Percolation of Interdependent Networks with Inter-similarity

Abstract

Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For example, the coupled world wide port network and the global airport network are intersimilar since many pairs of linked nodes (neighboring cities), by direct flights and direct shipping lines exist in both networks. Nodes in both networks in the same city are regarded as interdependent. If two neighboring nodes in one network depend on neighboring nodes in the another we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results suggest that intersimilarity has considerable effect on reducing the cascading failures, however, a theoretical understanding on this effect on the cascading process is currently missing. Here, we map the cascading process with inter-similarity to a percolation of networks composed of components of common links and non common links. This transforms the percolation of inter-similar system to a regular percolation on a series of subnetworks, which can be solved analytically. We apply our analysis to the case where the network of common links is an Erdős-Rényi (ER) network with the average degree $K$, and the two networks of non-common links are also ER networks. We show for a fully coupled pair of ER networks, that for any $K\ge 0$, although the cascade is reduced with increasing $K$, the phase transition is still discontinuous. Our analysis can be generalized to any kind of interdependent random networks system.

References in corpus (3)

• Mitigation of Malicious Attacks on Networks
• Diffusion dynamics on multiplex networks
• Percolation on interacting networks

Cited by in corpus (35)

• Multilayer Networks
• The structure and dynamics of multilayer networks
• Percolation on complex networks: Theory and application
• Percolation in real interdependent networks
• Towards real-world complexity: an introduction to multiplex networks
• Cascading Failures in Complex Networks
• Eradicating Catastrophic Collapse in Interdependent Networks via Reinforced Nodes
• Triple Point in Correlated Interdependent Networks
• Message passing theory for percolation models on multiplex networks with link overlap
• Link overlap, viability, and mutual percolation in multiplex networks
• Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
• Correlated Edge Overlaps in Multiplex Networks
• Weak percolation on multiplex networks
• Recent advances of percolation theory in complex networks
• Non-linear growth and condensation in multiplex networks
• Two distinct transitions in spatially embedded multiplex networks
• Group percolation in interdependent networks
• Cooperative epidemics on multiplex networks
• Percolation in real multiplex networks
• Multilayer Network Science: from Cells to Societies
• Exotic Critical Behavior of Weak Multiplex Percolation
• Asymmetry in interdependence makes a multilayer system more robust against cascading failures
• Cascading failures in coupled networks with both inner-dependency and inter-dependency links
• Towards a Realistic Model for Failure Propagation in Interdependent Networks
• Network Properties for Robust Multilayer Infrastructure Systems: A Percolation Theory Review
• Percolation of Hierarchical Networks and Networks of Networks
• Link persistence and conditional distances in multiplex networks
• The effect of randomness for dependency map on the robustness of interdependent lattices
• Dependency-based targeted attacks in interdependent networks
• Percolation of networks with directed dependency links
• Percolation on Networks with Antagonistic and Dependent Interactions
• Fragility and anomalous susceptibility of weakly interacting networks
• Weak percolation on multiplex networks with overlapping edges
• Hidden transition in multiplex networks
• Weak Multiplex Percolation