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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
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Erdős-Renyi graph restricted to largest connected component
Suppose we have an instance of Erdős-Renyi $G(n,p)$ graph with $p = d/n$. Thus the expected node degree is $d$ which we will fix, while letting $n \to \infty$. Then, there will be more than one connec …
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Behavior of eigenspaces of adjacency matrices of random graphs (not via perturbation theory)
For the sake of discussion, let us say that we have the adjacency matrix $A$ of a graph, on $n$ nodes, from a stochastic block model with 2 blocks. Another name for this (usually used in computer scie …