This is a java program to represent graph as a incidence list. The incidence matrix of G is a n × m matrix (b_{ij}), where n and m are the numbers of vertices and edges respectively, such that b_{ij} = 1 if the vertex v_i and edge x_j are incident and 0 otherwise. If this relationship is represented by a list, list is known as incidence list.

Here is the source code of the Java Program to Represent Graph Using Incidence List. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to represent graph as a incidence list`

import java.util.HashMap;

import java.util.List;

import java.util.Map;

import java.util.LinkedList;

import java.util.Scanner;

public class Represent_Graph_Incidence_List

`{`

private Map<Integer, List<Integer>> incidenceList;

private int v;

public Represent_Graph_Incidence_List(int vertices)

`{`

v = vertices;

incidenceList = new HashMap<Integer, List<Integer>>();

for (int i = 1; i <= v; i++)

incidenceList.put(i, new LinkedList<Integer>());

`}`

public void setEdge(int to, int from, int edge_number)

`{`

List<Integer> slist = incidenceList.get(to);

slist.add(edge_number);

List<Integer> dlist = incidenceList.get(from);

dlist.add(edge_number);

`}`

public List<Integer> getEdge(int vertex)

`{`

return incidenceList.get(vertex);

`}`

public static void main(String args[])

`{`

int v, e, count = 1, to, from, edgeNumber;

Scanner sc = new Scanner(System.in);

`Represent_Graph_Incidence_List glist;`

`try`

`{`

System.out.println("Enter the number of vertices: ");

v = sc.nextInt();

System.out.println("Enter the number of edges: ");

e = sc.nextInt();

glist = new Represent_Graph_Incidence_List(v);

System.out

.println("Enter the edges in the graph : <edgenumber> <to> <from>");

while (count <= e)

`{`

edgeNumber = sc.nextInt();

to = sc.nextInt();

from = sc.nextInt();

glist.setEdge(to, from, edgeNumber);

`count++;`

`}`

System.out

.println("The Incidence List Representation of the graph is: ");

System.out.println("Vertex EdgeNumber");

for (int vertex = 1; vertex <= v; vertex++)

`{`

System.out.print(vertex + "\t:");

List<Integer> edgeList = glist.getEdge(vertex);

for (int j = 1;; j++)

`{`

if (j != edgeList.size())

System.out.print(edgeList.get(j - 1) + "\t");

`else`

`{`

System.out.print(edgeList.get(j - 1));

break;

`}`

`}`

System.out.println();

`}`

`}`

catch (Exception E)

`{`

System.out.println("Something went wrong");

`}`

sc.close();

`}`

`}`

Output:

$ javac Represent_Graph_Incidence_List.java $ java Represent_Graph_Incidence_List Enter the number of vertices: 5 Enter the number of edges: 5 Enter the edges in the graph : <edgenumber> <to> <from> 1 1 2 2 2 4 3 5 4 4 4 3 5 5 1 The Incidence List Representation of the graph is: Vertex EdgeNumber 1 :1 5 2 :1 2 3 :4 4 :2 3 4 5 :3 5

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