Unicyclic Components in Random Graphs
arXiv:cond-mat/0403453 · doi:10.1088/0305-4470/37/18/L01
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.
4 pages, 2 figures