Recent advances of percolation theory in complex networks

Abstract

During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous transitions, the percolation transitions occurring in complex systems are often of different types such as discontinuous, hybrid, and infinite-order phase transitions. Thus, percolation has received considerable attention in network science community. Here we present a very brief review of percolation theory recently developed, which includes those types of phase transitions, critical phenomena, and finite-size scaling theory. Moreover, we discuss potential applications of theoretical results and several open questions including universal behaviors.

arXiv commentarXiv admin note: text overlap with arXiv:1611.03588

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• The theory of percolation on hypergraphs
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• Degree-Ordered-Percolation on uncorrelated networks
• A hybrid percolation transition at a finite transition point in scale-free networks
• Solving a directed percolation inverse problem
• Discontinuous emergence of a giant cluster in assortative scale-free networks
• A simple model of knowledge percolation
• Critical behaviors of cascading dynamics on multiplex two-dimensional lattices