%0 Journal Article
%T Core organization of directed complex networks
%A N. Azimi-Tafreshi
%A S. N. Dorogovtsev
%A J. F. F. Mendes
%J Computer Science
%D 2012
%I arXiv
%R 10.1103/PhysRevE.87.032815
%X The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from $k$-cores, which are principally different subgraphs in networks. If the vertex mean degree of a network is sufficiently large, the core is a giant cluster containing a finite fraction of vertices. We find that generalization of this pruning algorithm to directed networks provides a significantly more complex picture of cores. By implementing a rate equation approach to this pruning procedure for directed uncorrelated networks, we identify a set of cores progressively embedded into each other in a network and describe their birth points and structure.
%U http://arxiv.org/abs/1212.5981v2