Title: The connectivity measurement in complex directed networks by motif structure

Authors: Zhuqing Jiao; Huan Wang; Kai Ma

Addresses: School of Information Science and Engineering, Changzhou University, Changzhou, Jiangsu, 213164, China ' School of Information Science and Engineering, Changzhou University, Changzhou, Jiangsu, 213164, China ' School of Information Science and Engineering, Changzhou University, Changzhou, Jiangsu, 213164, China

Abstract: Complex networks are high abstracts of ubiquitous real complex systems in nature, biology and human society. Motif structures are the basic patterns and important topologies of complex networks even complex systems, and they play roles in classification and analysis of structural properties. In this paper, the connectivity measurement in complex directed networks are discussed based on motif structure. Firstly, the characteristic parameters of motif structure are analysed based on triangular subgraphs existing in the network, and the adjacency matrix is introduced to describe the relationships between adjacent nodes in the motifs. Then, the connecting strengths and the clustering coefficients of directed networks are calculated by the adjacency matrix, so as to measure the importance of the nodes and their connecting edges in both unweighted and weighted directed networks. Finally, the correlation between the motif connecting strengths and traditional connecting strengths are studied as well as between the motif clustering coefficients and traditional clustering coefficients in several typical directed networks, respectively. The results of instance analysis show that the motif measure methods with adjacency matrix, which can comprehensively and conveniently describe the importance of motifs in directed network connections, not only help to improve and expand the traditional connectivity measurements, but also provide a novel thought for the study of complex networks.

Keywords: complex networks; motif structure; directed networks; connectivity measurement; triangular subgraphs; adjacency matrix; connecting strengths; clustering coefficients.

DOI: 10.1504/IJSNET.2016.078374

International Journal of Sensor Networks, 2016 Vol.21 No.3, pp.197 - 204

Received: 09 May 2016
Accepted: 10 May 2016

Published online: 15 Aug 2016 *

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