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arXiv · 2207.11471

Rank-k random graphs and finite type branching processes

Suman Chakraborty·Kjell Raaijmakers·Remco van der Hofstad
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Abstract

In this note, we investigate fundamental relations between exploration processes in random graphs, and branching processes. We formulate a class of models that we call {\em rank-$k$ random graphs}, and that are special in that their neighborhood explorations can be obtained by a {\em thinning} of multi-type branching processes. We show that any rank-2 random graph can be described in terms of thinning of a 2-type branching process, while for higher rank, it is not clear how many types are needed.

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Suman Chakraborty, Kjell Raaijmakers, Remco van der Hofstad. 2022-07-23. Rank-k random graphs and finite type branching processes. https://arxiv.org/abs/2207.11471

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