Unicyclic Components in Random Graphs
E. Ben-Naim and P.L. Krapivsky
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, $U_k\simeq (4k)^{-1}$ for $k\gg 1$. As a result, the
total number of unicyclic components grows logarithmically with the
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