Abstract
A model algorithm is proposed to imitate a series of of consecutive conflicts between leaders in social groups. The leaders are represented by local hubs, i.e., nodes with highest node degrees. We simulate subsequent hierarchical partitions of a complex connected network which represents a social structure. The partitions are supposed to appear as actions of members of two conflicted groups surrounding two strongest leaders. According to the model, links at the shortest path between the rival leaders are successively removed. When the group is split into two disjoint parts then each part is further divided as the initial network. The algorithm is stopped, if in all parts a distance from a local leader to any node in his group is shorter than three links. The numerically calculated size distribution of resulting fragments of scale-free Barabási-Albert networks reveals one largest 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. A mean field calculation of the size of the largest fragment is in a good agreement with numerical results. The model assumptions are validated by an application of the algorithm 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 Republicans. This result confirms that during conflicts, hubs are centers of polarization.
Highlights
The calculations have been performed for N = 1000. For both variants A and B and M = 1, 2 and 3, the size distributions of the fragments of the network for the obtained final partition are shown in Figs 3, 4 and 5
Leadership is often represented by the high degree of a node; this representation finds its support in real data [10, 11]
The difference of the parameters b of the Weibull distributions we have found in different ranges of the fragment size s indicates that small fragments are produced according to a different rule than larger ones
Summary
We simulate subsequent hierarchical partitions of a complex connected network which represents a social structure. The algorithm is stopped, if in all parts a distance from a local leader to any node in his group is shorter than three links. The obtained fragments are clearly polarized; either they belong to Democrats, or to Republicans This result confirms that during conflicts, hubs are centers of polarization. An additional condition is that nearest neighbours of each leader remain attached to him during all stages of the partition For a given procedure of separating rival leaders as far as they can appear, we intend to find the size distribution of obtained fragments of the network. The procedure is to divide the network into fragments, centered around local leaders i.e. nodes with highest connections degrees.
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