Network clustering coefficient without degree-correlation biases.
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 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.
Soffer
Sara Nadiv
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Department of Mathematics, Rutgers University Piscataway, New Jersey 08854, USA.
Vázquez
Alexei
A