Bipartite four-cycle density
= Bipartite four-cycle density
{title2=$t_4(G)=\mathbb E_{x,x',y,y'}G(x,y)G(x,y')G(x',y)G(x',y')$}
This is the part-preserving <homomorphism density> of a four-cycle in a <bipartite graph> with independently uniform labels $x,x'$ in the first part and $y,y'$ in the second. Repeated labels are included. It equals the fourth power of the <four-cycle norm> of the adjacency <indicator function>. It differs at finite sizes from a count requiring four distinct <vertices>.