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

According to the DeGroot-Friedkin model of a social network, an individual's social power evolves as the network discusses individual opinions over a sequence of issues. Under mild assumptions on the connectivity of the network, the social power of every individual converges to a constant nonnegative value as the number of issues discussed increases. If the network has a special topology, namely the "star topology", then all social power accumulates with the individual at the centre of the star. This paper studies the strategic introduction of new individuals and/or interpersonal relationships into a social network with the star topology so as to reduce the social power of the centre individual. In fact, several strategies are proposed. For each strategy, we derive necessary and sufficient conditions on the strength of the new interpersonal relationships, based on local information, which ensures that the centre individual no longer has the greatest social power within the social network. Interpretations of these conditions reveal that the strategies are remarkably intuitive and that certain strategies are favourable compared to others, all of which is sociologically expected.