A note on the component structure in random intersection graphs with tunable clustering

Details A note on the component structure in random intersection graphs with tunable clustering A note on the component structure in random intersection graphs with tunable clustering

2007-09-10

arxiv.org/abs/0709.1416v2

The Electronic Journal of Combinatorics, Vol. 15(1), N10, 2008

Mathematics

Probability

8 pages, Published at http://www.combinatorics.org/Volume_15/PDF/v15i1n10.pdf by the Electronic Journal of Combinatorics (ht

Scientific paper

We study the component structure in random intersection graphs with tunable clustering, and show that the average degree works as a threshold for a phase transition for the size of the largest component. That is, if the expected degree is less than one, the size of the largest component is a.a.s. of logarithmic order, but if the average degree is greater than one, a.a.s. a single large component of linear order emerges, and the size of the second largest component is at most of logarithmic order.

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