Percolation on networks with weak and heterogeneous dependency

Abstract

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdős-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.

arXiv comment8 pages, 8 figures

References in corpus (13)

• Catastrophic cascade of failures in interdependent networks
• The spread of epidemic disease on networks
• The structure and dynamics of multilayer networks
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• k-core organization of complex networks
• Clique percolation in random networks
• Avalanche Collapse of Interdependent Network
• The critical effect of dependency groups on the function of networks
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Percolation of Partially Interdependent Scale-free Networks
• Percolation of partially interdependent networks under targeted attack
• Hybrid Phase Transition into an Absorbing State: Percolation and Avalanches
• Clique percolation in random graphs

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• Percolation on complex networks: Theory and application
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