E Ben-Naim and P L Krapivsky 2004 J. Phys. A: Math. Gen. 37 L189 doi:10.1088/0305-4470/37/18/L01
Unicyclic components in random graphs
FREE ARTICLEE Ben-Naim1 and P L Krapivsky2
Show affiliationsLETTER TO THE EDITOR
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, Uk 
(4k)−1 for k 
1. As a result, the total number of unicyclic components grows logarithmically with the system size.
- PACS
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
05.70.Fh Phase transitions: general studies
- MSC
- Subjects
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Soft matter, liquids and polymers
- Dates
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Issue 18 (7 May 2004)
Received 18 March 2004
Published 20 April 2004
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Unicyclic components in random graphs
E Ben-Naim and P L Krapivsky 2004 J. Phys. A: Math. Gen. 37 L189
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