rising above specific grading elements and functions inherent in a separate network, but also to obtain general, invariant formulas and conclusions. Here the structure (network) is the leading one, and from what it is built, from what nodes and from what kind of edges by its nature – this is of secondary importance, it is little, and often not paid attention at all. Therefore, for mathematical approaches, two networks are different if their structures are different.
  An invariant is a value, sign or relation that remains unchanged under certain transformations.
  Note. Explanations for which their source is not specifically indicated are based on the texts and definitions for them in Wikipedia.
  Social researchers are most interested in what social objects are nodes and what social dynamics are embedded in the edges connecting them. In sociological approaches, networks are considered as large communities of people connected by a common culture, common goals and values, a common attitude to the world or to a particular problem. In parallel with this, their connection, called a network (this is much more a metaphor, a mental construct) is considered – as a cause, as an ideology, as an identity. Therefore, in sociological approaches, two networks are different if their active social agents and the nature of the connections between them are different.
Identity is exactly the specificity that mathematical models cannot effectively „capture“. But in order to understand the network and understand its properties, it is necessary to understand its binding identity and its influence on the social dynamics of the network [4], because the identity, the community of views, the principles, the ideology, on the basis of which the network participants are „glued together“, influence its structure. On the other hand, sociologists underestimate the essence of the network structure, they tacitly assume that the network (the similarity of the network) is important, and what laws the functioning of the structure is subject to, in general, has little influence on the nature of individual and group relations in the network.
  We live in an increasingly networked society. According to one point of view, society is becoming networked as a consequence of the new nature of the distribution of information, and more precisely – of symbolic resources, i.e. society is what its communications are. And in the age of new communication and information technologies, the nature of which is increasingly networked, society will naturally adapt to these revolutionary changes in communications. Therefore, in the world of social networks, society will be networked. This can be formulated somewhat more radically like this: since there are social networks (for example, Facebook), the society will also be networked.
  This point of view is justified – society adapts its structures to the way in which communication occur. But the other point of view is more logical – that such social transformations occur in society, that strengthen its horizontal reorientation at the expense of the vertical one, and in such a society, naturally, communications proceed in a different way – they are „forced“ to become networked in order to reflect the network nature of society, i.e. communications is what society is. In the network (networked) society, social networks also naturally arise. And this can be formulated somewhat more radically like this: social networks (such as Facebook) exist because society is networked.
  In the scientific literature, there are studies of a wide range of network structures with distribution in various areas of social and biological life, inanimate matter, technology, space. We will present a classification of the main types of networks: social, informational, technological, biological, cognitive, etc. [5, 6, 7, 8].
  Cognitive – cognitive, associated with content, with concepts.
  SOCIAL NETWORKS are networks of relationships between social objects. Here are examples of such networks: Facebook and Twitter; networks of people related to kinship, friendship, religion, sexual relations, professional contacts, hobbies; networks of business relations – of executive directors, members of management boards of large companies, of owners (shareholders) with shares in different companies, or of companies having shares in each other; networks of scientists having joint scientific publications (co-authorship) or citing each other in such publications; networks of actors and actresses (e.g. in Hollywood) who appeared at least once together in the same film; trade and service networks and network marketing („face-to-face“); networks of epidemics – diseases and „social“ (the infection of people with infectious viruses or with viruses of ideas); networks of financial flows (financial networks) [9]; networks of managers in literature, art and science, of sports managers; networks of phone calls, emails, viber, whatsapp, skype and icq contacts and many more.
  INFORMATION NETWORKS are networks of relationships between information objects. Here are examples of such networks: citations in scientific publications (for example, A cites B, B cites C and D, C cites B and E, etc.), forwarding in WWW networks; patent references; Wikipedia; search engines on the Internet; the blogosphere; peer-to-peer networks (partner networks [10]); the spread of computer viruses.
  TECHNOLOGICAL NETWORKS are networks of relationships between technological objects. Here are examples of such networks: Internet as a hardware (physical) network of interconnected computers; WWW (World Wide Web) as a software (logical) network; electrical networks; telephone lines; transport networks (trains, buses, planes); letter and parcel delivery services; underground city sewer; pipeline networks for the transfer of strategic raw materials, such as oil and gas.
  BIOLOGICAL NETWORKS are networks of relationships between biological objects. Here are examples of such networks: neural networks (neurons are specialized nerve cells in the brain of humans and animals); the human genome and gene networks; networks of metabolic (exchange) processes; networks of reactions between proteins (of protein interactions); networks of blood vessels; networks of cells (colonies of bacteria, network-like tissues in multicellular organisms); biodiversity networks, such as mutual networks, i.e. networks of mutually beneficial interactions (connections within and between different types of plants, animals, people); networks of food chains in nature: predator-prey relationships; host-parasite networks; „symbiosis“ type networks – mutually beneficial existence of different living organisms; networks of insects that instinctively support biosocial systems (ants, bees, wasps, termites); ecological networks, econets (in some birds, dolphins, great apes); the spread of disease-causing viruses.
  COGNITIVE NETWORKS are networks of relationships between cognitive, i.e. knowledge-related objects [11]. Here are examples of such networks: networks of characters in literary works – in such as the „Iliad“ (an epic poem created by the legendary ancient Greek poet Homer, 8th century BC), „David Copperfield“ (1849, a novel by the English writer Charles Dickens , 1812 – 1870), „Les Miserables“ (1862, a novel by French writer Victor Hugo, 1802 – 1885), „Anna Karenina“ (1877, a novel by Russian writer Leo Tolstoy, 1828 – 1910), „The Adventures of Huckleberry Finn“ ( 1884, a novel by the American writer Mark Twain, 1835 – 1910); networks of characters in holy books, for example in the Bible; networks of characters from ancient Greek mythology (mortals, gods, monsters, nymphs and sirens); type 1 linguistic networks consisting of words of words with syntactic connections between them, for example the words in „1984 (1948, a novel by the English writer George Orwell, 1903 – 1950), and a dictionary built into text programs such as Word works on a similar principle); type 2 linguistic networks characterizing the connections between languages in a given region; networks of notes in the works of the German composer Johann Sebastian Bach (1685 – 1750), the unique Austrian composer Wolfgang Amadeus Mozart (1756 – 1791), the German genius, one of the greatest composers in human history Ludwig van Beethoven (1770 – 1827), of the Polish composer Frederic Chopin (1810 – 1849), of contemporary Chinese composers and in pop music; networks of individual parts, figures, colors in the paintings of cubist and/or futurist artists – Dutchman Pieter (Pete) Mondrian (1872 – 1944), Russian (and Polish) Kazimir Malevich (1879 – 1935), Spanish Pablo Picasso (1881 – 1973) ), French Braque (1882 – 1963) [12, 13].
  Nymphs – long-lived, not always immortal, beautiful demi-goddesses, personification of the life-giving forces of nature [14].
  Sirens – sea creatures, half-birds, half-girls, who bewitched the sailors with magical songs, dragging them to the rocks, where their ships were wrecked [15].
  Cubism – a modernist trend in the visual arts, characterized by the use of geometrized conditional forms and the desire to „shred“ real objects into stereometric primitives.
  Futurism – general name for artistic avant-garde movements, interested primarily in the form and not so much in the content of the poems, often inventing their own words and using vulgar vocabulary, professional jargon, the language of the document and the poster.
  Avant-gardism – a general name for art movements that are characterized by a desire for a radical renewal of artistic practices, a break with established principles and traditions and a search for new, unusual content, expressive means and forms of works.
  OTHER NETWORKS – networks that do not belong to the above types. Here are examples of such networks: geophysical networks; networks of rivers (and tributaries of a river) and lakes; network molecules from atoms of the inert gases; networks of stars and black holes (in the mega world); superstring networks (in the microworld).
  Geophysics – a complex of sciences that use physical methods to study the internal structure of the Earth, the physics of volcanoes, oceans, lakes, rivers, glaciers; atmospheric physics (meteorology, climatology).
  Inert gases – a collective name for chemical elements created as a result of the non-participation of these elements in chemical reactions. It was subsequently discovered that some of them could interact, but the name remained.
  A black hole is a region of space-time in which the gravitational pull is so strong that nothing, not even light, can escape it.
  Simply put, according to Superstring Theory, the smallest „particles“ that make up the matter are strings, which, when vibrating differently, are seen as the microparticles we know.

Network-like and maximally „flattened“ structures are found more and more often – not only in terrorist and organized criminal groups, but also in civil society, in communities with their own goals and interests, in lobbying groups and in pressure groups.
  Modern challenges are increasingly networked. And the scientists have found that networks can successfully fight with networks. But the state, the institutions of the national security system, thinking and action in the field of security retain their hierarchical structure, their pro-hierarchical complexes, reflexes and instincts.
  In hierarchical structures, the rules and procedures by which they function play a stabilizing role, create a reliable order in the organization, but become a „brake“ to the adoption of the new. Hierarchies can hardly „tolerate“ innovations (especially those related to reorganization of structure, information flows, and interaction between units and people). Even if the innovation is still adopted, the hierarchical structure incorporates it too slowly into its norms and rules [16].
  There is no fear of change in network structures – they are striving for it. The „2S2C“ rule works in them: Solidarity, Synergy, Cohesion, Cooperation.
  Synergy – a total effect of the interaction of two or more factors, characterized by the fact that their interaction significantly exceeds or is qualitatively different from the effect of the sum of the actions of the two factors separately.
  Hierarchical structures are dominated by organization from outside and from above – someone's external will structures and controls them through a one-way link „Order → Execution“.
  Network structures are dominated by organization from within and below – they are structured and controlled through a cyclical relationship Assignment → Performance Monitoring → Performance Conclusions → Optimized Assignment. This is the two-way relationship Assignment ↔ Execution.
  Control is the glue, the binding substance in hierarchical structures – in them the subordinate of my subordinate is also my subordinate; whereas in network structures the glue, the binding substance, is trust – in them my friend's friend is also my friend.
  In hierarchical structures, the leading ones are formal power, coercion, impact; in network structures – leadership, motivation, influence. In network structures, there is no need for overseers to keep an eye on how everyone else works and control everyone in the organization.   There is no need for filters sifting information up and down, nor watchdogs standing jealously in front of the leader's office to keep people from lower levels in the hierarchy out.
  Two hierarchical structures, even if they are homogeneous, interact mainly at the will of those who lead them (at the management level), while two network structures, even if they are heterogeneous, interact through mutual penetration, through interweaving.
  The problem with hierarchical structures is that they can give good results in normal life, but they are extremely inadequate in an extreme situation and are a particularly vulnerable place in crisis management, because in them people usually rely on the habitual, the well-known and the comforting; their attention is easily lulled, their goals become blurred, and their perception of reality is distorted.
  In hierarchical structures, competition is stronger than cooperation and more destructive than constructive. Therefore, they are mainly of the Newtonian type, i.e. they look like machines, in them everything is strictly ordered, mechanical, the elements are like bolts and the external environment is perceived as constant.
  In network structures, cooperation is much stronger than competition, and much more constructive than destructive. Therefore, these structures are mainly of the Prigogine type, i.e. with great complexity, which is determined both by the number of links and how they interact. These structures resemble living organisms, everything in them is flexible and self-optimizing, the elements are perceived as an integrating part of the whole, they act not so much by order or fear, but by internal necessity and with an understanding of common goals, values and interests, and the external environment is perceived as constantly changing, requiring constant vigilance of the senses.
  According to the great English mathematician and physicist Isaac Newton (1642 – 1727), space and time are absolute and independent of each other; there are strict and knowable laws that predetermine the existence and development of material and immaterial objects, and these objects cannot influence either space and time, or the laws to which they obey – this is a mechanistic world, a world of prescribed and unchangeable rules.
  Ilya Prigozhin (1917 – 2003) – Belgian scientist-physicochemist of Russian origin, winner of the Nobel Prize in Chemistry in 1977. Prigogine's type or Prigogine's logic – a dependence between cause and effect, in which they influence each other, periodically and unpredictably they change places and are so intertwined that the effect often affects the cause that produced it and of which it is a function at the given moment.
  When talking about hierarchical (i.e., with more levels) and network (i.e., with fewer levels) structures, one should not think that it is all about the architecture. This is a new era in management, in organizational behavior, in relation to goals and resources. It imposes new requirements on the structures of the security system on the international and national level. Some time ago US Secretary of Defense Donald Rumsfeld (1932 – 2021; the youngest in the post, 1975 – 1977, and the oldest in the post, 2001 – 2006) said something that was only understood as a remark regarding the adequacy of NATO, and was not deciphered as the command of the times: It is no longer the Coalition that determines the Mission, but the Mission determines the Coalition [17].
  So far we have relied on resource-oriented strategies, i.e. we have resources, skills, capacity and we strive for goals, priorities, tasks that we can realize through these resources. Now we are moving towards goal-oriented strategies, i.e. we have goals, tasks, priorities that need to be realized and we need to find resources, skills, capacities, abilities through which to implement these goals, tasks, priorities.
  We can no longer arm ourselves once and for all with some abilities and imagine that we have enough of them for everything and always; today Goal determines Resources, not Resources determine Goal. The emphasis is shifting to flexibility – flexible knowledge, flexible structures, flexible approaches, and flexible countermeasure geometries. There are no more „frozen“ organizations and architectures once and for all. If the challenges and adversaries are flexible and mobile, then so must be institutions and the people in them. Today we will fight with special intelligence means, tomorrow with financial means, the day after tomorrow with information and media resources, the day after the day after tomorrow with means of culture and identity, ideology and social activities. It is necessary to create pools of resources – ministries and departments are too hierarchical, prone to bureaucracy and bureaucratic thinking, but it is necessary to create flexible, mobile coalitions of professionals. The specialization will not be by types of activity, but by challenges – crime, terrorism, the demographic crisis, quality of life, etc. And the value of each expert will depend not on the will of his immediate superior or any party, but on his skills and professionalism, uniqueness and ability to participate in as many of these pools of resources as possible and flexible, mobile coalitions of professionals as possible.
  In other words, we must have mission strategies and mission goals, mission focus and mission thinking. From this follows the main problem for the State: the State still cannot but be hierarchically organized – this is related to its character, to the goals and objectives that it implements, to the way it functions and makes decisions; however, the State today cannot deal with new risks if it does not adopt new approaches and resources, if it does not start „networking“! The State must combine hierarchy, as it is a State, with networking in order to be able to respond adequately to new risks. The state that creates an effective hybrid organizational network will win the strategic initiative [18]. This means striving for structures that are less hierarchical (no new layers are created) and flatter (the structure is „flattened“), and moving towards a network architecture with the minimum necessary hierarchy and the most adaptive organization, which emphasizes consolidation and integration, coordination and decentralization, over command and centralization. If the enemy has a variable geometry, then the institutions with which we confront and fight him must also have such a geometry.
  When talking about the practical applications of network structures, what should be prioritized is the need for a change in thinking. Networks are not a fad, they are not just a tool and visual illustration; are not a concept introduced for a faster understanding of the studied phenomena. Networks are these phenomena; they are the form and content of life; today they are the optimal possible way to fully study the processes in various fields of knowledge and practice.
There are a number of areas of application of network structures – military affairs (Network-Centric warfare); countering terrorism and organized crime, protecting critical infrastructure, fighting various diseases, studying historical processes, social protests and much more.
  Network-centric warfare, Net-centric warfare – a theoretical system of concepts and views, implemented in practice in some modern military conflicts. In the Network-centric war, divisions, units and formations of the types of armed forces and types of troops are organized in information and command according to the network-centric architecture, which guarantees the achievement of information, communication and technological superiority over the enemy.
  The Network Society is the result of the development of human civilization. Of course, is impossible to argue that its appearance was the only possible as an alternative. But the inexorable law of history is that only what happened happened. In History there is no „If..., then...“, „What if...?“ The path chosen by humanity from a given moment is one of the existing alternatives, but once realized, it is the only possible one for historical science.
  If for us the Network Society is the only possible one, it is because it has been realized. And the main reasons for its realization lie in changes in society and changes with the environment (geopolitical, geoeconomic, geosocial and geocultural) in which society functions. It is not acceptable the thesis about a random coincidence of happy circumstances or a happy coincidence of random circumstances that led to the emergence of the Network Society, of which the development of modern communication and information technologies was the most important. The Network society would have emerged even without the explosion of communication and information technologies, but it was precisely its strongest features that allowed it to evaluate their meaning, to arm itself with them and to „deal with“ the other alternatives (they probably existed, but we cannot retrospectively guess whether they were only hypotheses or were alternatives).
  The processes and changes in various spheres of human activity – in politics, economics, energy, culture, sports, etc. – indicate that, although extremely important, communication and information technologies are not the only important factors for the emergence of the Network Society. A number of these processes and changes, to one degree or another, are not directly related to new communication and information technologies.
  The network and its inherent horizontalization of structures and communications have long been the subject of analysis in economics. For at least 2-3 decades, ideas for a new company architecture, organizational culture, new methods of management and control have been developed. Long before the Internet, it became clear that the horizontal, network-organized Microsoft would gradually gain the upper hand over the vertical, hierarchically organized IBM; and that the networked McDonald's will become much more than an international structure of catering establishments, becoming a sign of the times, a type of culture of service and attitude to the customer, a part of globalization and its symbol (McDonaldization). We see how transnational companies (TNCs) weave their networks and make big profits not only through the use of the specifics of individual countries (cheap labor, low environmental requirements), not only due to economies of scale and the ability to work in different regions and thereby combine its globality with local specifics, but also due to the properties inherent in network structures – efficiency, speed, the possibility of mobilization, self-organization, (self)synchronization. Through networking, TNCs float in their own waters. They recognized the competitive advantages, the sometimes invisible but often visible advantages of networks, and quickly began to flatten hierarchies, increase decentralization, allow their branches to self-organize as networks, as networks of networks, to scale and achieve the required level of complexity and flexibility without particularly compromising efficiency and manageability.
  Communication and information technologies are developing very fast, but society is changing slowly. By analogy with the thesis of the English priest and economist Thomas Malthus (1766 – 1834), it can be said that in political, economic, social and cultural aspects, society changes according to arithmetic progression, while communication and information technologies advance according to geometric progression. That is why technology is significantly ahead of society with its capabilities and pace of development. And the people who do not use these technologies satisfactorily – are they outside the Network Society? Yes, they are offline, but they are also connected in part of the networks of modern society, they are part of the Network Society. Society moves by its own laws, which are at least partly independent of technology.
  An arithmetic progression is a sequence of numbers a1, a2, a3…, in which each subsequent number, starting from the second, is obtained from the previous one by adding one number d (difference of the progression), such that a1, a2=a3+d, a3=a2+d, … an=an-1+d.
   A geometric progression is a sequence of numbers b1, b2, b3…, in which each subsequent number, starting from the second, is obtained from the previous one by multiplying by one number q (the denominator of the progression), so that b≠0, q≠0, b1, b2=b1q, b3=b2q, … bn=bn-1q.
  Socially, the network contains two properties that are in constant conflict. On the one hand, it most easily „includes“ those outside it. The social cost of „joining“ the network is the lowest because the network is constantly striving to grow, growth is part of its life. And that price keeps falling as the networked participants grow. On the other hand, the network is a certain type of culture, norms, values, without the assimilation of which, without meeting the standards for which, „membership“ in the network is formal (the connection is very weak), and its benefits tend to zero. In other words, the cognitive cost of connecting „to the network“ is the highest, and steadily increasing as the network evolves.
  There are other features of the network that are the subject of study by representatives of the social sciences. It is also about the network as a social coordinator – no one can coordinate efforts, attitudes, positions, messages and disagreements better than it. It is, finally, about the network as a social integrator – after all, it is actually an outstretched hand, one call: „Join, connect, get involved!“.
  The network society makes fundamentally new demands on the strategic managers of the state, on its elite, on the politicians. They should be imbued with the thought that the Network Society implies that its members are called to be at least one level of complexity higher than previous societies.
  The network requires, as has been said, a certain culture, it works through certain technologies, it imposes certain models of behavior and approaches to explaining the world. Therefore, politicians must have thinking and actions corresponding to the Network Society, behave (pro-)network and use tools appropriate and worthy of the Network Society. The anti-network behavior of politicians „pulls“ society back, slows down its development. On the other hand, the Network Society is a test and responsibility of a higher order for ordinary people, for citizens. Tempted by the opportunity to participate in various real and virtual networks, they can much more easily lose their value orientation and allow their own principles to be eroded. When the price of entry into the community is high, it requires a very long and consistent set of values, self-work, reflections and doubts. A person lives with the thought of this community, even with the idea of it, and even before he enters the community, he is already there in spirit. Whereas with the extremely low cost of entry into many of today's communities, empathy with them is far less. These communities are imaginary, but they are more than that – they are imagined. A person is, figuratively speaking, only one foot in them, he participates in them with the feeling that he is doing an experiment, that he is trying – to see how it is there. At the first disagreement, he is ready to „disconnect“, at the first „unlike“ he is ready to „unfriend“ himself. From here to value promiscuity is at most one step. And if in private life it is a right of choice that must be respected, even if not always respected as behavior, in politics it carries the risk of forming irresponsible, destructive, flexible and easy to manipulate, weakly connected spiritually and strongly imbued with negativism majority.
  Promiscuity – indiscriminate and unrestricted intimate relationships with many partners.
  In his book „The Web of Life“, the Austrian and American physicist Fritjof Capra (1939) wrote that the basic pattern of life is the network pattern [19]. The pattern or form of life is the Network. But if the Network is the form of Life, then Security is the content of the Life of the Network. The network is the most effective producer of Security. The life of the Web is devoted to the production of Security. The life of the Network is Security. The Network may not be the universal solution to the question of Security, but it is the best of all existing Security manufacturers.
  Pattern – a natural representation, a regular idea, template, image found in nature and human activity.
  One of the prominent creators in the study of networks, the American physicist of Hungarian origin Albert-László Barabászy (1967) wrote that when studying scale-free networks, he followed the creativity, attitude to the world and the creative spirit of the Bulgarian Christo (Hristo Yavashev, 1935 – 2020) and his wife, who was born on the same day as him, the Frenchwoman Jean-Claude (1935 – 2009). Christo and Jean-Claude hide, pack the item to help us see and understand it better. In order to detect networks in various complex systems, we need to hide, to mask their general appearance and all the details of visibility. Then already, looking only at the nodes and edges, we will be able to see and observe the architecture of complexity, called the Network, and networkedness, called Complexity. Only distancing, detaching from specifics, from details, allows us to see the universal organizing principle underlying the systems under study. It is the concealment, the covering that reveals, that deciphers the fundamental laws of the evolution of the networked world and helps to understand how this intricate, woven and intertwined architecture affects such diverse processes, phenomena and events. Since concealment, packaging allows you to penetrate into the deep essence, deep nature, deep design of things, then the next step is also logical – to remove the packaging. Our goal has become much clearer – to understand complexity. And to achieve this goal, we need to move beyond the structure to focus on the dynamics that govern nodes and edges. Networks are the skeleton of complexity, the highways for various processes that make our world alive, bright, real and beautiful. We need to see nodes as real people, real subjects or real objects, and edges as real connections, real links, real communications filled with real content, real goals and real strategies. Networks provide the key to understanding, but understanding is not limited to them. To continue further, we must go beyond networks – to the individuality, essence, identity of each specific process, each specific system [20]. But we should never forget that in order to make a breakthrough in understanding and and making sense of the world, we needed to see this world as it is gradually becoming and will inevitably become – a world of network structures, a world of network interactions, a world of networking. The World of the Network Society...
  For scale-free networks, see below.
  The network society is based on a network organization (horizontalized and decentralized). And a number of effects are invariably inherent to the structure and dynamics of any network organization. Below we will make a systematization of these effects.
  1. The „SIMILAR LAW OF DISTRIBUTION“ Effect – this effect can be called much more mathematically – Power law of distribution
  A huge number of networks in the real world demonstrate this amazing property. The main content of the Similar Law of Distribution is that these networks grow quantitatively and develop qualitatively not according to a random principle and not in all possible directions, but preferentially, preferably – i.e. in such a way that a very small number of nodes (hubs) manage to concentrate for themselves the lion's share of the connections that make up the fabric of the network structure, and therefore they are much larger, and much more connected with other nodes than all other nodes. In other words, some nodes, like in an Orwell farm, are more equal than others.
  Hub – a network node with special functions of a collector and distributor of signals from and to other nodes; focus, centre.
  In George Orwell's novel Animal Farm (1945), the last of the seven basic commandments governing the keeping of animals on a farm is: „All animals are equal, but some animals are more equal than others.“
  The existence of such a property is undoubtedly surprising, even stunning. With all the variety of elements, connections between elements, areas of their manifestation and functions performed by them, different networks are similar to each other – they are largely identical in how they grow and develop in space and time!
  The similar law of distribution of a huge number of networks can be described as follows: the contribution, influence, abilities and information are not distributed randomly in the network to all nodes and in all directions but are concentrated in a small number of nodes called „hubs“ or „concentrators“ [21]. In these hubs, in these privileged concentrators, there is an accumulation of vast amounts of connections or – depending on the network – concentrations of abilities and powers, resources and energy; webs of communication channels, of accumulations of information, of skills to attract and cooperate, of opportunities to influence. These are actually the most valuable links of the network (for certain networks, they are also their most vulnerable points, their weaknesses and weaknesses, their Achilles' heel).
  The Similar law of distribution of the studied network structures is called in mathematical sciences the Power law of distribution. Networks that propagate according to this law are called scale-free or scale-invariant networks – more on that below.
  A few words about the Power Law of Distribution or Power Law Degree Distribution.
  Let us first point to the much better known Gaussian distribution (called the Normal and depicted with a bell curve) and even more precisely the Poisson probability distribution of possible values – when the most probable values have the highest frequency, and those with lower probabilities decrease continuously, symmetrically; everything is predictable, as if predetermined (Figure 1).
  Normal Distribution or Gaussian Distribution – the law of probability distribution, which is a continuous distribution of probabilities grouped around the mean. It plays a very important role in various fields of knowledge. Its graph is symmetrical, bell-shaped, with a maximum in the average value; it is known as the Gaussian function. This model reflects the patterns of phenomena under the influence of many random and independent causes and factors. It is named after the German mathematician Carl Friedrich Gauss (1777 – 1855).
  Bell curve, bell-shaped curve – a graphic representation of the Normal distribution curve, shaped like a bell. For example, in the distribution of male height, the bell-shaped curve means that if we conditionally assume that most of the men are from 1.65 m to 1.85 m tall, with an average height of 1.75 m, then there are fewer men with a height of 1.50 m and 2.00 m and they are located symmetrically on both sides; men 1.35 m and 2.15 m tall are less common, men 1.20 m and 2.30 m tall are even rarer, men 1.05 m and 2.45 m tall are very rare, it is almost extremely rare to meet men 0.90 m and 2.60 m tall and it would be a complete anomalous miracle and completely impossible for the existence of men height 0.75 m and 2.75 m.
  The Poisson distribution – probability distribution of the so-called discrete type. Discreteness is a property opposite to continuity, i.e. discontinuity; something that changes between several different states; consisting of separate parts, structures, meanings. This distribution is a modeling of a random discrete variable that expresses the probability of given events occurring in a certain, fixed interval of time, representing a certain number of possible events realized in a fixed time, provided that these events occur with a fixed average intensity and independently one from another. It is named after the French mathematician and physicist Simeon Denis Poisson (1781 – 1840).
  Power law distribution – in it, unlike in the Poisson distribution, there is such a dependence between two quantities that the relative change of one quantity leads to a proportional relative change in the other quantity, which is independent of the initial value of these two quantities, that is, one quantity changes as a certain degree of the other – for example, a square or a cube: if L is the length of the side of the square, respectively of the cube, and it is increased by 2 times, then the area of the square will increase by 4 or 2 2 times, i.e. from L L2 will become 4L2, and the volume of the cube will increase 8 or 23 times, i.e. from L3 will become 8L3 [22]. If the height of men obeyed the Gradual Distribution, there would be men, though very few in number, but not negligibly few, with a height of 0.75 m and 2.75 m. In other words, this distribution also gives a chance to the smaller probabilities („for every train there are its passengers“, as they say in Bulgaria), the elements of the „Long Tail“ – see Figure 2.


  Figure 1. Normal distribution with a Bell Curve [23]  


   Figure 2. Power Distribution with a Long Tail [24]
  2. The „SCALE-FREE“ Effect – the absence of any specific scale or, to put it another way – scale invariance, fractality (self-similarity)
  Fractal – a mathematical object, that has the property of self-similarity, i.e. each part is similar to the set as a whole set.
  In order to comprehend the concept of scale-freeness, or the same thing – scale invariance, we must imagine it as a phenomenon in which there is no typical value that helps to recognize the object, i.e. something to evaluate it and give a fairly clear idea of the object – for example, the aforementioned average male height. Scale-free invariance is a property inherent in fractal, self-similar objects – they do not change when the scale of observation changes [25]. With the normal distribution with the bell-shaped curve, the values are scale-dependent.
  And let's make it clear right away.
  In the example of men's height, the distribution is concentrated around the mean value – in this case 1.75 m. With a step of 15 cm in both directions, the number of men decreases gradually and the decrease is commensurate with (is a function of) the mean value 1.75 m – that is the scale! All other „heights“ decrease symmetrically compared to this average value and seem to be related, even „tied“ to it.
  Mathematicians consider the probability Pk that a node connects to k other nodes. Pk gives the degree of distribution of the network and means that given node is of degree k. At the same time, Pk is the fraction of network vertices that have degree k.
  Network structures that propagate randomly on a random basis are called random networks. In them, we have a Poisson distribution with a bell-shaped curve of the nodes and their connectivity between them. The Poisson distribution means that most of the nodes have a degree close to the mean (average), and that the number of nodes of a given degree decreases exponentially, i.e. very rapidly as one moves away from the mean [26]. However, most real network structures are incompatible with random development. In them, as was said, the Power Law Degree Distribution operates, for short called the Power Law.
  Exponential growth – growth of a quantity, in which the rate of growth is proportional to the value of the quantity itself. This is a very fast increase. When we have a discrete area of determination (with equal intervals), this growth is called geometric because the meanings form a geometric progression. In mathematics, an exponential function is that function which is equal to its own derivative. Denoted by ex or exp(x); e – Napier's constant (e = 2.71828...). It is named after the Scottish mathematician John Napier (1550 – 1617).
  In random networks with the Poisson distribution and the bell curve, it is difficult to find a node with a significantly larger or smaller number of connections than the average for the network, i.e. the average value of the possible number of connections per node, which we will denote by ‹k›. The Poisson distribution has a convex peak, which indicates that the large majority of nodes have approximately the same number of connections, namely ‹k› – as with the average, typical node; and at the same time, very few nodes have a number of connections significantly different from ‹k›. On either side of this prominent vertex, the distribution tapers off rapidly, making significant deviations from the mean very rare. This means that this type of network has one specific value, a specific scale, and its meaning is ‹k›. Thus, this average number of connections ‹k› becomes a particularly important characteristic for random networks – through it they have a characteristic value (number, magnitude), i.e. scale in its node connectivity, determined by the average number of connections per node and fixed by the vertex of the node degree distribution curve. In addition, the quantity Pk decreases exponentially, which means that in any such network there will be almost no nodes with significantly more or significantly fewer connections than ‹k›.
  In real, („non-random“) Power law networks (with a Power law distribution), a fundamentally different quantitative and qualitative picture is observed. The Pawer law distribution allows the existence of a very large number of nodes with a small number of connections, incl. with significantly fewer links than the average for the network, and with a very small number of nodes with a large number of links, including those with significantly more links than the average for the network.
  This is the same as having, as explained, a small number of 2.70 m tall men. This is why in these networks ‹k› is not an essential characteristic – it does not provide any important information, because in them no node is typical of a network with its parameters. In such networks, there is no vertex similar to the vertex of the distribution curve in random networks, and they do not have a characteristic value (number, magnitude), i.e. scale. It is precisely the fact that power networks do not have their inherent magnitude, measure, or scale that led Albert-László Barabászy and the Hungarian-born American physicist and biologist Réka Albert (1972) to call networks with a Power law distribution „scale-free networks“ or „scale-invariant networks“ [27]. For an illustration of what was said, see Figure 3.


  Figure 3. Dependencies between the number of links and the number of nodes. The number of links is plotted along the horizontal axis; and on the vertical axis is the number of nodes. a) Poisson distribution with a typical node – the vertex of the graph with an average degree ‹k›; b) Power law distribution – there is no typical node, i.e. vertices with a mean, other than that the distribution decreases much more slowly and is therefore more likely to have vertices with more connections [28, 29].
  3. The „SMALL WORLD“ Effect (or the „WORLD IS SMALL“ Effect), also known as „Six Degrees of Separation“.
  In 1967, the American sociologist Stanley Milgram (1933 – 1984) put forward the thesis that every person in the world can reach every other person through a chain of 5 or 6 people [30]. Thus was born the term „Six Degrees of Separation“; in fact, it is not so much a term as a real social phenomenon. And this means that, despite the seven and a half billion inhabitants of our planet, we live in a small world.
  Behind this thesis is an experiment conducted by Stanley Milgram. There is a target person – a stockbroker from Sharon, Massachusetts, working in Boston, the capital of the state. 217 people were involved in an experiment asking them to try to contact a stockbroker (target person) through correspondence. The letters contain a description of the experiment, a photo, name, address, information about the broker and instructions that each participant should send a letter to someone – a relative, friend, acquaintance, but only if they know the person personally and for whom they believe that he probably can bring them closer to the target person. The selected recipient must repeat the procedure and forward the letter to someone else, and so on, until the letter reaches the target person. 64 letters arrive to the target person. The other 153 letter chains break along the way. The total average number of intermediate steps (intermediaries) is 5.2. Rounding is done to a number that includes this average length (5.2) of the path from the first destination to the final destination (target person, broker), i.e. 6, a really small number that will go down in history with the well-known name „Six Degrees of Separation“. By the way, it has been calculated that there are more degrees for the WWW network – 19, and for the Internet – 10 [31, 32, 33, 34, 35, 36, 37].
  In fact, Milgram himself never used the phrase „Six Degrees of Separation“. This phrase is taken from the play of the same name by American actor and screenwriter John Guire (1938), which was a success on Broadway in 1990 and was made into a film of the same name in 1993. In it, one of the heroines says: „I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation between us and everyone else on this planet. The president of the United States, a gondolier in Venice, just fill in the names. I find that extremely comforting that we're so close, but... I also find it like Chinese water torture that we're so close, because you have to find the right six people to make the connection. It's not just big names, it's anyone... I am bound - you are bound - to everyone on this planet by a trail of six people… Six degrees of separation between us and everyone else on this planet. It's a profound thought“ [38]. That's why our world is small – everyone is at arm's length, or rather - at 6 arm's length, i.e. in 6 steps along the network fabric that has bound humanity into one and single organism.
  Chinese drop – method of torture; consists of slowly dripping water on the victim's forehead, which drives him insane.
  Further, the network logic of the „Small World“ (in the sense of “World is Small”) phenomenon was thoroughly developed by the Australian mathematician Duncan Watts (1971) and the American mathematician Stephen Strogatz (1959). Therefore, similar type of network structures in the scientific literature are called „Small World“ Networks or „Strogatz-Watts“ Networks (SW networks); respectively „World is Small“ Networks or „Watts-Strogatz“ Networks (WS networks).
  The existence of such an elegant and natural in a social sense of the type of networks „Small World“ with a similar topology indicates the possibility of randomness, disorder in network structures to self-organize into regularity, in order. And this gives a radical interpretation of the „Small World“ model – it is an effective step towards the self-organization of a network of few or many randomly or disorderly connected nodes into a stable and ordered structure. By this, the network acquires a new physiognomy, becomes natural and logical, becomes a Network, and it gives living systems (for example, biological ones) more serious evolutionary chances, creates conditions for survival and development, provides competitive advantages and guarantees of sustainability.
  4. The „THE RICH GET RICHER“ Effect (or THE MATTHEW EFFECT), the so-called the preferred (preferential) attachment.
  When new nodes appear, they prefer to connect to existing hubs, clusters of connections and communications, i.e. to the nodes with which other elements are most often associated, to the nodes that are most preferred. And this happens at the expense of other nodes, which turn out to be unpreferred or weakly preferred. That is why this effect is called not only „The Rich Get Richer“, but also, following the American sociologist Robert Merton, the „Matthew Effect“, since in the Holy Gospel of Matthew it is written: „For unto every one that hath shall be given, and he shall have abundance.“ (Matthew 25:29) [39]. And the people say: „Money goes to money“, „Where it flowed, it will flow there again“ or „Evil does not come into the house alone“.
Such an attachment, in which the more connected a node is, the greater the probability that the new node will connect specifically to it, is called a preferential attachment (the privileged or preferential connection). With it, if we have two nodes, one of which has twice as many connections as the other, then the probability that the new node will connect to the first is twice the probability that it will still connect to the second one [40]. This could also be explained in the following way: new nodes connect to existing ones with a probability proportional to the number of connections that old nodes already have, i.e. they are more likely (that is, more readily) to connect with the formed hubs than with some relatively „lonelier“, less „attractive“, less „influential“ nodes. This is the meaning that is contained in the preferential attachment (privileged or preferential connection), and it further explains the other effects in the network structures related to the evolution of the networks, which makes them of the scale-free type, and which, along with that, is statistically recreated through the Power law – the mathematical illustration of the Similar distribution law.
  The problem is that „The Rich Get Richer“ model is based on identity, on values, and if identity is blurred and values weakened, the danger encoded in this model, its inherent defect, can be realized: if the structure, dynamics and competition between nodes become enemies with each other, this inevitably leads to the alternative model „The Winner Takes All“ [41]. In other words, although the network structure guarantees the mechanism “ The Rich Get Richer ”, then if there are no longer gluing, rallying, social, integrating synergistic benefits (trust, love, reciprocal altruism, chances for all, security), i.e. the goods that raise the system to a higher level of organization and complexity, then inevitably – sooner or later – the network structure will come under the influence of and move in its development to the mechanism „The Winner Takes All“.
  Altruism – principle or practice of caring for the welfare of another person.
  Reciprocal – mutual, joint, correlative, solidary.
  Reciprocal altruism – mutual altruism in which individuals make gestures, provide help, make self-sacrifice towards each other and expect the same gesture, help, self-sacrifice in return.
  5. The „CLUSTERING“ Effect (clustering – grouping, gathering in groups, accumulation, crowding)
  A cluster is an association of several homogeneous or similar elements, that can be considered as an independent unit with certain properties. This effect means that due to the huge supply of connections and contacts, and since the respective node/actor, especially if it is a social agent/actor, is unable to maintain this oversupply of these connections and contacts, it restricts them to a narrow, a closed and difficult to expand circle of other social agents/actors. Most often they come together to increase their abilities by interacting with each other.
  The English evolutionary psychologist Robin Dunbar (1947) studied the relationship between the group size of each primate species and the size of the part of the brain occupied by the neocortex. The larger the group, the more neocortex is needed to understand, organize, coordinate and control the social life of the group. (Emerging as conscious social beings, our human ancestors chose to live in much larger groups than their primate relatives [42]. This led to more neocortex, hence a larger brain, and hence a higher intelligence invested in more ingenuity, social interaction and the pursuit of success in the struggle for survival and development.) From here he introduces the „Dunbar's Number“ (Dunbar's Number) – an average number, namely 150, of people that we are able to we know personally, to feel an emotional attachment to them. Over the past few hundred thousand years, our brain has not changed significantly in terms of size, structure, capabilities and functioning. Therefore, both then and now, it can empathically perceive all the same 150 people close to our hearts and important to us [43]. In this sense, despite today's oversupply of more and more new opportunities for contacts, for relations and relationships with people who are very different in spiritual values and material situation, a person – including due to the maximum (pre-determined) capacity of his brain – voluntarily and involuntarily „clusters“ to maintain such close and valuable social relationships with an average of 150 people.
  Primates – a group of mammals that includes proboscis prosimians, apes, and humans.
  Cortex or cerebral cortex – the membrane of the brain that covers the cerebral hemispheres. It provides the possibilities for perception, communication, memorization, judgment, will – this is our consciousness.
  Neocortex or new cortex – the main part of the cerebral cortex, carrying out the highest level of coordination of the brain's work and the formation of the most complex forms of behavior.
  Clustering means the appearance in the network of a closely related community of nodes with similar properties [44]. In random networks, clustering is practically absent, and therefore in them the probability of friendship between two people is no greater than the probability of friendship between two randomly selected people. In non-random, i.e. in real networks, however, the probability of two people becoming friends can be extremely high if they belong to the same cluster. The problem, let's say again, is related to the fact that a person cannot maintain close contact with everyone whom network structures offer him for contact, and he voluntarily or involuntarily limits himself in his communications, closes himself in a narrow circle of people with whom he communicates fully – this circle, while no narrower than before the spread of networking, is not much wider either. In other words, a person constantly makes a choice, or rather, the selection of those with whom he contacts (connects) in networks, constantly clusters, closes in clusters. Clustering is both a property characteristic of network structures (intrinsically characteristic) and a reaction to their structure and dynamics (externally introduced).
  In the theory of network structures, the term assortative mating is used, i.e. selective binding – binding in which the individual in the social networks (the living being in the biological networks) selects individuals who are similar to him (positive selective binding) or opposite (negative selective binding) according to a feature or to features. In technological and biological networks, negative assortativity is more common, i.e. the opposite is associated with the opposite; in social networks – positive assortativity, i.e. the like is associated with the like. This enhances clustering – people choose each other according to their interests; some of these circles can become closed communities, especially when there are formal (membership criteria) or informal (wealth, fame, status) restrictions on inclusion. In the theory of networks, there is also such a phenomenon – nodes with the largest number of connections to other nodes are most strongly interconnected – a hub of hubs.
  Assortative mating – directed mating, genetically determined more frequent mating between representatives of a given species, very similar in a given trait (positive crossing) or opposite in relation to it (negative crossing).
  Due to clustering, a person remains in a small community of self-similar people, or at least people who have similar information and social experience; therefore, some relatively more distant acquaintances and communications can supply this person with more up-to-date and useful information.
  Let's explain this. As a result of the huge supply of new nodes, people, agents with which a person can connect, he reacts by clustering (grouping into small clusters, within which each node is closely related to others, but connected to a small number of nodes outside the cluster), which means the following: people in the network can be divided into groups, so there will be many connections (edges) within the group and few connections (edges) outside it [45, 46] – a well-known rule of social networks: „A friend of my friend is also my friend!“. A given node/person determines who to contact through assortative selection. However, a serious problem arises – the protective reaction of a person in this oversupply of proposals for binding: closing in a narrow circle of people similar to him or, at least, people with similar social status or similar social practices, or similar social tastes and habits, or similar social ideas and knowledge. And this small and somewhat closed community of similar social entities of his needs an ozonizing effect, for example, new information, something that it cannot provide for itself. And this is where the phenomenon called „The Strength of Weak Ties“ by the American sociologist Mark Granovetter (1943) [47] works effectively.
  Analyzing different communities of people, Mark Granovetter defines the strength of a relationship as „a (probably linear) combination of the amount of time, the emotional intensity, the intimacy (mutual confiding), and reciprocal services which characterize the tie“ [48]. If the ties between A and B and between A and C are strong, because both B and C are similar to A and probably similar to each other, it is very likely that their tie will also be strong. Similarly, it can be assumed that if the ties between A and B and between A and C are weak, because both B and C are too little similar to A, it is likely that they are too little similar to each other, so that their tie will be weak. One possible distinction between strong and weak ties is that of (close) friends are strong ties, and (distant) acquaintances are weak ties. Mark Granovetter introduced the concept of a „bridge“ – a line in the network providing the only tie between two elements. If the tie between A and B is a bridge, then it is the only path along which information flows from every element connected to A to every element connected to B, and therefore from every element indirectly connected to A to every element related indirectly to B. Because of the intense connectedness in a group made up of strong ties, no strong tie is a bridge. But a weak link can be a bridge between A and B, as well as a bridge between a strongly bound around A group and a strongly bound around B group. In general, every bridge is a weak tie.
  For something (rumor, news, valuable information) to spread over a large social distance, i.e. in order for it to reach a larger number of people, it must pass through weak rather than strong ties (since strong ties are closed in small communities) [49]. And Mark Granovetter writes that people with predominantly strong ties and very few weak ties „will be deprived of information from distant parts of the social system and will be confined to the provincial news and views of their close friends. This deprivation will not only insulate them from the latest ideas and fashions but may put them in a disadvantaged position in the labor market, where advancement can depend…, on knowing about appropriate job openings at just the right time” [50]. A very strong narrow socialization would also turn into a very weak broad socialization and even asocialization. That is why weak ties, strange as it sounds when we call them weak, are of great importance in the socialization of people, in strengthening integration and cohesion in society. Weak ties are those through which information circulates most easily, public opinion is created, morals and attitudes are formed, the values of cultural artifacts are distributed, and fashion finds its way [51].
  Influence in network structures is decisive up to the third most distant element in the network connection, further it weakens.
  American social network researchers Nicholas Christakis (1962) and James Fowler (1970) call this effect the „Three Degrees of Influence Rule“. Its meaning is as follows: Regardless of the fact that „Small World“ networks have six degrees of separation, there are three degrees of perceptible influence in these networks.
  Here are their arguments in brief. The „Small World“ effect means that the average distance between any two participants in the network is 6 - 6 contacts (or 6 acquaintances, 6 handshakes) - i.e. if we take two random participants A and B, on average B will be a friend of a friend of a friend of a friend of a friend of a friend of A. Although each participant is connected by 6 degrees of separation with any other participant, he cannot to exert a significant influence on all other participants, but only on those who are up to 3 degrees of separation from him. Others that are more than 3 degrees of separation (i.e. 4, 5 or 6) are close enough to him to be able to contact him due to the network architecture („Small World“) but far enough away for him that he can influence them – shape their tastes and preferences, change their attitudes and plans, feel close to them, consider them to belong to his close circle of friends and (figuratively speaking) with his „blood group“ such as beliefs, values, priorities. Or if there are 6 degrees of separation between A and B, A can effectively influence only participants who are his friends (1 degree of separation), or are friends of his friends (2 degrees of separation), or are friends of friends of his friends (3 degrees of separation). To everyone else – those who are friends of friends of friends of friends of A (4 degrees of separation), or are friends of friends of friends of friends of friends of A (5 degrees of separation), or like B are friends of friends of friends of friends of friends of friends of A (6 degrees of separation), A cannot really influence effectively...
  The rule of three degrees of influence, derived theoretically and experimentally verified by Nicholas Christakis and James Fowler, means that I am connected with each network member with a maximum of 6 degrees of separation (this is a physical, architectural connection) and I can influence these network members with whom I have up to 3 degrees of separation (this is a psychological, personal connection). Regardless of the network binding and connectivity, I am in effective interaction, i.e. I am attached only to my friends (1 degree of separation), to the friends of my friends (2 degrees of separation), and to the friends of my friends' friends (3 degrees of separation). Further along the network, influence and cohesion, feelings and affections are blurred, deprived of meaning, weakened, becoming increasingly more and more formal [52].
  The structure and dynamics of networks make especially inherent in them a phenomenon that, in principle, is found everywhere, „from atoms to animals, from people to planets“ [53] – the synchronization of the elements that make up the system (in this case, the network). This means that the elements of the network perform certain actions or movements in the same rhythm and with the same amplitude.
  Synchronization – process of bringing one or more parameters of different objects to the same value.
  Synchronization in most cases has two manifestations – the elements of the system not only perform the same actions (spatial synchronization), but also these actions are performed through one and the same intervals (time synchronization). When there is synchronization both in space and in time, this amazing phenomenon is synchronization squared. It is like imagining two people running and sometimes jumping at the same time, so that the intervals at which they jump while running are the same. It is such a square synchronization, when associated with aesthetic experiences (rather than destructive effects), that can be called harmony.
  Synchronization in network structures is also an element of modern brain science. One of the most intensively studied networks is the neural networks in the human (and animal) brain [54, 55, 56]. Some disorders of mental activity result from the abnormal and sometimes sudden destructive synchronization of a large number of neurons. In epilepsy, for example, this causes rhythmic convulsions associated with seizures [57]. Therefore, „synchronization is perhaps most important to the way a network of neurons performs its functions“ and it is likely that the „Small World“ effect inherent in this network is of great importance in the occurrence of synchronization [58].
  The analysis of the behavior of networks consisting of a large number of oscillating elements (oscillators) indicates that the mode of synchronization occurs most easily when the individual oscillator is influenced by the formed uniform rhythm of the surrounding oscillators. With fireflies, each one „tunes in“ to the blinking of its neighbors. It is the same with soldiers marching in formation, with cheers and chants in concert halls and stadiums, with choral singing and dancing. In scale-free networks, the main cores of synchronization are formed by the highly connected hubs that absorb the neighboring small clusters [59, 60].
  Oscillation – periodic oscillations around the equilibrium position, for example, a pendulum, a body suspended on a spring, alternating current.
  Synchronization in systems, and especially in those with a network structure, is a result of their complexity. To a large extent, it is a spontaneous phenomenon, the basis of which is imitative behavior – the making of individual decisions, a consequence of group, collective or system-wide reactions to internal or external influences. With them, one can undoubtedly talk about trust between individuals, but to a significant extent it is a first signal, impulsive, meaningless. On the principle of contagion, trust is passed on through network links or by observing how others, and especially those closest to the network, react. But the essence and role of trust is much greater than this instinctive form of it. Trust is much more than blindly copying the behavior of others just because they are part of our community. Trust has much more serious dimensions and has been the subject of extensive research in social systems (communities, societies).
  We know that when a person has a serious problem, he mobilizes all his contacts and acquaintances, friends and family ties, i.e. all his social capital. In fact, this concept was introduced in sociology and social psychology by Robert Putnam (1941): Social capital can be defined as „as a set of informal values or norms shared among members of a group that permits cooperation among them“ [61]. Social capital can be defined as „as a set of informal values or norms shared among members of a group that permits cooperation among them“ [62].
  In resource-oriented strategies, as was said, a person or system seeks to use the resources they possess (knowledge, abilities) and look for tasks where they can be applied. In goal-oriented strategies, a person or a system analyzes what goals (missions, options, tasks, opportunities) need to be achieved, and seeks to find resources (knowledge, abilities) through which they can be achieved.
  Security institutions remain predominantly hierarchical, but problems are becoming networked, and this requires changes in structures and approaches, principles and resources. The era of networks requires a radically different way of thinking.
  Hierarchical structures have a static and non-adaptive, difficult to change and complex, vertically built architecture with many levels of control and subordination. They pursue resource-oriented (resource-based) strategies. They strive (prefer) to do above all that and as what and how they know to do it and to do it as much and then as and when they wish to do it.
  Network structures have a dynamic and adaptive, flexible, simplified, horizontally built architecture with a small number of levels of control and subordination. They pursue goal-oriented (goal-based) strategies. They strive (endeavor) to do first and foremost that and as what and how it should be done and to do it as much and then as and when it needs to be done.
  Nowadays, we can no longer think that it is necessary once and for all to arm ourselves with some abilities and imagine that these abilities will always be enough for us, in all situations. Today, everything is different – now the Goal determines the Resources, and not the Resources – the Goal. We must go to the problem and meet its requirements, and not look for problems that meet our requirements. We must work not what we know, but know what we must work. We are entering the deep waters of personal or systemic realization, when work will be sought not for the person (team, organization), but for the work a person (team, organization) will be sought.
  10. The „TURNING POINT“ Effect
  Development follows one type of logic up to a certain point (turning point, tipping point) [63], and after this point the system radically changes its behavior; when quantitative accumulations turn into qualitative changes; when the previous development of a certain process or phenomenon is replaced by a completely different development of the same process or phenomenon.
  As connectivity increases, networks become more complex and move toward disequilibrium until they reach a turning point, when a discontinuous phase shift occurs, interrupting the previously gradual development up to that point. Networks, that are structures and dynamics of complex adaptive systems, as a rule, are always networks of other networks, with a clear manifestation of fractal properties, demonstrating the same structure at every organizational level and in every operational phase. An example of such a development is the model of behavior of various types of systems, which can be illustrated by the pile of sand (corn kernels, rice, etc.). When sand is poured in a thin stream onto a horizontal plane, a well-formed pile is initially formed. After a certain point (critical threshold, phase transition point, dynamic equilibrium point, tipping point), however, even a tiny bit of added sand collapses the pile and it goes down like an avalanche [64]. The moment when an avalanche begins in the heap is determined not by how much sand will be added – a pinch or a tiny grain – but by the internal properties of this heap! Analogous processes of slow change without particular consequences until one moment and avalanche-like development after that have been observed and analyzed in snow avalanches (naturally), forest fires, earthquakes, wars, diseases [65]. In network structures, therefore, change „does not happen gradually, but at one decisive moment“, i.e. we have a turning point (the process turns into an epidemic), a phase transition, a Power law distribution [66].
  Because of the ability of a complex system to undergo a radical change in its qualitative state through certain critical or tipping points, it is often called self-organized criticality (SOC). In some systems, the transition from one qualitative state to another, from one behavior to another is due to external influences; in others, it is more often the result of the internal specifics of the system (structure, interaction, ability to evolve).
  The network structures with their architecture and dynamics seem to be created to tolerate the occurrence of such processes, moreover – under certain conditions they exist precisely through them. In other words, networks, as a rule, work in a regime on the edge of chaos – a kind of compromise between order and sudden change; and in this mode and through it, they can most effectively coordinate processes in complex systems built by them, and at the same time continue to evolve [67]. Therefore, networks are an extremely useful illustrative example of self-organizing criticality with great practical application. In various types of networks, avalanche-like processes occur spontaneously or under the influence of various factors. Sometimes such a process is a cascade, cascading process. They talk about cascade processes, cascading, when, due to minor defects or a small number of affected elements, successive (caused one after another), sometimes reaching catastrophic consequences, failures in complex systems occur (during accidents in the power plant network; when the Internet goes down; in cancer diseases – cancer cell division is a cascade process; in the spread of infections among people and of viruses in computer programs and computers, in traffic accidents on highways, etc.). Cascading is not necessarily associated with the occurrence of destructive phenomena. They are also observed with the explosive popularity of the creator (writer, director, composer, singer), cultural product (book, film, song, painting), of an idea, product, clothing (fashion), restaurant. Sometimes it is not even clear how and when the passion for them begins, most people reason or act on intuition like this: Well, everyone likes it, everyone buys it, everyone goes to this restaurant, i.e. what matters is not our own opinion, but what everyone (or many around us) likes...
  Cascade - concepts related to falling, going down (a series of small waterfalls, from arranged playing cards, from checkers for the game of dominoes); an architectural complex with an artificial waterfall or waterfalls; a series of hydroelectric plants on a river.
  11. The „BLACK SWAN“ Effect
Network structures are an environment that is exceptionally suitable for the emergence and response to „Black Swan“ phenomena [68]. A „black swan“ is an event that: (1) occurs extremely rarely; (2) its occurrence does not follow from the normal logic of the process; and (3) if it happens, its effect is enormous.
  Nassim Taleb explains:
   „In his Treatise on Human Nature, the Scots philosopher D¬vid Hume posed the issue in the following way (as rephrased in the now famous black swan problem by John Stuart Mill): No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion“ [69]. [And also:] „Before the discovery of Australia, people in the Old World were convinced that all swans were white, an unassailable belief as it seemed completely confirmed by empirical evidence. The sighting of the first black swan ... illustrates a severe limitation to our learning from observations or experience and the fragility of our knowledge. One single observation can invalidate a general statement derived from millennia of confirmatory sightings of millions of white swans. All you need is one single (and, I am told, quite ugly) black bird“ [70].
  David Hume (1711 – 1778) – Scottish economist and philosopher.
  John Stuart Mill (1806 – 1873) – English philosopher and economist.
  Empiricism – knowledge, obtained through experience, through experiment, with direct observation; a direction in cognition recognizing sensory experience as the source of knowledge. The validity of a theory is based on the evidence obtained through experience (the facts).
  Probably in 1843, John Stuart Mill first used the term „black swan“:
   „As there were black swans, though civilized people had existed for three thousand years on the earth without meeting with them…“ [71].
  The British philosopher of Austrian origin Karl Popper (Karl Popper, 1902 – 1994) also used the „black swan“ in 1959:
  “Any unsuccessful attempt to find a red or yellow swan corroborates both the following two theories which contradict each other in the presence of the statement ‘there exists at least one swan’: (i) ‘All swans are white’ and (ii) ‘All swans are black” [ 72].
  At the beginning of this section, we gave a general definition of the „Black Swan“. It stems from Nassim Taleb's own understanding of the concept: A „Black Swan“ is an event that has the following three qualities: (1) it is anomalous because nothing in the past foreshadowed it; (2) it has tremendous attributes: (1) it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility; (2) it carries an extreme impact. (3) in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable [73].
  Let us also add the following reasoning of Nassim Taleb:
   „Some events can be rare and consequential, but somewhat predictable… They are near-Black Swans… These events are rare but expected. I call this special case of „gray“ swans Mandelbrotian [i.e. of the French and American mathematician Benoit Mandelbrot (1924 – 2010)] randomness… Mandelbrotian Gray Swan: Black Swans that we can somewhat take into account – earthquakes, blockbuster books, stock market crashes – but for which it is not possible to completely figure out the properties and produce precise calculations“ [74].
  Thus, according to Nassim Taleb, there are the following types (categories) of „swans“:
  › Frequent and predictable, expected events – “white swans”.
  › Rare and (somewhat) predictable, expected events – „grey swans“;
  › Rare and unpredictable, unexpected events – „black swans“;
  The question naturally arises:
  What kind of „swans“ are events of the fourth type – i.e. frequent and (somewhat) unpredictable, unexpected events?
  We will characterize such events as „silvery swans“ (Table 2):
  › Frequent and (somewhat) unpredictable, unexpected events – „silvery swans“.

  Table 1. The supplemented „swans“ according to Nassim Taleb
  For a more detailed analysis of swan types, see Study 7.
  12. The Effect „Unknown Unknowns“
  In the network society, the main problems that it will face without sufficiently developed and sufficiently tested proven strategies will be of the type of „unknown unknowns“.
Donald Rumsfeld warns that in today's very dynamic times, we must consider and take into account four types of cognitive (knowledge-related) quantities (challenges, risks, dangers and threats) [75]:
  → known knowns – about which we know that we know;
  → known unknowns – about which we know that we do not know;
  → unknown knowns – about which we do not know that we know;
  → unknown unknowns – about which we do not know that we do not know.
  None of these four types of quantities should be underestimated, but especially difficult to predict are the fourth type of quantities – unknown unknowns. To „capture“ them, i.e. identification, analysis and evaluation with the subsequent development and implementation of strategies and policies of influence (management), network structures are more adequate and more effective than hierarchical ones.
  Managing security (personal, community, corporate, national, international) in the spirit of the aforementioned thesis of Donald Rumsfeld is increasingly reminiscent of blindfold shooting at a moving target (i.e. unknown unknowns). At first we need to stop the target (i.e. unknown knowns) or remove the blindfold (i.e. known unknowns). But long gone are the days when we could, as a rule, shoot at a stationary target and without a blindfold (i.e. known knowns).
  Our world is interconnected and interdependent. In this sense, the concepts (scientific categories) are as well interconnected and interdependent. That is why it is so important to draw lines of demarcation that, up to a certain point, unite them, and beyond that point, separate them. We have always been concerned and occupied with the question of the unity and completeness of concepts in Security Science. Study 5 represents, in our opinion, a very successful attempt to unite the main concepts with which our analysis is concerned.
  Here, once again, we clarify the similarities between Nassim Taleb's „swans“ and Donald Rumsfeld's cognitive quantities. Although these „swans“ and quantities do not completely intersect (and this is impossible at all), there is something in common between them to a large extent, which could be formulated as follows:
  • „White swans“ (frequent and predictable/expected events) coincide in no small degree with known knowns.
  • „Gray swans“ (rare and predictable/expected events) coincide in no small degree with known unknowns.
  • „Silver swans“ (frequent and unpredictable/unexpected events) coincide in no small degree with unknown knowns.
  • „Black swans“ (rare and unpredictable/unexpected events) coincide in no small degree with unknown unknowns.

  Table 2. Binding of the supplemented „swans“ according to Nassim Taleb and the cognitive quantities according to Donald Rumsfeld
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  Brief explanation:
  The texts of my Studies have been translated into English by me. They have not been read and edited by a native English speaker, nor by a professional translator. Therefore, all errors and ambiguities caused by the quality of the translation are solely mine. But I have been guided by the thought that the purpose of these Studies is to give information about my contributions to the Science of Security by presenting them in a brief exposition, and not to demonstrate excellent English, which, unfortunately, I cannot boast of.