Load balanced diffusive capture process on homophilic scale-free networks

Diffusive capture processes are known to be an effective method for information search on complex networks. The biased N$N$ lions–lamb model provides quick search time by attracting random walkers to high degree nodes, where most capture events take place. The price of the efficiency is extreme traffic concentration on top hubs. We propose traffic load balancing provided by type specific biased random walks. For that we introduce a multi-type scale-free graph generation model, which embeds homophily structure into the network by utilizing type dependent random walks. We show analytically and with simulations that by augmenting the biased random walk method with a simple type homophily rule, we can alleviate the traffic concentration on high degree nodes by spreading the load proportionally between hubs with different types of our generated multi-type scale-free topologies.