A Sidorenko graph is a finite graph 
satisfying
 |
for every nonempty finite simple graph 
,
where 
is the graph homomorphism density, 
is the set
of edges of 
, and 
is the complete graph
on two vertices (Zhao 2023). Every Sidorenko graph
is bipartite. Indeed, a nonbipartite graph
has no graph homomorphism into 
, so its density there is zero while 
. Trees, even cycle
graphs, complete bipartite graphs,
and hypercube graphs are Sidorenko graphs (Conlon
and Lee 2021). Sidorenko's conjecture asserts
that every bipartite graph is a Sidorenko graph.
