Unicyclic Components in Random Graphs

Details Unicyclic Components in Random Graphs Unicyclic Components in Random Graphs

2004-03-18

arxiv.org/abs/cond-mat/0403453v1

J. Phys. A 37, L189 (2004)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1088/0305-4470/37/18/L01

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.

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