Edge Exchangeable Graphs: Connectedness, Gaussianity and Completeness
Edward Eriksson
TL;DR
This paper investigates the asymptotic properties of edge exchangeable random graphs, providing conditions for connectedness, normality of vertex count, and completeness.
Contribution
It offers new theoretical characterizations of key properties of edge exchangeable graphs based on their generating measures.
Findings
Necessary and sufficient condition for eventual forever connectedness.
Sufficient condition for asymptotic normality of vertex count.
Necessary and sufficient condition for the graph to be eventually forever almost complete.
Abstract
We characterize some asymptotic properties of edge exchangeable random graphs in terms of the measure used to generate them. In particular, we give a necessary and sufficient condition for eventual forever connectedness, a sufficient condition for asymptotic normality of the vertex count, and a necessary and sufficient condition for the produced graph to be eventually forever almost complete.
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