THE USAGE OF GRAPH THEORY CONCEPTS FOR THE COMPLEX NETWORKS ANALYSIS

Abstract

The article considers and investigates the usage of graph theory concepts for the complex networks analysis. Abstract from their physical nature, the topological properties of these networks are considered, which significantly determine the functioning of networks and are the subject of study of complex networks. Each node of the network can be connected with other nodes by a certain number of connections that may have a direction, or nodes can be connected with each other by symmetrical connections. Also in modern systems of analysis and visualization of networks such concepts as degrees of vertices, ranking, clustering, modularity, algorithms of laying of graphs, etc. are widely used. To calculate the parameters of the network as a whole use the number of nodes, the number of edges, the geodetic distance between nodes, the average distance from one node to another, density – the ratio of the number of edges in the network to the maximum possible number of edges for a given number of nodes; number of triads, diameter of the network (maximum geodetic distance). Structural network analysis includes: click detection (subgroups that are more interconnected than other click nodes); identification of network components; finding bridges (nodes, the removal of which breaks the network into incoherent parts); groups of equivalent nodes (which have the most similar communication profiles). One of the areas of complex networks analysis is their visualization, which allows to obtain important information about the structure and properties of the network without accurate calculations. Software tools for the complex networks analysis support the calculation of all the described parameters of the nodes, the network as a whole, provide its structural analysis and visualization, work with different data formats. For the complex networks analysis, the main visualization tools are described, in the vast majority, freely distributed, free programs.