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According to the DeGroot-Friedkin model of a social network, an individual'ssocial power evolves as the network discusses individual opinions over asequence of issues. Under mild assumptions on the connectivity of the network,the social power of every individual converges to a constant strictly positivevalue as the number of issues discussed increases. If the network has a specialtopology, termed "star topology", then all social power accumulates with theindividual at the centre of the star. This paper studies the strategicintroduction of new individuals and/or interpersonal relationships into asocial network with star topology to reduce the social power of the centreindividual. In fact, several strategies are proposed. For each strategy, wederive necessary and sufficient conditions on the strength of the newinterpersonal relationships, based on local information, which ensures that thecentre individual no longer has the greatest social power within the socialnetwork. Interpretations of these conditions show that the strategies areremarkably intuitive and that certain strategies are favourable compared toothers, all of which is sociologically expected.

Modification of Social Dominance in Social Networks by Selective Adjustment of Interpersonal Weights