Identifying Influential Nodes to Inhibit Bootstrap Percolation on Hyperbolic Networks

Abstract

This work involves agent-based simulation of bootstrap percolation on hyperbolic networks. Our goal is to identify influential nodes in a network which might inhibit the percolation process. Our motivation, given a small scale random seeding of an activity in a network, is to identify the most influential nodes in a network to inhibit the spread of an activity amongst the general population of agents. This might model obstructing the spread of fake news in an on line social network, or cascades of panic selling in a network of mutual funds, based on rumour propagation. Hyperbolic networks typically display power law degree distribution, high clustering and skewed centrality distributions. We introduce a form of immunity into the networks, targeting nodes of high centrality and low clustering to be immune to the percolation process, then comparing outcomes with standard bootstrap percolation and with random selection of immune nodes. We generally observe that targeting nodes of high degree has a delaying effect on percolation but, for our chosen graph centralisation measures, a high degree of skew in the distribution of local node centrality values bears some correlation with an increased inhibitory imnact on percolation.