Physics Colloquium - Friday, Sept. 1st, 2006, 4:00 P.M.

E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200

Eduardo Lopez
Los Alamos National Laboratory

Physics of Flow in Complex Networks

To study transport properties of scale-free and Erdos-Renyi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k) which is scale-free with exponent -lambda in which all links have unit resistance. We predict a broad range of values of G, with a decaying power-law tail distribution Phi(G) with exponent -g_G=-(2* Λ-1), and confirm our predictions through simulations. The power-law tail in Phi(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Renyi 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 Erdos-Renyi networks are well approximated by c*kA*kB/(kA+kB) 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. These results are compared to a frictionless model of transport and found to be in agreement. The transport backbone picture appears to be applicable to real Internet data.