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Expected subgraph count in the Erdős-Rényi model
ID: expected-subgraph-count-in-the-erdos-renyi-model
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Expected subgraph count in the Erdős-Rényi model
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
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
.
(1)
This follows by
writing
X
H
as
a
sum
of
indicator random variables
.
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