Geodesic
A note on the component structure in random intersection graphs with tunable clustering
The electronic journal of combinatorics, Tome 15 (2008)

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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.
DOI : 10.37236/885
Classification : 05C80
Mots-clés : component structure, random intersection graphs, tunable clustering, phase transition, largest component, logarithmic order 
Andreas N. Lagerås; Mathias Lindholm. A note on the component structure in random intersection graphs with tunable clustering. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/885
@article{10_37236_885,
     author = {Andreas N. Lager\r{a}s and Mathias Lindholm},
     title = {A note on the component structure in random intersection graphs with tunable clustering},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/885},
     zbl = {1160.05335},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/885/}
}
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