LONG-RANGE CONNECTIONS, REAL-WORLD NETWORKS AND RATES OF DIFFUSION

Abstract

Long-range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics. Here, we review the evidence for long-range connections in real-world networks and discuss the nature of the nonlocal diffusion arising from different distance-dependent laws. Particular attention is devoted to the characterization of diffusion in finite networks for moderate large times and to the comparison of distance laws of exponential and power type.