A Practical Introduction to Data Structures and Algorithm Analysis

392 Chap. 11 Graphs0 1 2 3 40201 111421311341(a)(b)01234134214(c)Figure 11.3 Two graph representations. (a) A directed graph. (b) The adjacencymatrix for the graph of (a). (c) The adjacency list for the graph of (a).Example 11.1 The entry for Vertex 0 in Figure 11.3(c) stores 1 and 4because there are two edges in the graph leaving Vertex 0, with one goingto Vertex 1 and one going to Vertex 4. The list for Vertex 2 stores an entryfor Vertex 4 because there is an edge from Vertex 2 to Vertex 4, but no entryfor Vertex 3 because this edge comes into Vertex 2 rather than going out.The storage requirements for the adjacency list depend on both the number ofedges and the number of vertices in the graph. There must be an array entry foreach vertex (even if the vertex is not adjacent to any other vertex and thus has noelements on its linked list), and each edge must appear on one of the lists. Thus,the cost is Θ(|V| + |E|).Both the adjacency matrix and the adjacency list can be used to store directedor undirected graphs. Each edge of an undirected graph connecting Vertices Uand V is represented by two directed edges: one from U to V and one from V toU. Figure 11.4 illustrates the use of the adjacency matrix and the adjacency list forundirected graphs.