In graph theory, a branch of mathematics, the rank of an undirected graph has two unrelated definitions. Let n equal the number of vertices of the graph. * In the matrix theory of graphs the rank r of an undirected graph is defined as the rank of its adjacency matrix.Analogously, the nullity of the graph is the nullity of its adjacency matrix, which equals n − r. * In the matroid theory of graphs the rank of an undirected graph is defined as the number n − c, where c is the number of connected components of the graph. Equivalently, the rank of a graph is the rank of the oriented incidence matrix associated with the graph.Analogously, the nullity of the graph is the nullity of its oriented incidence matrix, given by the formula m − n + c, where n and c are as above and m is the number of