Formally, a graph is called forcing if every graphon W such that t(F, W) = t(K2, W)e(F) is constant.
[citation needed] The first forcing graph to be considered is the 4-cycle C4, as it bears a close relationship with other conditions of quasi-randomness.
It was shown in the same paper by Chung, Graham, and Wilson that every even cycle C2t and complete bipartite graphs of the form K2,t with t ≥ 2 are forcing.
[1] Conlon, Fox, and Sudakov expanded this last result to include all bipartite graphs with two vertices in one part that are complete to the other part[3] Forcing families provide a natural generalization of forcing graphs.
The other direction is yet to be proven, but no forcing graph that does not have both of these properties has been found.