Unicyclic Components in Random Graphs
Statistical Mechanics
2007-05-23 v1 Disordered Systems and Neural Networks
Data Structures and Algorithms
Probability
Abstract
The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this distribution decays algebraically, U_k ~ 1/(4k) for k>>1. As a result, the total number of unicyclic components grows logarithmically with the system size.
Cite
@article{arxiv.cond-mat/0403453,
title = {Unicyclic Components in Random Graphs},
author = {E. Ben-Naim and P. L. Krapivsky},
journal= {arXiv preprint arXiv:cond-mat/0403453},
year = {2007}
}
Comments
4 pages, 2 figures