Дослідження показника мережевої релаксації як характеристики вузлів мережі

The development of the Internet caused a number of problems, which are related, first of all, with a massive quantity of data in the Web-space, including needless data. It turned out that many tasks which arise while working with the network information space, have much in common with mathematical sciences. This fact opens wide opportunities to apply powerful mathematical tool. In particular, knowledge in the field of discrete mathematics, the theory of graphs and networks is used for research of network structures. The research of statistical properties that characterize the behavior of networks; network modeling; forecasting of behavior of complex networks while structural properties change are actual problems of complex networks theory. The article is devoted to the research of a new characteristic of the nodes of network structures — the relaxation time. HITS and PageRank algorithms are used for research relaxation time of nodes after giving them a perturbation. It was found that the relaxation of some already traditional indicators of network, after the perturbation of individual nodes, is affected by its topology, namely: the absence or presence of outgoing links in the perturbed nodes and their number; the presence of outgoing links in perturbed nodes, which are only «authors»; the presence of outgoing links to nodes that are primary sources of «important» nodes; the presence of «authoritative» nodes that refer to a perturbed node; the entry of the disturbed node into a separate small cluster, etc. The relaxation time was used to research the structure of the language network that built for the subject domain «Internet of things». In this study, an algorithm for forming a directed network of words and word combinations - an algorithm for forming network of natural terms hierarchy (NNTH) was used for building the language network. By using of the relaxation time the most important components of the network that related with the subject domain «Internet of things» were determined. The numerical characteristic of network nodes, which suggested in the study can be used for researching and analyzing the structure of the network, and enable to identify of the most important and structural elements.