Network cloning unfolds the effect of clustering on dynamical processes

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.

arXiv comment9 pages, 8 figures

References in corpus (19)

• The structure and function of complex networks
• Multilayer Networks
• Critical phenomena in complex networks
• Random graphs with clustering
• A message passing approach for general epidemic models
• Percolation on sparse networks
• Resilience to damage of graphs with degree correlations
• Random graphs containing arbitrary distributions of subgraphs
• Binary-state dynamics on complex networks: pair approximation and beyond
• Accuracy of Mean-Field Theory for Dynamics on Real-World Networks
• The unreasonable effectiveness of tree-based theory for networks with clustering
• Dynamical Systems on Networks: A Tutorial
• Bond percolation on a class of clustered random networks
• Deciphering the global organization of clustering in real complex networks
• Weighted percolation on directed networks
• A message-passing approach for threshold models of behavior in networks
• Dynamics on Modular Networks with Heterogeneous Correlations
• Analytical results for bond percolation and k-core sizes on clustered networks
• Cascades on clique-based graphs

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