The graph homomorphism density of a finite simple graph 
in a finite simple graph 
with at least one graph vertex is
 |
where 
counts all graph homomorphisms from 
to 
.
It is the probability that a uniformly
chosen function from 
to 
takes every graph edge of
to a graph edge of 
. The function may identify
vertices that are not adjacent.
For the complete graph 
, 
.
This normalization is used in Sidorenko's conjecture.
