Building catastrophes: Networks designed to fail by avalanche-like breakdown

Abstract

We present a simple method for constructing networks designed to fail catastrophically due to an avalanche-like breakdown. Our method simulates an avalanche in reverse, building a network designed to fail by avalanche-like breakdown. Some restrictions are imposed on the output flow rates of the nodes. An expression for the critical output flow rate of a node is derived. Nodes in the network are considered to have failed when their output flow rate exceeds this value. Two cases are considered: networks where total flow in the network increases with network size; and networks where the total flow is constant. We also consider networks in which nodes have weighted output flow rates. The topology of the generated networks is studied, and it is seen that networks that are almost homogeneous in node degree may still fail catastrophically. Finally we present some possible extensions to the method. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.