Department of Mathematics, UCI

It has recently been recognized that a large number of complex networks are scale-free, having a power-law degree distribution. Here we propose that the emergence of many scale-free networks is tied to the efficiency of transport and flow processing across these structures. In particular, we show that for large networks on which flows are influenced or generated by gradients of a scalar distributed on the nodes, scale-free structures will ensure efficient processing, while non scale-free structures, such as random graphs, will become congested. As an application, we then make a connection to a simple agent-based model of a market and study the effects of the social network on the evolution of the collective/market.