Clustering coefficient without degree correlations biases

Details Clustering coefficient without degree correlations biases Clustering coefficient without degree correlations biases

2004-09-26

arxiv.org/abs/cond-mat/0409686v1

Phys. Rev 71, 057101 (2005)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show that this signature of hierarchical structure is a consequence of degree correlation biases in the clustering coefficient definition. We introduce a new definition in which the degree correlation biases are filtered out, and provide evidence that in real networks the clustering coefficient is constant or decays logarithmically with vertex degree.

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