Local Centers of the Social Network

Abstract

For the social network of n nodes, one might be interested in finding k nodes to disseminate the information as quickly as possible or to identify key nodes of high "local centrality". I propose two algorithms for determining k "local centers" of the network and work on a real case.

Fuzzy k-Means Local Centers of the Social Networks

“…The fuzzy k-means algorithm, applied to the largest component of the network with k = 10, identifies Nodes 17,30,94,102,119,141,182,242,315,392 The average distance between local centers was 12.6, smaller than the corresponding average distance 13.8 between local centers by the k-means algorithm of Huh (2011). Possibly, such phenomenon is general in the networks composed of several communities.…”

“…For the social networks, Huh (2011) proposed the k-means algorithm to identify k nodes of the highest local centrality. In this study, we develop a fuzzy k-means algorithm to locate k local centers of the network.…”

“…See Figure 1. On the other hand, the k-means algorithm of Huh (2011) incorrectly classifies Nodes 9, 25, 26, and 32.…”