Issue |
EPL
Volume 98, Number 1, April 2012
|
|
---|---|---|
Article Number | 16001 | |
Number of page(s) | 6 | |
Section | Condensed Matter: Structural, Mechanical and Thermal Properties | |
DOI | https://doi.org/10.1209/0295-5075/98/16001 | |
Published online | 28 March 2012 |
Exact solution of bond percolation on small arbitrary graphs
Département de physique, de génie physique, et d'optique, Université Laval - Québec (Qc), Canada G1V 0A6
Received:
7
February
2012
Accepted:
2
March
2012
We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution of the node partitions (i.e., the constrained distribution of the size of each component) in undirected graphs. Besides opening the way to the theoretical prediction of percolation on arbitrary graphs of large but finite size, we show how our results find application in graph theory, epidemiology, percolation and fragmentation theory.
PACS: 64.60.aq – Networks / 64.60.ah – Percolation / 02.10.Ox – Combinatorics; graph theory
© EPLA, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.