Physics Colloquium - Friday, Sept. 1st, 2006, 4:00 P.M.
E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200
Physics of Flow in Complex Networks
Los Alamos National Laboratory
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.