Difference between Tree edge and Back edge in graph
Last Updated :
13 Jan, 2021
Tree Edge: It is an edge that is present in the tree obtained after performing DFS on the graph. All the Green edges are tree edges as shown in the below image.
Back Edge: It is an edge (u, v) such that v is an ancestor of node u but not part of the DFS Traversal of the tree. Edge from 5 to 4 is a back edge. The presence of a back edge indicates a cycle in a directed graph.
Consider an undirected graph is given below, the DFS of the below graph is 3 1 2 4 6 5. In the below diagram, if the DFS is applied to this graph, a tree is obtained which is connected using green edges.
Tabular between the back Edge and tree Edge:
S.N. |
Tree Edge |
Back Edge |
1 |
It connects the node to its descendants. |
It connects the node to its ancestors. |
2 |
It is the path traversed during DFS. |
It is the path not visited during DFS. |
3 |
They can form bridges. |
They can never form bridges. |
4 |
If it is disconnected, the number of connected components may increase. |
Even if it is disconnected, the number of connected components remains the same. |
5 |
It never creates a cycle. |
It can create a cycle. |
Share your thoughts in the comments
Please Login to comment...