fully random graph

[[concept]]

Fully Random Graph

Fully random graphs are a way to sample a graph from a graphon. Like a weighted graph (sample), the nodes are sampled uniformly from the unit interval ( $u_{i} \sim U [0, 1]$ ).

The edges are sampled as

[A_{n}]_{i j} = [A_{n}]_{j i} \sim Bernoulli (W (u_{i}, u_{j}))

So the resulting graph is undirected and unweighted .

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fully random graphs converge to the graphon in probability
ways to sample graphs from graphons
2025-03-26 lecture 15

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