Critical phenomena in complex networks
release_2yfakisahrh4vcl3m7pgd23s4y
by
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
2007
Abstract
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.
In text/plain
format
Archived Content
There are no accessible files associated with this release. You could check other releases for this work for an accessible version.
Know of a fulltext copy of on the public web? Submit a URL and we will archive it
0705.0010v4
access all versions, variants, and formats of this works (eg, pre-prints)