Shortest-Path Percolation on Random Networks

We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a certain budget. As pairs of nodes are demanded and edges are removed, the macroscopic connected component of the graph disappears, i.e., the graph undergoes a percolation transition. Here, we study such a shortest-path-percolation transition in homogeneous random graphs where pairs of demanded origin-destination nodes are randomly generated, and fully characterize it by means of finite-size scaling analysis. If budget is finite, the transition is identical to the one of ordinary percolation, where a single giant cluster shrinks as edges are removed from the graph; for infinite budget, the transition becomes more abrupt than the one of ordinary percolation, being characterized by the sudden fragmentation of the giant connected component into a multitude of clusters of similar size.