Generalized K-Core Percolation in Networks with Community Structure

Abstract

Community structure underpins many complex networked systems and plays a vital role when components in some modules of the network come under attack or failure. Here, we study the generalized k-core (Gk-core) percolation over a modular random network model. Unlike the archetypal giant component based quantities, Gk-core can be viewed as a resilience metric tailored to gauge the network robustness subject to spreading virus or epidemics paralyzing weak nodes, i.e., nodes of degree less than k, and their nearest neighbors. We develop two complementary frameworks, namely, the generating function formalism and the rate equation approach, to characterize the Gkcore of modular networks. Through extensive numerical calculations and simulations, it is found that G2-core percolation undergoes a continuous phase transition while Gk-core percolation for k \geq 3 displays a first-order phase transition for any fraction of interconnecting nodes. The influence of interconnecting nodes tends to be more visible nearer the percolation threshold. We find by studying modular networks with two Erd\H os--R\' enyi modules that the interconnections between modules affect the G2-core percolation phase transition in a way similar to an external field in a spin system, where Widom's identity regulating the critical exponents of the system is fulfilled. However, this analogy does not seem to exist for Gk-core with k \geq 3 in general.

Study on Power Grid Partition and Attack Strategies Based on Complex Networks

“…Detecting communities in a network can help us find the objects with the same function in the system, study the relationship among different communities, infer the missing attributes in the nodes, and make a reasonable prediction of the undiscovered relationship between nodes so as to better understand the underlying structure of the network and the information contained in it. Community discovery has been successfully applied in many areas of real life, such as anti-terrorism detection, behavior prediction, recommendation system, and so on [23,24]. Community detection in a network is one of the hotspots in modern network science.…”

Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

“…Here, we summarize the results related to the selection or the clustering of points in PF, with applications for MOO algorithms. Polynomial complexity resulting in the use of 2D PF structures is an interesting property; clustering problems have a NP-hard complexity in general [17,44,45].…”

Multi-objective NSGA-II based community detection using dynamical evolution social network

“…While some researchers have focused on the community structure and its influence on the resilience of the network as a whole [19], many researchers have focused on the community detection from the perspective of multi-objective optimization. In the work of [16], the multi-objective evolutionary Algorithm has been used for identifying overlapping community structure in a complex network.…”