Controlling the Katz-Bonacich Centrality in Social Network: Application to Gossip in Online Social Networks

Recent papers studied the control of spectral centrality measures of a network by manipulating the topology of the network. We extend these works by focusing on a specific spectral centrality measure, the Katz-Bonacich centrality. The optimization of the Katz-Bonacich centrality using a topological control is called the Katz-Bonacich optimization problem. We first prove that this problem is equivalent to a linear optimization problem. Thus, in the context of large graphs, we can use state of the art algorithms. We provide a specific applications of the Katz-Bonacich centrality minimization problem based on the minimization of gossip propagation and make some experiments on real networks.

[1]  Albert-László Barabási,et al.  Control Centrality and Hierarchical Structure in Complex Networks , 2012, PloS one.

[2]  Asuman Ozdaglar,et al.  Competing over Networks , 2015 .

[3]  Abhijit Banerjee,et al.  Gossip: Identifying Central Individuals in a Social Network , 2014, ArXiv.

[4]  Karrie Karahalios,et al.  FeedVis: A Path for Exploring News Feed Curation Algorithms , 2015, CSCW Companion.

[5]  Antoni Calvó-Armengol,et al.  Delinquent Networks , 2009, SSRN Electronic Journal.

[6]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  James R. Bunch,et al.  Sparse Matrix Computations , 2014 .

[8]  Arun G. Chandrasekhar,et al.  The Diffusion of Microfinance , 2012, Science.

[9]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[10]  Stéphane Gaubert,et al.  Ergodic Control and Polyhedral Approaches to PageRank Optimization , 2010, IEEE Transactions on Automatic Control.

[11]  U. Temurshoev.  Who's Who in Networks - Wanted: The Key Group , 2008 .

[12]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[13]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[14]  Xiang Li,et al.  Power of individuals - Controlling centrality of temporal networks , 2014, ArXiv.

[15]  Kostas Bimpikis,et al.  Cournot competition in networked markets , 2014, EC.

[16]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

[17]  R. E. Kalman,et al.  Contributions to the Theory of Optimal Control , 1960 .

[18]  P. Bonacich.  Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[19]  Shigeyuki Hosoe,et al.  On the irreducibility condition in the structural controllability theorem , 1979 .

[20]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[21]  M. T. Wasan.  Stochastic Approximation , 1969 .

[22]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[23]  Sébastien Bubeck,et al.  Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems , 2012, Found. Trends Mach. Learn..

[24]  M. Heath.  Sparse matrix computations , 1984, The 23rd IEEE Conference on Decision and Control.

[25]  D. Lusseau,et al.  The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations , 2003, Behavioral Ecology and Sociobiology.

[26]  Vito Latora,et al.  Controlling centrality in complex networks , 2011, Scientific Reports.

[27]  Yves Zenou,et al.  Who's Who in Crime Network. Wanted the Key Player , 2004 .