Effect of Mixing Assortativity on Extreme Events in Complex Networks

We investigate the effect of mixing assortativity on the occurrence of extreme events in complex networks. The bias random walk model is adopted with a preferential transition probability tuned by a parameter α. We derive exact expressions for the stationary distribution probability and for the occurrence probability of extreme events. They reveal that the occurrence of extreme events strongly depends on the mixing assortativity of the network. It is shown that, for non-assortative (r_k=0), assortative (r_k=0.15) and disassortative (r_k=?0.15) scale-free networks, the minimal occurrence of extreme events will happen at α=?1.0, α=?0.6 andα=0.2, respectively.