The clustering coeffiient 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.
%0 Journal Article
%1 soffer2005network
%A Soffer, Sara Nadiv
%A Vazquez, Alexei
%D 2005
%K analysis clustering coefficient correlation degree network sna transitivity
%N 057101
%T Network clustering coeffiient without degree-correlation biases
%V 71
%X The clustering coeffiient 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.
@article{soffer2005network,
abstract = {The clustering coeffiient 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.},
added-at = {2011-08-20T00:47:15.000+0200},
author = {Soffer, Sara Nadiv and Vazquez, Alexei},
biburl = {https://www.bibsonomy.org/bibtex/2ac18c35c824c511cedc1018126306976/folke},
file = {/home/dhruv/projects/work/papers/papers/Soffer_2005.pdf},
interhash = {afe21a9bff266507213d4c20ca6b70fe},
intrahash = {ac18c35c824c511cedc1018126306976},
keywords = {analysis clustering coefficient correlation degree network sna transitivity},
month = may,
number = 057101,
read = {nil},
timestamp = {2011-08-20T00:47:15.000+0200},
title = {Network clustering coeffiient without degree-correlation biases},
volume = 71,
year = 2005
}