The graph homomorphism density of a finite simple graph 
in a nonempty finite simple
graph 
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.
