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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.

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