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Expected subgraph count in the Erdős-Rényi model

If a fixed graph

H

has

v

vertices,

e

edges, and

N_{H} (n)

unlabelled copies in

K_{n}

, then the number

X_{H}

of its copies in

G (n, p)

satisfies

E X_{H} = N_{H} (n) p^{e} .

This follows by writing

X_{H}

as a sum of indicator random variables.

Table of contents 131 2
- Sparse clique-count concentration Expected subgraph count in the Erdős-Rényi model 48
- Vertex-disjoint sparse clique copies Expected subgraph count in the Erdős-Rényi model 43

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