Difference between Tree edge and Back edge in graph
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.|