Dependency of a network's resilience to forcing directions

Abstract

The resilience of a network to edge failure and system collapse is dependent not only on the magnitude of the forces experienced by the network components but also crucially on the interconnection pattern of the network. In this work, we model the evolution of a grid network and an Erdos-Renyi network by taking into account the forces that exist between connected nodes. We find that for a grid network, the resulting fraction of disconnected edges follows a linear trend with a slope of 0.50 wherein a grid network having its sources of force loadings positioned randomly in the network retains half of its edges, f =0.496 ±0.007 ,but when the nodes are arranged in order of force influence, the network totally collapses. However, for an Erdos-Renyi network, the system totally fragments regardless of the positioning of the influential nodes. We further show that the time tf it takes for the networks to reach its equilibrium network structure follows a power law relationship, regardless of node positioning and connectivity.