Characterizing cycle structure in complex networks

Abstract A cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects dynamics. An in-depth understanding of which cycles are important what role they play on dynamics, however, still lacking. In this paper, we define number matrix, a matrix enclosing information about network, ratio, an index quantifies node importance. Experiments real networks suggest ratio contains rich addition to well-known benchmark indices. For example, rankings by largely different from degree, H-index, coreness, very similar Numerical experiments identifying vital nodes for synchronization maximizing early reach spreading show performs overall better than other benchmarks. Finally, highlight significant difference between distribution shorter model networks. We believe our analyses may yield insights, metrics, models, algorithms science.