Dynamic bond percolation in networks

Bond percolation is a network process that traditionally addresses the question when there is a path between two sites or two clusters in a network. This has been used to study the circulation of goods or flows in networked structures as well as network resilience. This paper proposes and analyzes a dynamic bond percolation model where bonds (i.e., edges) open (i.e., form) or close (i.e., terminate) according to random micro interactions. We model the edge dynamics through topology independent and topology-dependent processes - spontaneous formation or termination of edges and the formation of edge {a, b} between two sites a and b that depends on the current number of existing edges at a and b. We show that the resulting network process is Markov and reversible, and we determine analytically its equilibrium distribution, avoiding having to solve a eigenvalue-eigenvector problem that quickly becomes intractable for even moderate sized networks.