Network cloning unfolds the effect of clustering on dynamical processes

TL;DR

This paper introduces network L-cloning, a method to generate ensembles of networks with preserved degree distributions but reduced clustering, enabling analysis of how short loops influence dynamical processes and the accuracy of tree-based theories.

Contribution

The paper presents a novel network cloning technique that preserves degree distributions while systematically reducing clustering, facilitating the study of loop effects on network dynamics.

Findings

Dynamics on L-cloned networks are well-described by tree-based theories for large L.

Short loops significantly affect the accuracy of certain dynamical models.

L-cloning allows controlled investigation of loop effects in complex networks.

Abstract

We introduce network $L$-cloning, a 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 \LC network, and hence its clustering coefficient, is reduced by a factor of $L$ compared to those of the original network. Furthermore, the density of loops of any fixed length approaches zero for sufficiently large values of $L$. Other variants of $L$-cloning allow us to keep intact the short loops of certain lengths. As an application, we employ these network cloning methods 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 adjacency tree-based theories, examples of which include the message passing technique, some pair approximation methods, and the belief propagation algorithm used respectively to study bond percolation, SI epidemics, and the Ising model.