Dynamics on Modular Networks with Heterogeneous Correlations

Abstract

We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and LFR networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.

12 pages, 13 figures

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• Bond percolation on multiplex networks
• Network cloning unfolds the effect of clustering on dynamical processes
• Disassortativity of percolating clusters in random networks
• A framework for analyzing contagion in assortative banking networks
• Epidemic Spreading and Digital Contact Tracing: Effects of Heterogeneous Mixing and Quarantine Failures
• Message-Passing Methods for Complex Contagions
• Complex Contagions with Timers
• Analytical Formulation of the Block-Constrained Configuration Model
• Emergence of coexisting percolating clusters in networks
• Fragility and anomalous susceptibility of weakly interacting networks
• Complex Contagions and hybrid phase transitions in unclustered and clustered random networks
• Exact analytical solution of irreversible binary dynamics on networks