Depth First Search :

Depth first works by selection one vertex V of G as a start vertex; V is marked visited. Then each unvisited vertex adjacent to V is serached in trun using depth first serach recursively.This process continues until a dead end (i.e)a vertex with no adjacent unvisited vertices is encountered.At a deadend the algorithm backsup one edge to the vertex it came from and tries to continue visiting unvisited vertices from there.

Advantages:

 1.To check whether the undirected graph is connected or not.

 2.To check whether the connected undirection graph is biconnected or not.]

 3.To check the a Acyclicity of the directed graph.

Algorithm Steps:

Step 1: Choose any node in the graph . Designate it as the search node and mark    it as vivited.

Step 2: Using the adjacency matrix of the graph, find a node adjacent to the search node that has not been visited yet. Designate this as the new search node and mark it as visited.

Step 3: Repeat step 2 using t he new search node. If no nodes satisfying(2)  can be found, return to the previous search node and continue from there.

Step 4: When a return to the previous search in(3) is impossible,the serach from the originally choosen search node is complete.

Step 5: If the graph still contains unvisited nodes,choose any node that has  not been visited and repeat step(1) through(4).