Core organization of directed complex networks

Abstract

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.

10 pages, 7 figures

References in corpus (6)

• Critical phenomena in complex networks
• k-core organization of complex networks
• Core percolation on complex networks
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Analytic solution of a static scale-free network model
• Correlations in connected random graphs

Cited by in corpus (7)

• Phase Transitions in Cooperative Coinfections: Simulation Results for Networks and Lattices
• Generalization of core percolation on complex networks
• Core-Periphery Structure in Directed Networks
• Irreversibility in Bacterial Regulatory Networks
• Generalized $k$-core pruning process on directed networks
• A local algorithm and its percolation analysis of bipartite $z$-matching problem
• Control core of undirected complex networks