Characterizing cycle structure in complex networks

The ubiquitous existence of cycles is one of important originations of network complexity, as cycle is the simplest structure that brings redundant paths in connectivity and feedback effects in dynamics. Hence the in-depth analyses on cycle structure may yield novel insights, metrics, models and algorithms for network science. By measuring the extent to which a node is involved in other nodes' smallest cycles, this paper proposes an index, named cycle ratio, to quantify the importance of individual nodes. Experimental tests on real networks suggest that cycle ratio contains rich information in addition to well-known benchmark indices, that is, the node rankings by cycle ratio are largely different from rankings by degree, H-index and coreness, while the rankings by the three benchmarks are very similar to each other. Further experiments show that cycle ratio performs overall better than the three benchmarks in identifying critical nodes that maintain network connectivity and facilitate network synchronization.

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