Incidence Matrix

Let G be a graph with V(G) = {1;⋯n} and E(G) = {e ₁;⋯e _m }: Suppose each edge of G is assigned an orientation, which is arbitrary but fixed. The (vertex-edge)incidence matrix of G, denoted by Q(G); is the n × m matrix defined as follows. The rows and the columns of Q(G) are indexed by V(G) and E(G), respectively. The (i; j)-entry of Q(G) is 0 if vertex i and edge e _j are not incident, and otherwise it is 1 or -1 according as e _j originates or terminates at i, respectively. We often denote Q(G) simply by Q. Whenever we mention Q(G) it is assumed that the edges of G are oriented.