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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.

2 votes

What are some useful invariants for distinguishing between random graph models?

It really depends on your applications/goals, and the graphs you consider. Do you want to compare graph sequences or graphs of a fixed size? First let's consider sequences. The problem with propert …
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1 vote

Zero-one law in binomial random graph model $G(n,p)$

I'm not an expert on that specific question, and it's certainly the most difficult regime of $\mathcal{G}(n,p)$ to understand, so I'll just show the path. First, the question can be generalized as $p …
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3 votes
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first order languages over graphs (and other discrete models)

To complement J.-E. Pin's answer, many other structures have been considered in the literature, like words [1], discrete metric spaces [2], maps [3] or simplicial complexes [4]. In [5] the relations b …
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