Infinite random graphs
Ziemowit Kostana, Jaros{\l}aw Swaczyna, Agnieszka Widz

TL;DR
This paper investigates a class of infinite random graphs generated by probabilistic processes, extending classical models like the Rado graph, and establishes a foundational basis for these generalized structures.
Contribution
It introduces a broader class of infinite random graphs without uniform edge probabilities and proves they have a two-element basis, expanding understanding of such graph classes.
Findings
Existence of generalized infinite random graphs with non-uniform probabilities
These graphs form a class with a two-element basis
Examples illustrating the diversity of such graphs
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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Taxonomy
TopicsLimits and Structures in Graph Theory · Stochastic processes and statistical mechanics · advanced mathematical theories
