Podcast Ch 24 b Title Graphs and Digraphs

Podcast Ch 24 b • Title: Graphs and Digraphs • Description: The Graph Interface; the Digraph class; Program 24. 1 • Participants: Barry Kurtz (instructor); John Helfert and Tobie Williams (students) • Textbook: Data Structures for Java; William H. Ford and William R. Topp

Creating and Using Graphs

Creating and Using Graphs (continued)

Student Question For a graph with n vertices, what is the minimum and maximum number of edges? Minimum: ______ Maximum: ______ For n = 5 draw the graph with the maximum number of edges

The Di. Graph Class • The Di. Graph class implements the Graph interface and adds other methods that are useful in applications. – A constructor creates an empty graph. – The methods in. Degree() and out. Degree() are special methods that access a properties that are unique to a digraph. – The static method read. Graph() builds a graph whose vertices are strings.

The Di. Graph Class (cont) • Di. Graph method read. Graph() inputs the vertex values and the edges from a textfile. – File format: (Number Source 1 Source 2. . . Sourcen of Edges n) Destination 1 Weight 1 Destination 2 Weight 2 Destinationn Weightn

The Di. Graph Class (cont) • The method to. String() provides a representation of a graph. For each vertex, the string gives the list of adjacent vertices along with the weight for the corresponding edge. The information for each vertex also includes its in-degree and out-degree.

The Di. Graph Class (cont) File samplegraph. dat 5 // data for the vertices A B C D E 6 // data for the edges A B 3 A C 2 B C 6 C B 4 C D 1 E B 5 // input vertices, edges, and weights from sample // graph. dat Di. Graph g = Di. Graph. read. Graph("samplegraph. dat"); // display the graph System. out. println(g)

The Di. Graph Class (cont) Output: A: in-degree 0 Edges: B(3) B: in-degree 3 Edges: C(6) C: in-degree 2 Edges: B(4) D: in-degree 1 Edges: E: in-degree 0 Edges: B(5) out-degree 2 C(2) out-degree 1 out-degree 2 D(1) out-degree 0 out-degree 1

Student Question Di. Graph<String> g; System. out. println(g); Run: A: in-degree 1 Edges: C(7) B: in-degree 0 Edges: C(9) C: in-degree 3 Edges: D: in-degree 2 Edges: E(3) E: in-degree 1 Edges: A(2) out-degree 2 D(5) out-degree 2 D(1) out-degree 0 out-degree 1 out-degree 2 C(6) Draw this graph

Student Question (a) In the pictured graph, identify a cycle with 3 or more vertices. (b) A directed acyclic graph (DAG) is a directed graph with no cycles. In the pictured graph, identify an edge which can be deleted so that the resulting graph is a DAG.

Program 24. 1

Program 24. 1 (continued) import java. io. File. Not. Found. Exception; ds. util. Set; ds. util. Iterator; ds. util. Di. Graph; public class Program 24_1 { public static void main(String[] args) throws File. Not. Found. Exception { // construct graph with vertices of type // String by reading from the file // "graph. IO. dat" Di. Graph<String> g = Di. Graph. read. Graph("graph. IO. dat"); String vtx. Name; // sets for vertex. Set() and adjacent // vertices (neighbors) Set<String> vtx. Set, neighbor. Set;

Program 24. 1 (continued) // output number of vertices and edges System. out. println("Number of vertices: " + g. number. Of. Vertices()); System. out. println("Number of edges: " + g. number. Of. Edges()); // properties relative to vertex A System. out. println("in. Degree for A: " + g. in. Degree("A")); System. out. println("out. Degree for A: " + g. out. Degree("A")); System. out. println("Weight e(A, B): " + g. get. Weight("A", "B")); // delete edge with weight 2 g. remove. Edge("B", "A"); // delete vertex "E" and edges (E, C), // (C, E) and (D, E) g. remove. Vertex("E");

Program 24. 1 (continued) /* add and update attributes of the graph */ // increase weight from 4 to 8 g. set. Weight("A", "B", 8); // add vertex F g. add. Vertex("F"); // add edge (F, D) with weight 3 g. add. Edge("F", "D", 3); // after all updates, output the graph // and its properties System. out. println("After all the graph updates"); System. out. println(g); // get the vertices as a Set and // create set iterator vtx. Set = g. vertex. Set(); Iterator vtx. Iter = vtx. Set. iterator();

Program 24. 1 (concluded) // scan the vertices and display // the set of neighbors while(vtx. Iter. has. Next()) { vtx. Name = (String)vtx. Iter. next(); neighbor. Set = g. get. Neighbors(vtx. Name); System. out. println(" Neighbor set for " + "vertex " + vtx. Name + " is " + neighbor. Set); } } }

Number of vertices: 5 Number of edges: 8 in. Degree for A: 1 out. Degree for A: 3 Weight e(A, B): 4 After all the graph updates A: in-degree 0 out-degree 3 Edges: B(8) C(7) D(6) B: in-degree 2 out-degree 0 Edges: C: in-degree 1 out-degree 1 Edges: B(3) D: in-degree 2 out-degree 0 Edges: F: in-degree 0 out-degree 1 Edges: D(3) Neighbor set for vertex D is [] Neighbor set for vertex F is [D] Neighbor set for vertex A is [D, B, C] Neighbor set for vertex B is [] Neighbor set for vertex C is [B] Program 24. 1 (Run)

Di. Graph<String> g; g. add. Vertex("G"); g. add. Edge("F", "G", 1); g. add. Edge("G", "D", 2); g. set. Weight("E", "D", 5); g. remove. Edge("D", "E"); g. remove. Vertex("C"); Original Graph Student Question Updated Graph