Network cloning unfolds the effect of clustering on dynamical processes
Physical Review E, (May 14, 2015)DOI: 10.1103/PhysRevE.91.052807
Abstract
We introduce network L-cloning, a novel technique for creating ensembles of
random networks from any given real-world or artificial network. Each member of
the ensemble is an "L-cloned network" constructed from L copies of the original
network. The degree distribution of an L-cloned network and, more importantly,
the degree-degree correlation between and beyond nearest neighbors are
identical to those of the original network. The density of triangles in an
L-cloned network, and hence its clustering coefficient, are reduced by a factor
of L comparing to those of the original network. Furthermore, the density of
loops of any fixed length approaches zero for sufficiently large values of L.
As an application, we employ L-cloning to investigate the effect of short loops
on dynamical processes running on networks and to inspect the accuracy of
corresponding tree-based theories. We demonstrate that dynamics on L-cloned
networks (with sufficiently large L) are accurately described by the so-called
ädjacency tree-based theories", which is a class of theoretical approaches for
modeling various networked behaviors including percolation, SI epidemic
spreading, and the Ising model.