Network navigation with non-Lèvy superdiffusive random walks

We introduce a formalism based on a continuous time approximation to study the characteristics of random walks with jumps to random locations of the networks (Pagerank random walks). We find that the diffusion of the occupancy probability has a dynamics that exponentially “forgets” the initial conditions and settles to a steady state that depends only on the characteristics of the network. In the special case in which the walk begins from a single node, we show that the largest eigenvalue of the transition value (λ1=1) does not contribute to the dynamic and that the probability is constant in the direction of the corresponding eigenvector. We study the process of visiting new nodes, which we find to have a dynamic similar to that of the occupancy probability. Finally, we determine the average transit time between nodes 〈T〉.