Two-Dimensional Centrality of Asymmetric Social Network
The purpose of the present study is to introduce a procedure to derive the centrality of an asymmetric social network, where the relationships among actors are asymmetric. The procedure is based on the singular value decomposition of an asymmetric matrix of friendship relationships among actors. Two kinds of the centrality are introduced; one is the centrality of extending friendship relationships from the actor to the other actors, and the other is the centrality of accepting friendship relationships from the other actors to the actor. The present procedure is based on the two largest singular values not only on the largest singular value. Each actor has two sets of the centrality; each consists of the centrality of extending and of the centrality of accepting friendship relationships. An application to help or advice relationships among managers in a company is shown.
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