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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