PageRank centrality with non-local random walk-based teleportation

PageRank is a popular measure of centrality that is often applied to rank nodes in real-world networks. However, in many cases, the notion of teleportation is counterintuitive because it implies that whatever is moving around the network will jump or 'teleport' directly from one node to any other, without considering how far apart the nodes are. To overcome this issue, we propose here a general measure of PageRank centrality whereby the teleportation probabilities depend, in some way, on the distance separating the nodes. We accomplish this by drawing upon recent advances in non-local random walks, which allow the proposed measure to be tailored for various real-world networks and applications. To illustrate the flexibility of the proposed measure and to demonstrate how it differs from PageRank centrality, we present and discuss experimental results for a selection of real-world spatial and social networks, including an air transportation network, a collaboration network and an urban street network.