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A model algorithm is proposed to study subsequent partitions of complexnetworks describing social structures. The partitions are supposed to appear asactions of rivaling leaders corresponding to nodes with large degrees. Thecondition of a partition is that the distance between two leaders is at leastthree links. This ensures that the layer of nearest neighbours of each leaderremains attached to him. As a rule, numerically calculated size distribution offragments of scale-free Albert-Barabasi networks reveals one large fragmentwhich contains the original leader (hub of the network), and a number of smallfragments with opponents that are described by two Weibull distributions.Numerical simulations and mean-field theory reveal that size of the largerfragment scales as the square root of the initial network size. The algorithmis applied to the data on political blogs in U.S. (L. Adamic and N. Glance,Proc. WWW-2005). The obtained fragments are clearly polarized; either theybelong to Democrats, or to the GOP.

Consecutive partitions of social networks between rivaling leaders