Percolation of interdependent networks with intersimilarity

Abstract

Real data show that interdependent networks usually involve intersimilarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent [Parshani et al. Europhys. Lett. 92, 68002 (2010)]. For example, the coupled worldwide 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 other network, we call these links common links. The fraction of common links in the system is a measure of intersimilarity. Previous simulation results of Parshani et al. suggest that intersimilarity has considerable effects on reducing the cascading failures; however, a theoretical understanding of this effect on the cascading process is currently missing. Here we map the cascading process with intersimilarity to a percolation of networks composed of components of common links and noncommon links. This transforms the percolation of intersimilar 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 noncommon links are also ER networks. We show for a fully coupled pair of ER networks, that for any K≥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 network systems.

Message passing theory for percolation models on multiplex networks with link overlap

“…While recent message passing methods had so far mostly dealt with multiplex networks without link overlap, here we have shown that this approach can be generalized to the latter, more difficult, case. Our results show explicitly that one can describe the mutual component without resorting to super-nodes [39,40], which were used for investigating two-layer multiplexes with overlap. Additionally, our approach allows the immediate treatment of the percolation transition in multiplex networks with an arbitrary number of layers M, extending greatly the variety of multiplex networks that can be studied.…”

“…The second approach is instead based only on a traditional local treelike approximation [41]. Interestingly, it turns out that a message passing algorithm that admits an epidemic spreading interpretation [42,43], inspired by the algorithm originally proposed for multiplex network without link overlap, does not capture the MCGC [39][40][41], but instead characterizes a new type of directed percolation. This process can be interpreted as a variation of a bootstrap percolation dynamics [22,44] or as the viability percolation problem [40] in the limit in which the resource nodes are vanishing.…”

“…Recently, two approaches were used to describe the transition in duplex networks (i.e.,, networks formed by M = 2 layers) with link overlap. The first approach consists of a coarse-grained description of the multiplex network in terms of supernodes [39,40]. The second approach is instead based only on a traditional local treelike approximation [41].…”

Percolation in multiplex networks with overlap

“…Recently, we came to know about two papers where percolation on two-layer Poisson graphs with overlap is studied [42,43].…”

Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles

“…This phenomenon can explain why a significant overlap is observed so often in multiplex datasets [11,13,14] and might have different implications for brain networks, transportation networks, social networks and in general any spatial multiplex. In fact it has been observed that the outcome of the dynamical processes depends significantly on the presence of the overlap [42,43].…”