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arXiv · 2601.16013

Infinite random graphs

Ziemowit Kostana·Jarosław Swaczyna·Agnieszka Widz
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Abstract

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of points are all equal. We give examples of such generalized random graphs, and show that the class of graphs under consideration has a two-element basis.

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Ziemowit Kostana, Jarosław Swaczyna, Agnieszka Widz. 2026-01-22. Infinite random graphs. https://arxiv.org/abs/2601.16013

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