Showing papers on "Random walk closeness centrality published in 2005"

Centrality measures based on current flow

Abstract: We consider variations of two well-known centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the current-flow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for current-flow betweenness.

The Betweenness Centrality Of Biological Networks

Abstract: (ABSTRACT) In the last few years, large-scale experiments have generated genome-wide protein interaction networks for many organisms including Saccharomyces cerevisiae (baker's yeast), Caenorhabditis elegans (worm) and Drosophila melanogaster (fruit fly). In this thesis, we examine the vertex and edge betweenness centrality measures of these graphs. These measures capture how " central " a vertex or an edge is in the graph by considering the fraction of shortest paths that pass through that vertex or edge. Our primary observation is that the distribution of the vertex betweenness centrality follows a power law, but the distribution of the edge betweenness centrality has a " Poisson-like " distribution with a very sharp spike. To investigate this phenomenon, we generated random networks with degree distribution identical to those of the protein interaction networks. To our surprise, we found out that the random networks and the protein interaction networks had almost identical distribution of edge be-tweenness. We conjecture that the " Poisson-like " distribution of the edge betweenness centrality is the property of any graph whose degree distribution satisfies power law. Acknowledgments I would sincerely like to thank my advisor T. M. Murali, who has been one of the most patient and helpful guides one can ask for. Working on this thesis has been a great learning experience for me and I am grateful to him for giving me this opportunity. I would like to thank Dr. Madhav Marathe and Dr. Anil Kumar Vullikanti for their valuable inputs, and numerous ideas that considerably improved this thesis. I am also thankful to my parents, sister and family for all the love and support.

Relating network topology to the robustness of centrality measures

Abstract: : This paper reports on a simulation study of social networks that investigated how network topology relates to the robustness of measures of system-level node centrality. This association is important to understand as data collected for social network analysis is often somewhat erroneous and may, to an unknown degree, misrepresent the actual true network. Consequently, the values for measures of centrality calculated from the collected network data may also vary somewhat from those of the true network, possibly leading to incorrect suppositions. To explore the robustness, i.e., sensitivity, of network centrality measures in this circumstance, we conduct Monte Carlo experiments whereby we generate an initial network, perturb its copy with a specific type of error, then compare the centrality measures from two instances. We consider the initial network to represent a true network, while the perturbed represents the observed network. We apply a six-factor full-factorial block design for the overall methodology. We vary several control variables (network topology, size and density, as well as error type, form and level) to generate 10,000 samples each from both the set of all possible networks and possible errors within the parameter space. Results show that the topology of the true network can dramatically affect the robustness profile of the centrality measures. We found that across all permutations that cellular networks had a nearly identical profile to that of uniform-random networks, while the core-periphery networks had a considerably different profile. The centrality measures for the core-periphery networks are highly sensitive to small levels of error, relative to uniform and cellular topologies. Except in the case of adding edges, as the error increases, the robustness level for the 3 topologies deteriorates and ultimately converges.