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P. Merely, Semimetals University, Budapest, Hungary Weak Links The Universal Key to the Stability of Networks and Complex Systems How can our societies be stabilized in a crisis? Why can we enjoy

The answer is subject to a number of interdependence factors. The nature and scope of interconnectedness are not necessarily determined by the degree of interconnectedness of the participants, any more than is the nature and scope of physical connections determined by the number of connecting points in a network or the physical complexity of the system. The Universal Key to the Stability of Networks and Complex Systems may be formulated as saying: “there are many ways to answer the question of what is the nature and scope of the interconnectedness of a system, but not all of them are necessarily answerable by a single theory.” The Universal Key to the Stability of Networks and Complex Systems is an attempt to provide a unified approach to the study of both the nature and scope of interconnectedness in all domains, and is intended to be a basis for further development which has been based on insights gained from many disciplines. The chapters in the book are organized into the following groups: I. Universal Connectivity. II. Existential Connectivity. III. Network Analysis. IV. Network Dynamics. V. Social-System Analysis VI. Dynamics of Multilevel and Network Systems. VII. Dynamics of Multilevel and Network Distributed Systems What does the concept of universal connectivity have to do with the study of complex systems? In the first half of this book you will see that for a complex system, a key to the stabilization of the system is the existence of general principles to help establish a network structure. For example, we can observe in nature a clear hierarchy of types of network. These categories include those with low connectivity (e.g., the sea, forests), those with high connectivity (e.g., trees, people), and those with interconnections (e.g., cities, ships). We can also observe that the number of interactions and interactions with each system component is significantly related to its overall structure (e.g., trees with a lot of connections, which are generally considered to be dense). How do different types of complexity relate together in a hierarchical network? The answer is that there are some relationships which only occur between elements of a complex system, and other relationships which are shared between all entities in the system. The first type of relationship is that of functional dependence. Complex systems which share the same function are considered to be similar, and are referred to as related groups.

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