Java Program to Generate a Graph for a Given Fixed Degree Sequence

This is a java program to generate a graph from given degree sequence. The degree sequence of an undirected graph is the non-increasing sequence of its vertex degrees.The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. A sequence which is the degree sequence of some graph, i.e. for which the degree sequence problem has a solution, is called a graphic or graphical sequence. As a consequence of the degree sum formula, any sequence with an odd sum, such as (3, 3, 1), cannot be realized as the degree sequence of a graph. The converse is also true: if a sequence has an even sum, it is the degree sequence of a multigraph. The construction of such a graph is straightforward: connect vertices with odd degrees in pairs by a matching, and fill out the remaining even degree counts by self-loops.

Here is the source code of the Java Program to Generate a Graph for a Given Fixed Degree Sequence. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

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package com.hinguapps.combinatorial;
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import java.util.ArrayList;
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import java.util.List;
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import java.util.Scanner;
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public class GraphUsingDegreeSequence
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{
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    Integer[][] adjecencyMatrix;
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    List<Integer> degreeSequence;
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    private void addEdges(Integer v, Integer e)

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    {
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        for (int i = 0; i < adjecencyMatrix.length && e > 0; i++)

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        {
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            if (degreeSequence.get(i) != 0)

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            {
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                adjecencyMatrix[v][i] = adjecencyMatrix[i][v] = 1;

                Integer val = degreeSequence.get(i);

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                if (val > 0)
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                    degreeSequence.set(i, val - 1);

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                e--;
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            }
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        }
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    }
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    public void generateGraph()
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    {
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        adjecencyMatrix = new Integer[degreeSequence.size()][degreeSequence

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                .size()];
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        for (int i = 0; i < adjecencyMatrix.length; i++)

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        {
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            for (int j = 0; j < adjecencyMatrix.length; j++)

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            {
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                adjecencyMatrix[i][j] = 0;

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            }
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        }
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        for (int i = 0; i < degreeSequence.size(); i++)

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        {
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            Integer e = degreeSequence.get(i);

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            degreeSequence.set(i, 0);
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            addEdges(i, e);
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        }
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    }
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    public void printGraph()
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    {
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        System.out.println("The matrix form of graph: ");

        for (int i = 0; i < adjecencyMatrix.length; i++)

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        {
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            for (int j = 0; j < adjecencyMatrix.length; j++)

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            {
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                System.out.print(adjecencyMatrix[i][j] + " ");

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            }
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            System.out.println();
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        }
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    }
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    public static void main(String[] args)

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    {
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        Scanner sc = new Scanner(System.in);

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

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        Integer n = sc.nextInt();
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        System.out
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                .println("Enter the Degree Sequence: <Degree sequence is always in non-increasing order>");

        GraphUsingDegreeSequence gds = new GraphUsingDegreeSequence();

        gds.degreeSequence = new ArrayList<Integer>();

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        while (n > 0)
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        {
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            gds.degreeSequence.add(sc.nextInt());

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            n--;
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        }
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        System.out.println("Entered degree sequence: "

                + gds.degreeSequence.toString());

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        gds.generateGraph();
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        gds.printGraph();
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        sc.close();
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    }
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}
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Output:

$ javac GraphUsingDegreeSequence.java
$ java GraphUsingDegreeSequence
 
Enter the number of vertices: 
7
Enter the Degree Sequence: <Degree sequence is always in non-increasing order>
5 3 3 2 2 1 0
Entered degree sequence: [5, 3, 3, 2, 2, 1, 0]
The matrix form of graph: 
0 1 1 1 1 1 0 
1 0 1 1 0 0 0 
1 1 0 0 1 0 0 
1 1 0 0 0 0 0 
1 0 1 0 0 0 0 
1 0 0 0 0 0 0 
0 0 0 0 0 0 0

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