2016/03/10 by Dunbiao Niu, Xin Yuan, Y. L. Xin +3
Mathematics · Physics and Astronomy · #Artificial intelligence #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Condensed matter physics #Critical exponent #Criticality #Dependency (UML) #Directed percolation #Interdependent networks #Mathematics #Node (physics) #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Phase transition #Physics #Probabilistic logic #Statistical physics #Stochastic processes and statistical mechanics #Topology (electrical circuits) #physics.soc-ph
paper · pdf · doi:10.1103/physreve.93.042312
7 pager 5 figure
arxiv created 2016/03/10 · openalex publication_date 2016/04/20 · arxiv updated 2016/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 Erdős-Rényi networks.