EXTENDED CLUSTERING COEFFICIENTS:GENERALIZATION OF CLUSTERING COEFFICIENTS IN 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 Pδ(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 Pδ(h)C(h) ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ(h)C(h) is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ(h) and C(h). Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.
作 者： Wenjun XIAO Wenhong WEI Weidong CHEN Yong QIN Behrooz PARHAMI 作者单位： Wenjun XIAO,Wenhong WEI,Weidong CHEN,Yong QIN(Department of Computer Science, South China University of Technology,Guangzhou 510641, China)Behrooz PARHAMI(Department of Electrical & Computer Engineering, University of California,Santa Barbara, CA 93106-9560, USA)
刊 名： 系统科学与系统工程学报（英文版） 英文刊名： JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING 年，卷(期)： 2007 16(3) 分类号： N94 关键词： Clustering coefficient small-world extended clustering coefficient distance distribution