Percolation of networks with directed dependency links

Abstract

The self-consistent probabilistic approach has proven itself powerful in studying the percolation behavior of interdependent or multiplex networks without tracking the percolation process through each cascading step. In order to understand how directed dependency links impact criticality, we employ this approach to study the percolation properties of networks with both undirected connectivity links and directed dependency links. We find that when a random network with a given degree distribution undergoes a second-order phase transition, the critical point and the unstable regime surrounding the second-order phase transition regime are determined by the proportion of nodes that do not depend on any other nodes. Moreover, we also find that the triple point and the boundary between first- and second-order transitions are determined by the proportion of nodes that depend on no more than one node. This implies that it is maybe general for multiplex network systems, some important properties of phase transitions can be determined only by a few parameters. We illustrate our findings using Erdos-Renyi (ER) networks.

arXiv comment7 pager 5 figure

References in corpus (20)

• The structure and function of complex networks
• Error and attack tolerance of complex networks
• Catastrophic cascade of failures in interdependent networks
• Synchronization in complex networks
• The spread of epidemic disease on networks
• Network robustness and fragility: Percolation on random graphs
• Resilience of the Internet to random breakdowns
• k-core organization of complex networks
• Robustness of a Network of Networks
• Avalanche Collapse of Interdependent Network
• The critical effect of dependency groups on the function of networks
• Avoiding catastrophic failure in correlated networks of networks
• Percolation in Directed Scale-Free Networks
• Percolation in Interdependent and Interconnected Networks: Abrupt Change from Second to First Order Transition
• Multiple percolation transitions in a configuration model of network of networks
• Percolation of Interdependent Networks with Inter-similarity
• Percolation in networks composed of connectivity and dependency links
• Percolation of a general network of networks
• Percolation of partially interdependent networks under targeted attack
• The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack

Cited by in corpus (2)

• Cross-feeding Creates Tipping Points in Microbiome Diversity
• Enhanced robustness of single-layer networks with redundant dependencies