The shortest distance in random multi-type intersection graphs

Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multi-type random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph. © 2010 Wiley Periodicals, Inc. DOI: https://doi.org/10.1002/rsa.20351 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-58144 Accepted Version Originally published at: Barbour, A D; Reinert, G (2011). The shortest distance in random multi-type intersection graphs. Random Structures Algorithms, 39(2):179-209. DOI: https://doi.org/10.1002/rsa.20351 ar X iv :1 00 1. 53 57 v1 [ m at h. PR ] 2 9 Ja n 20 10 The shortest distance in random multi-type intersection graphs A. D. Barbour∗ and G. Reinert† Universität Zürich and University of Oxford Abstract Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multitype random intersection graph have a defective distribution, which is well described by a mixture of translated and scaled Gumbel distributions, the missing mass corresponding to the event that the vertices are not in the same component of the graph.