An undirected graph need not explicitly store two separate directed edges to represent a single undirected edge. An alternative would be to store only a single undirected edge (I, J) to connect...

An undirected graph need not explicitly store two separate directed edges to represent a single undirected edge. An alternative would be to store only a single undirected edge (I, J) to connect Vertices I and J. However, what if the user asks for edge (J, I)? We can solve this problem by consistently storing the edge such that the lesser of I and J always comes first. Thus, if we have an edge connecting Vertices 5 and 3, requests for edge (5, 3) and (3, 5) both map to (3, 5) because 3 <> Looking at the adacency matrix, we notice that only the lower triangle of the array is used. Thus we could cut the space required by the adjacency matrix from |V| 2 positions to |V|(|V|−1)/2 positions. Read Section 12.2 on triangular matrices. The reimplement the adjacency matrix  representation of Figure 11.6 to implement undirected graphs using a triangular array.