Identifying optimal targets of network attack by belief propagation

Abstract

For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is intrinsically related to the feedback vertex set problem that was successfully tackled by spin glass theory and an associated belief propagation-guided decimation (BPD) algorithm [H.-J. Zhou, Eur. Phys. J. B 86 (2013) 455]. In the present work we apply the BPD alrogithm (which has approximately linear time complexity) to the network optimal attack problem, and demonstrate that it has much better performance than a recently proposed Collective Information algorithm [F. Morone and H. A. Makse, Nature 524 (2015) 63-68] for different types of random networks and real-world network instances. The BPD-guided attack scheme often induces an abrupt collapse of the whole network, which may make it very difficult to defend.

Fast and simple decycling and dismantling of networks

“…These are two fundamental network-optimization problems with a wide range of applications, related to optimal vaccination and surveillance, information spreading, viral marketing, and identification of influential nodes. Considerable research efforts have been devoted to the network decycling and dismantling problems recently12345678.…”

“…However, finding the best possible approximate solutions for as large classes of networks as possible is an open and actively investigated direction. Recent theoretic and algorithmic progress on both these problems12356 came from the fact that, on random sparse networks with degree distributions having a finite second moment, methods from physics of spin glasses provide accurate algorithms for both decycling and dismantling. These sparse random networks are locally tree-like and do not contain many short loops.…”

Network clustering and community detection using modulus of families of loops

“…Loops offer more pathways within them compared to treelike topologies; thus rich loop structures improve network robustness [2] and impact propagating and transporting processes in networks [3]. Previous approaches on analysis of loop structures focus on loops with lengths of order 3-5 separately [4,5] and a few such as Refs.…”

Fragmenting networks by targeting collective influencers at a mesoscopic level

“…Among them, a major criterion of the influential node is that the removal of a node, or immunization, efficiently fragments the network into small pieces. Because the problem of finding the minimal set of nodes to be immunized to fragment the network is NP-hard2, various immunization algorithms to determine the order of the nodes to be removed to realize efficient fragmentation of the network have been proposed23456789101112, sometimes with the constraint that the information about the network is only partially available61314151617. Notably, although immunizing hubs (i.e., nodes with a large degree) first is intuitive and much better than randomly selecting nodes to be immunized181920, many immunization algorithms outperform the hub-first immunization algorithm.…”