Layered network models (overview)

Network science is an essential tool for describing and analyzing complex systems in the social, biological, physical, information and engineering sciences. Initially, almost all studies on networks used an abstraction, in which systems are represented bv an ordinary graph: the „vertices11 (or ,,nodes“) of the graph represent some entity or agent, and the connection between a pair of nodes is represented by an „edge“ (or „link”). Loops and multi-edges are usually ignored. Although this approach is rather naive, it has been extremely successful. With the development of research on complex systems, it became necessary to move towards more complex and realistic models than a simple graph. For example, different heterogeneous properties of edges: they can be directional, have different strengths (i.e., „weights11), and exist only between nodes that belong to different sets (for example, bipartite networks), or be active only at a certain time. Much later, more and more efforts were made to investigate networks with multiple types of connections and the so-called „networks of networks11. Such systems were explored decades ago in disciplines such as sociology and design, but relatively recently serious research has been carried out on multi-level complex networks and generalizations of terminology and tools in this area. One such generalization is the multilayer network model. In telecommunication networks, problems naturally arise that arc solved at several levels of the network. For example, the task of routing in a circuit-switched data network with several logical layers (different technologies) and different interfaces, which can lead to invalid paths. This paper shows a negative example of a graph with edge properties. The tasks of designing a multi-level WLAN structure, a two-lcvcl SDH / WDM network were solved, a scheme was developed to protect (restore) a two-lcvcl optical network. To assess the distribution of traffic, a two-lcvcl model (LCN) was introduced, consisting of physical and logical layers. All of these models arc not universal (i. e., they cither depend on a specific technology, or arc applicable to specific types of networks, or only take into account connections between neighboring layers). However, for modeling multi-level embedded networks of various natures, for more than 30 years several universities in Russia, Kyrgyzstan and Kazakhstan have been using the model of a hyper net and its development. Hyper nets make it possible to adequately describe multi-level networks with an arbitrary number of levels. The hyper net (or S-hypcr net) model consists of a physical layer and a logical laver(s) and is thus an abstraction of computer networks. Probably the largest number of applications of the theory of hyper nets and S-hypcr nets arc in telecommunications and transport. Nevertheless, the theory of S-hypcr nets is applicable to the analysis and synthesis of other systems of network structure. The multilayer network model can be used to represent most types of complex systems (for example, in sociology, epidemiology, biomedicine, etc.) that consist of several networks or include disparate and / or multiple interactions between objects. Modeling real networks with a more complex model than a graph has long been a necessity. However, questions about the unification of models, and most importantly, terminology began to arise only in the last decade. This article presents two of the most common layered networking models to date. It is shown that the choice of this or that model (even when solving the same problem) is based on the features of the network. For example, the application of the hvper-network model will most likely be appropriate when modeling a multi-layer telecommunication or transport network. A list of the studied literature was also given, as well as the author’s works in the table, which showed the model’s belonging to one or another class of multi-level networks. Each of the above models describes only a subset of the set of multi-layer networks. It is possible to develop both existing models and introduce new ones for networks that are not yet integrated into the general theory. Therefore, research in this area will remain relevant and have many applications.