
Abstract For the social network of n nodes, one might be interested in finding k nodes to disseminate the informationasquicklyaspossibleortoidentifykeynodesofhigh“localcentrality”. Iproposetwoalgorithmsfordetermining k “local centers” of the network and work on a real case.Keywords: Social network analysis, neighborhood, closeness, local centers. 1. Background and Aim Social network is a social structure made up of individuals called nodes, which are connected by oneor more specific types of interdependency, such as friendship, kinship, common interest, financialexchange, dislike, sexual relationships, or relationships of beliefs, knowledge or prestige ( Wikipedia “social network”, retrieved 2010/11/05). In most social networks, a number of nodes are more centralthan the others in various respects such as the closeness, the betweenness and the power (Wassermanand Faust, 1994). Huh’s (2010) booklet is a readable introduction to the social network analysis.Rather than detecting a batch of central nodes which are often clustered together, one may beinterested in finding out several nodes that are “locally” central. For instance, Figure 1 shows thenetwork in which five stars of five vertices are connected to a star of five vertices. In this simple case,the local central nodes are 7, 8, 9, 10 and 11. The aim of this paper is to identify the local centralnodes of a somewhat complex network.The usages of local centers are 1) the identification of the overall structure of the network and 2)the speedy delivery of the message or the goods to the most part of the network.In Section 2, I propose two algorithms for determining
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