Transpose of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G. That is, if G contains an edge (u, v) then the converse/transpose/reverse of G contains an edge (v, u) and vice versa.
Given a graph (represented as adjacency list), we need to find another graph which is the transpose of the given graph.
Example:
Transpose Graph
Input : figure (i) is the input graph. Output : figure (ii) is the transpose graph of the given graph.
We traverse the adjacency list and as we find a vertex v in the adjacency list of vertex u which indicates an edge from u to v in main graph, we just add an edge from v to u in the transpose graph i.e. add u in the adjacency list of vertex v of the new graph. Thus traversing lists of all vertices of main graph we can get the transpose graph. Thus the total time complexity of the algorithm is O(V+E) where V is number of vertices of graph and E is the number of edges of the graph.
Note : It is simple to get the transpose of a graph which is stored in adjacency matrix format, you just need to get the transpose of that matrix.
C++
// CPP program to find transpose of a graph. #include <bits/stdc++.h> using namespace std; // function to add an edge from vertex source to vertex dest void addEdge(vector<int> adj[], int src, int dest) { adj[src].push_back(dest); } // function to print adjacency list of a graph void displayGraph(vector<int> adj[], int v) { for (int i = 0; i < v; i++) { cout << i << "--> "; for (int j = 0; j < adj[i].size(); j++) cout << adj[i][j] << " "; cout << "
"; } } // function to get Transpose of a graph taking adjacency // list of given graph and that of Transpose graph void transposeGraph(vector<int> adj[], vector<int> transpose[], int v) { // traverse the adjacency list of given graph and // for each edge (u, v) add an edge (v, u) in the // transpose graph's adjacency list for (int i = 0; i < v; i++) for (int j = 0; j < adj[i].size(); j++) addEdge(transpose, adj[i][j], i); } int main() { int v = 5; vector<int> adj[v]; addEdge(adj, 0, 1); addEdge(adj, 0, 4); addEdge(adj, 0, 3); addEdge(adj, 2, 0); addEdge(adj, 3, 2); addEdge(adj, 4, 1); addEdge(adj, 4, 3); // Finding transpose of graph represented // by adjacency list adj[] vector<int> transpose[v]; transposeGraph(adj, transpose, v); // displaying adjacency list of transpose // graph i.e. b displayGraph(transpose, v); return 0; } |
Python3
# Python3 program to find transpose of a graph.
# function to add an edge from vertex
# source to vertex dest
def addEdge(adj, src, dest):
adj[src].append(dest)
# function to pradjacency list
# of a graph
def displayGraph(adj, v):
for i in range(v):
print(i, “–> “, end = “”)
for j in range(len(adj[i])):
print(adj[i][j], end = ” “)
print()
# function to get Transpose of a graph
# taking adjacency list of given graph
# and that of Transpose graph
def transposeGraph(adj, transpose, v):
# traverse the adjacency list of given
# graph and for each edge (u, v) add
# an edge (v, u) in the transpose graph’s
# adjacency list
for i in range(v):
for j in range(len(adj[i])):
addEdge(transpose, adj[i][j], i)
# Driver Code
if __name__ == ‘__main__’:
v = 5
adj = [[] for i in range(v)]
addEdge(adj, 0, 1)
addEdge(adj, 0, 4)
addEdge(adj, 0, 3)
addEdge(adj, 2, 0)
addEdge(adj, 3, 2)
addEdge(adj, 4, 1)
addEdge(adj, 4, 3)
# Finding transpose of graph represented
# by adjacency list adj[]
transpose = [[]for i in range(v)]
transposeGraph(adj, transpose, v)
# displaying adjacency list of
# transpose graph i.e. b
displayGraph(transpose, v)
# This code is contributed by PranchalK
0--> 2 1--> 0 4 2--> 3 3--> 0 4 4--> 0
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