In mathematics, the minimum rank is a graph parameter
The adjacency matrix of an undirected graph is a symmetric matrix whose rows and columns both correspond to the vertices of the graph.
More generally, a generalized adjacency matrix is any symmetric matrix of real numbers with the same pattern of nonzeros off the diagonal (the diagonal elements may be any real numbers).
is defined as the smallest rank of any generalized adjacency matrix of the graph; it is denoted by
Several families of graphs may be characterized in terms of their minimum ranks.