Biadjacency matrix ($M_{xy}=1_{\{xy\in E\}}$)

For a bipartite graph with ordered parts $X,Y$, its biadjacency matrix has rows indexed by $X$ and columns indexed by $Y$, with entry one for an edge and zero otherwise. It has size $|X|$ by $|Y|$, rather than the square full bipartite adjacency matrix on $X\bigsqcup Y$, which is the block matrix $\left(\begin{array}{cc}0& M\\ M^{\mathsf{T}}& 0\end{array}\right)$. Its singular values describe the normalized adjacency operator of a bipartite graph after division by $\sqrt{|X||Y|}$.