A self-organized graph evolution model with preferential network random walk

We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the first type cause an enhancement in link attachments, while the second types have a destructive behavior. The statistical properties of the resulting network, including weight distributions, clustering, spectral densities and average path length are evaluated. As the ratio of the population of two types is balanced, the network faces a phase transition. We show that in the transition point, the graph behaves as a scale-free network, with a scaling exponent of \sim -1.7.