Unicyclic Components in Random Graphs
<|reference_start|>Unicyclic Components in Random Graphs: 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.<|reference_end|>
@article{ben-naim2004unicyclic,
    title={Unicyclic Components in Random Graphs},
    author={E. Ben-Naim, P.L. Krapivsky},
    journal={J. Phys. A 37, L189 (2004)},
    year={2004},
    doi={10.1088/0305-4470/37/18/L01},
    archivePrefix={arXiv},
    eprint={cond-mat/0403453},
    primaryClass={cond-mat.stat-mech cond-mat.dis-nn cs.DS math.PR}
}