Anomalous Transport in Scale-Free Networks

To study transport properties of scale-free and Erdős-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)∼k^-λ in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution Φ_SF(G)∼G^-g_G, where g_G=2λ-1, and confirm our predictions by simulations. The power-law tail in Φ_SF(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdős-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical “transport backbone” picture we show that the conductances of scale-free and Erdős-Rényi networks are well approximated by ck_Ak_B/(k_A+k_B) for any pair of nodes A and B with degrees k_A and k_B, where c emerges as the main parameter characterizing network transport.