2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007;
Denver, Colorado
Session S7: Percolation
2:30 PM–5:30 PM,
Wednesday, March 7, 2007
Colorado Convention Center
Room: Korbel 4A-4B
Sponsoring
Unit:
GSNP
Chair: Robert Ziff, University of Michigan
Abstract ID: BAPS.2007.MAR.S7.3
Abstract: S7.00003 : Percolation properties of complex networks with weak and strong clustering
3:42 PM–4:18 PM
Preview Abstract
Abstract
Author:
M. Angeles Serrano
(School of Informatics, Indiana University)
A diversity of systems in the real world can be analyzed as complex
networks. This makes any theoretical development in the field
potentially applicable to many different areas. As a germane
example, percolation has helped us to understand, for instance, the
high resilience of scale-free networks in front of the random
removal of a fraction of their constituents, with important
implications for communication or biological systems among others.
In addition to its high theoretical interest, it serves as a
conceptual approach to treat more factual problems on networks, such
as the dynamics of epidemic spreading.
On the other hand, when large systems of interactions are mapped
into comprehensible graphs, just vertices and edges are usually
recognized as the primary building blocks. However, transitive
relations, represented by triangles and referred to as clustering,
should also be taken into account as a basic structure whose
presence and self-organization can drastically impact network
structure and properties.
In this framework, the introduction of clustering in the percolation
analysis of complex networks represents a theoretical challenge.
Previous approaches were based on the idea of branching process,
which works well when the network is locally treelike and thus the
clustering coefficient is very small. Real networks, however, are
shown to have a significant level of clustering. They can be
classified in networks with weak transitivity, in which triangles
are disjoint, and networks with strong transitivity, where edges are
forced to share many triangles. The class a network belongs to
changes its percolation properties. For networks with weak
clustering, we find analytically the critical point for the onset of
the giant component and its size. By means of numerical simulations,
we also prove that, when comparing with the unclustered counterpart,
weak clustering hinders the onset of the giant connected component
whereas it is favored by strong clustering. This is a direct
consequence of the differences in the k-core structure for the two
types of networks. In the particular case of scale-free networks,
and although clustering can strongly affect the size and the
resilience of the giant connected component, neither weak nor strong
transitivity can restore a finite percolation threshold which, in
turn, implies the absence of an epidemic threshold.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.MAR.S7.3