Critical phenomena in networks

A. V. Goltsev, S. N. Dorogovtsev, J. F. F. Mendes

Published 2002-04-28, updated 2003-01-21Version 2

We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly from the standard mean-field behavior. The critical behavior observed in various networks is analyzed and found to be in agreement with the theory.