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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 …
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 …
3
votes
Accepted
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 …