Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks

• Published in: PloS one Vol. 8; no. 1; p. e53095
• Main Authors: Piraveenan, Mahendra, Prokopenko, Mikhail, Hossain, Liaquat
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 22.01.2013; Public Library of Science (PLoS)
• Subjects: Biology; Complexity; Computer applications; Computer Graphics; Computer networks; Computer simulation; Computer viruses; Computers; Connectivity; Critical phenomena; Disease transmission; Electricity distribution; Engineering; Epidemics; Graph theory; Growth models; Infections; Mathematics; Medicine; Models, Theoretical; Networks; Nodes; Percolation; Phase transitions; Physics; Random walk; Social and Behavioral Sciences; Social networks; Social organization; Social Support; Stochastic Processes; Towns; Viruses; Australia; New South Wales Australia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0053095

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.