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 similar or equal to (4k)(-1) for k much greater than 1. As a result, the total number of unicyclic components grows logarithmically with the system size.