The clash of the Titans: How preferential attachment helps the survival of the smallest
Department of Theoretical Sciences, Satyendra Nath Bose National Centre for Basic Sciences, Block JD, Sector-III, Salt Lake, Kolkata - 700098, India
Received: 13 June 2014
Revised: 17 October 2014
Published online: 10 December 2014
We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolise the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.
© EDP Sciences, Springer-Verlag, 2014