  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 strictly positive
value as the number of issues discussed increases. If the network has a special
topology, termed "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 star topology 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 show that the strategies are
remarkably intuitive and that certain strategies are favourable compared to
others, all of which is sociologically expected.
