Transitive closure of a Graph

Data StructureGraph AlgorithmsAlgorithms

Transitive Closure it the reachability matrix to reach from vertex u to vertex v of a graph. One graph is given, we have to find a vertex v which is reachable from another vertex u, for all vertex pairs (u, v).


The final matrix is the Boolean type. When there is a value 1 for vertex u to vertex v, it means that there is at least one path from u to v.

Input and Output

Input:
1 1 0 1
0 1 1 0
0 0 1 1
0 0 0 1

Output:
The matrix of transitive closure
1 1 1 1
0 1 1 1
0 0 1 1
0 0 0 1

Algorithm

transColsure(graph)

Input: The given graph.
Output: Transitive Closure matrix.

Begin
   copy the adjacency matrix into another matrix named transMat
   for any vertex k in the graph, do
      for each vertex i in the graph, do
         for each vertex j in the graph, do
            transMat[i, j] := transMat[i, j] OR (transMat[i, k]) AND transMat[k, j])
         done
      done
   done
   Display the transMat
End

<2>Example

#include<iostream>
#include<vector>
#define NODE 4
using namespace std;

/* int graph[NODE][NODE] = {
   {0, 1, 1, 0},
   {0, 0, 1, 0},
   {1, 0, 0, 1},
   {0, 0, 0, 0}
}; */

int graph[NODE][NODE] = {
   {1, 1, 0, 1},
   {0, 1, 1, 0},
   {0, 0, 1, 1},
   {0, 0, 0, 1}
};

int result[NODE][NODE];

void transClosure() {
   for(int i = 0; i<NODE; i++)
      for(int j = 0; j<NODE; j++)
         result[i][j] = graph[i][j];    //initially copy the graph to the result matrix
   for(int k = 0; k<NODE; k++)
      for(int i = 0; i<NODE; i++)
         for(int j = 0; j<NODE; j++)
            result[i][j] = result[i][j] || (result[i][k] && result[k][j]);
   for(int i = 0; i<NODE; i++) {          //print the result matrix
      for(int j = 0; j<NODE; j++)
         cout << result[i][j] << " ";
      cout << endl;
   }
}

int main() {
   transClosure();
}

Output

1 1 1 1
0 1 1 1
0 0 1 1
0 0 0 1
raja
Published on 10-Jul-2018 13:24:03
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