Unicyclic Components in Random Graphs
classification
❄️ cond-mat.stat-mech
cond-mat.dis-nncs.DSmath.PR
keywords
componentsunicyclicdistributiongelationnumberrandomsizealgebraically
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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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