Wed, 20 Aug 2008 22:07:35 BST CiteULike: bigbossman Bonacich http://www.citeulike.org/user/bigbossman/author/Bonacich CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/bigbossman/article/279460 <i>The American Journal of Sociology, Vol. 92, No. 5. (1987), pp. 1170-1182.</i><br /><br />Although network centrality is generally assumed to produce power, recent research shows that this is not the case in exchange networks. This paper proposes a generalization of the concept of centrality that accounts for both the usual positive relationship between power and centrality and Cook et al.'s recent exceptional results. Power and Centrality: A Family of Measures Phillip Bonacich The American Journal of Sociology, Vol. 92, No. 5. (1987), pp. 1170-1182. 2005-08-11T18:58:41-00:00 1987 The American Journal of Sociology 92 5 1170 1182 centrality graphs networks power http://www.citeulike.org/user/bigbossman/article/967221 <i>pp. 155-171.</i><br /><br />We consider a discrete time Markov chain whose state space is the set of all NxN stochastic matrices with zero diagonal entries. This chain models the evolution of relationships among N individuals who exchange gifts according to probabilities determined by previous exchanges. We determine the stable equilibria for this chain, and prove convergence to a mixture of these. In particular, we show that for generic initial states, the chain converges to a randomly chosen set of constellations made up of disjoint stars. Each star has a center, which is the recipient of all gifts from the other individuals in that star, while the center distributes his gifts only to members of his own star. Asymptotics of a matrix valued Markov chain arising in sociology P Bonacich pp. 155-171. 2006-11-29T18:29:04-00:00 155 171 chain exchange markov networks