A simple graph I (V, E) consists of a nonempty finite set V of "vertices" (aka "nodes") and a finite set E of distinct unordered pairs of distinct elements of V called "edges". We say that an edge {v1, v2} joins the vertices v and v2. = If the vertices of G are labeled {1, 2,...,n}, we define the connection matrix Ar to be the n x n matrix whose i, j entry is 1 if is joined to j with an edge, and 0 if not. for 1