Vulnerability of complex networks

Abstract

We consider normalized average edge betweenness of a network as a metric of network vulnerability. We suggest that normalized average edge betweenness together with is relative difference when certain number of nodes and/or edges are removed from the network is a measure of network vulnerability, called vulnerability index. Vulnerability index is calculated for four synthetic networks: Erdös-Rényi (ER) random networks, Barabási-Albert (BA) model of scale-free networks, Watts-Strogatz (WS) model of small-world networks, and geometric random networks. Real-world networks for which vulnerability index is calculated include: two human brain networks, three urban networks, one collaboration network, and two power grid networks. We find that WS model of small-world networks and biological networks (human brain networks) are the most robust networks among all networks studied in the paper.

An approach to assess criticality of elements in the process of information infrastructure protection

“…Bompard [17] used a topological approach with complex network theory to define structural vulnerabilities of power systems. Mishkovski [18] developed one metric of vulnerabilities of complex networks.…”

Group-centrality and impact of large-scale localized faults in spatial networks

“…Centrality in such networks is usually interpreted to measure power and social stratification. But there are also instances of centrality applications in biological networks [7,8], communication networks [9,10], power networks [4] and transportation networks [11,12]. In spatial networks, centrality measures are used for design requirement and vulnerability studies.…”

“…In vulnerability analysis, centrality is used to identify critical locations and "vulnerability backbones" in the network from the network topology, and analyzing how well distributed a network is. Removing central nodes generally leads to increase in diameter, reduction of flow and lesser structural connectivity [4,10].…”

Does topological information matter for power grid vulnerability?

“…The importance of a component can be defined according to different metrics. Some studies quantified the node importance by node degree, 6,7,25,26 such as the vulnerability analysis of Western USA power grid, Nordic power grid, 25 and European power grids 26 under node removal, according to decreasing order of node degree; some studies quantified the node importance by component betweenness, such as the vulnerability analysis of power grids under intentional edge removal, according to descending order of betweenness centrality; [27][28][29][30] some studies measured the component importance by the amount of transported power load. 7,31,32 When more than one component are attacked, different strategies could be used to simulate the failures, depending on whether the component importance is based on initial network configuration or updated configuration after the previous removal, such as the vulnerability analysis of power grids under recalculated degree and recalculated betweenness.…”