Relaxation time in complex network

Abstract

New characteristics of nodes of network structures are proposed and researched in this work - the relaxation time of network and the individual relaxation time of node. The so-called decelerated iteration algorithms for HITS and PageRank are used to obtain the relaxation time. The relaxation time of network and the individual relaxation time of node were tested on the example of a weighted directed network of characters in the novel«Les Miserables». It was found that a topology of a network affects a relaxation of nodes after their perturbation. As a result of using relaxation time it was possible to identify the most important network components and rank them by the proposed characteristics. The resulted ranking compared to the ranking by HITS, PageRank and degree of nodes shows the uniqueness of the proposed relaxation time of network and individual relaxation time of node.