Attack Robustness and Centrality of Complex Networks

Abstract

Many complex systems can be described by networks, in which the constituent components are represented by vertices and the connections between the components are represented by edges between the corresponding vertices. A fundamental issue concerning complex networked systems is the robustness of the overall system to the failure of its constituent parts. Since the degree to which a networked system continues to function, as its component parts are degraded, typically depends on the integrity of the underlying network, the question of system robustness can be addressed by analyzing how the network structure changes as vertices are removed. Previous work has considered how the structure of complex networks change as vertices are removed uniformly at random, in decreasing order of their degree, or in decreasing order of their betweenness centrality. Here we extend these studies by investigating the effect on network structure of targeting vertices for removal based on a wider range of non-local measures of potential importance than simply degree or betweenness. We consider the effect of such targeted vertex removal on model networks with different degree distributions, clustering coefficients and assortativity coefficients, and for a variety of empirical networks.

Robustness Comparison of 15 Real Telecommunication Networks: Structural and Centrality Measurements

“…The opposite properties apply to assortative networks with r [ 0 that have an excess of links connecting nodes of similar degrees [11]. As can be found in [4], such networks exhibit greater vulnerability to certain types of targeted attacks. Based on hki, the heterogeneity (r k ) is a coefficient of variation of the connectivity.…”

“…This group of metrics attempts to identify which elements in a network are the most important or central [4]. Consequently, they could help disseminate information innetwork robustness as the differences between the centrality of the most central node and that of all others [21].…”

“…Both, [2,3] rank the better topologies based on their robustness metrics. In [4] an analytical comparison of well-known robustness metrics in some model and empirical networks, when random and targeted attacks occur, is performed. In [4] it is shown that the node degree centrality metric can be used as an effective strategy to remove nodes in simultaneous targeted attacks, whereas for sequential attacks it is betweenness centrality.…”

“…In [4] an analytical comparison of well-known robustness metrics in some model and empirical networks, when random and targeted attacks occur, is performed. In [4] it is shown that the node degree centrality metric can be used as an effective strategy to remove nodes in simultaneous targeted attacks, whereas for sequential attacks it is betweenness centrality. The temporal evolution of the topological robustness of backbone telecommunication networks by identifying their trends is analyzed in [1].…”

Complexity and robustness in hypernetwork models of metabolism

“…Historically, a number of studies have investigated the resilience of metabolic networks to random mutations (and targeted attacks), typically by measuring the effect on network connectedness of the random, or targeted, removal of nodes or edges (Wilhelm et al, 2004;Smart et al, 2008;Iyer et al, 2013). The critical point at which the network breaks down into isolated components, and hence can no longer function, is regarded as a proxy measure for network robustness (Callaway et al, 2000;Karrer et al, 2014).…”