Degree correlations in growing networks with deletion of nodes

Abstract

In this paper we study the degree distribution and the two-node degree correlations in growing networks generated via a general linear preferential attachment of new nodes together with a uniformly random deletion of nodes. By using a continuum approach we show that, under some suitable combinations of parameters (deletion rate and node attractiveness), the degree distribution not only loses its scale-free character but can even be supported on a small range of degrees. Moreover, we obtain new results on two-vertex degree correlations showing that, for degree distributions with finite variance, such correlations can change under a nonselective removal of nodes.