Tuning clustering in random networks with arbitrary degree distributions

Details Tuning clustering in random networks with arbitrary degree distributions Tuning clustering in random networks with arbitrary degree distributions

2005-07-22

arxiv.org/abs/cond-mat/0507535v1

Physical Review E 72, 036133 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevE.72.036133

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree $k$ are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and secondly the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

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