# American Institute of Mathematical Sciences

July  2014, 19(5): 1355-1372. doi: 10.3934/dcdsb.2014.19.1355

## Rethinking centrality: The role of dynamical processes in social network analysis

 1 Robert Bosch LLC, 4005 Miranda Ave, Palo Alto, CA 94304, United States 2 USC Information Sciences Institute, 4676 Admiralty Way, Marina del Rey, CA 90292, United States

Received  January 2012 Revised  June 2012 Published  April 2014

Many popular measures used in social network analysis, including centrality, are based on the random walk. The random walk is a model of a stochastic process where a node interacts with one other node at a time. However, the random walk may not be appropriate for modeling social phenomena, including epidemics and information diffusion, in which one node may interact with many others at the same time, for example, by broadcasting the virus or information to its neighbors. To produce meaningful results, social network analysis algorithms have to take into account the nature of interactions between the nodes. In this paper we classify dynamical processes as conservative and non-conservative and relate them to well-known measures of centrality used in network analysis: PageRank and Alpha-Centrality. We demonstrate, by ranking users in online social networks used for broadcasting information, that non-conservative Alpha-Centrality generally leads to a better agreement with an empirical ranking scheme than the conservative PageRank.
Citation: Rumi Ghosh, Kristina Lerman. Rethinking centrality: The role of dynamical processes in social network analysis. Discrete & Continuous Dynamical Systems - B, 2014, 19 (5) : 1355-1372. doi: 10.3934/dcdsb.2014.19.1355
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