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.
