  A model algorithm is proposed to study subsequent partitions of complex
networks describing social structures. The partitions are supposed to appear as
actions of rivaling leaders corresponding to nodes with large degrees. The
condition of a partition is that the distance between two leaders is at least
three links. This ensures that the layer of nearest neighbours of each leader
remains attached to him. As a rule, numerically calculated size distribution of
fragments of scale-free Albert-Barabasi networks reveals one large fragment
which contains the original leader (hub of the network), and a number of small
fragments with opponents that are described by two Weibull distributions.
Numerical simulations and mean-field theory reveal that size of the larger
fragment scales as the square root of the initial network size. The algorithm
is 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 they
belong to Democrats, or to the GOP.
