Abstract
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 δ (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 δ (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 P δ (h)C(h) is upper-bounded by a value that is considerably smaller than the product of maximum values for P δ (h) and C(h).
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Xiao, W., Qin, Y., Parhami, B. (2007). Extended Clustering Coefficients of Small-World Networks. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72590-9_9
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DOI: https://doi.org/10.1007/978-3-540-72590-9_9
Publisher Name: Springer, Berlin, Heidelberg
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