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Generalized quasirandom graphs. (English) Zbl 1127.05094
Summary: We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph \(H\), then these graphs have a structure that is asymptotically the same as the structure of \(H\). Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of \(|V(H)|\).

MSC:
05C80 Random graphs (graph-theoretic aspects)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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