Extreme events on complex networks and network robustness

Abstract

We live in a modern world surrounded by networks ranging from transportation system to nancial market. Network robustness is a matter of serious concern especially because a network can collapse completely due to overload failure. In this project my aim is to study overload failure of a network. Physical ow through a node is de ned by load and capacity, capacity is the maximum load that a node can handle. I will model this situation using extreme events where population of walker on a node is the load. I use random walk simulation to prescribe a degree dependent capacity for each node. If a node encounters an extreme event, we will consider that situation as a node failure which causes redistribution of its load. I show that scale free networks are vulnerable against overload failures because of heterogeneous degree distribution but homogeneous networks (complete graph, Erdos-Renyi) are robust against overload failure. I will also show that an overloaded network undergoes a transition and define three different phases of network failure. Real life networks, internet, power grid has high heterogeneous distribution of loads. We will discuss a method to increase total capacity of the network.