Extended Clustering Coefficients of Small-World Networks

The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 (for no connectivity) to 1 (for full connectivity). We define extended clustering coefficients C(h) of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C(1). Based on known results about the distance distribution P(h) in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law P(h)C(h) clogN/N, where c is a small constant

• Type: Conference
• Year: 2007
• Where: ICCS
• Authors: Wenjun Xiao, Yong Qin, Behrooz Parhami
• Keywords: Applied Computing, Clustering Coefficient, Direct Connectivity, Extended Clustering Coefficients, ICCS 2007