This paper researches new unique characteristics of networks . a network relaxation time and an individual node relaxation time, which characterize the stability of a complex network and, accordingly, each node separately to external perturbations. While researching of the complex networks, it is assumed that relaxation time is the number of iterative steps of the corresponding algorithm required to achieve the initial equilibrium numerical values of a certain characteristic after some external perturbation. In other words, the network relaxation time for each node characterize the resistance of a complex network and the individual node relaxation time characterize the resistance of each node to external perturbations, accordingly. In this work, to compute the relaxation time, the decelerated iterative HITS algorithm is used. It is shown, that these characteristics are unique numerical characteristic of network nodes, and they can be used to find the centroids of clusters and combine nodes into groups according to these characteristics . for complex networks clustering. The approbation of the presented characteristics of the relaxation time and the individual relaxation time was carried out on the example of clustering of random networks with clearly expressed clusters. In particular, a randomly generated matrix with dimension 30.30 and 3 clusters and a matrix with dimension 100.100 and 4 clusters were researched.

Keywords

Complex Network, Network Relaxation Time, Individual Node Relaxation Time, HITS, PageRank, Clustering, Centroids of Clusters