Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

Abstract

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Hybrid Societies: Challenges and Perspectives in the Design of Collective Behavior in Self-organizing Systems

“…In order to give a little, incomplete overview, we cite only a few of these, see Table 1. Despite the strict column-wise presentation of methods, there exist already approaches that combine several methods from different fields, such as the combination of game theory with networks (Perc and Szolnoki, 2010), percolation and networks (Piraveenan et al, 2013a), and hybrid systems with temporal networks (Boerkoel and Durfee, 2013). Furthermore, the field of evolutionary game theory investigates hybrid societies, especially the interaction of agents also with reference to collective behavior and self-organization (Perc and Szolnoki, 2010;Perc and Grigolini, 2013).…”

Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks

“…Degree, betweenness, and closeness centrality are measures of determining the criticality and importance of nodes [7,35,36]. Piraveenan et al [37] introduced a new centrality measure (percolation centrality) to analyze the importance of nodes during percolation in networks. They found that the average of percolation centrality overall possible single contagion source reduces to betweenness centrality.…”

Revisiting Models of Vulnerabilities of the Networks

“…There is a large number of graph "measures" usable for assessing the complexity of and for characterizing the structure of networks, see a subset of them explained in [3], [13], [14], [16], [18], [21], [23], [30], [31]. Many of these parameters relate to the connectivity degree of graphs, or on the centrality of the nodes; others are based on statistical foundations, such as entropy and Fisher information [1].…”

“…Therefore, for every application and targeted property, another choice of measures is probably recommended. As explained by Piraveenan et al [23] An irrational attacker may choose the target randomly, attacking with uniform (i.e., the same) probability any node or edge of the network. In that case, the (statistical) structural properties and flow properties of the graph are applicable for determining what the effect of the attack may be.…”