Multiple Hybrid Phase Transition: Bootstrap Percolation on Complex Networks with Communities

Abstract

Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying the bootstrap percolation on the complex networks with communities can bring us new and important insights of the spreading dynamics on social networks. It attracts a lot of scientists' attentions recently. In this letter, we study the bootstrap percolation on Erdős-Rényi networks with communities and observed second order, hybrid (both second and first order) and multiple hybrid phase transitions, which is rare in natural system. Moreover, we have analytically solved this system and obtained the phase diagram, which is further justified well by the corresponding simulations.

References in corpus (3)

• An information-theoretic framework for resolving community structure in complex networks
• Robustness of community structure in networks
• Percolation and Epidemic Thresholds in Clustered Networks

Cited by in corpus (7)

• Percolation on complex networks: Theory and application
• Cascading failures in interdependent systems under a flow redistribution model
• Social contagions with communication channels alternation on multiplex networks
• Tsallis information dimension of complex networks
• General and exact approach to percolation on random graphs
• Robustness of flow networks against cascading failures under partial load redistribution
• Newman-Ziff algorithm for the bootstrap percolation: application to the Archimedean lattices