CLASSIFIACTION OF EDGES IN GRAPH 

EDGES OF A DIRECTED GRAPH CAN BE DIVIDE INTO FOUR GROUPS 

1.Tree Edge 

2.Back Edge 

3.Forward Edge 

4.Cross Edge                

TREE EDGE :

an edge included in the DFS spanning forest.

BACK EDGE :

an edge to a vertex to its spanning tree ancestor.  

FORWARD EDGE :

an edge from a vertex to a spanning tree non son descendant.

CROSS EDGE :

an edge between two vertices is a cross edge when there is no ancestor and descendant relationship between them in spanning forest.

code to identify the edges

static int time=0;

void DFS(int v)

{

int i;

time++;

d[v]=time;

state[v]=visited;

for(i=0;i<n;i++)

{

     if(adj[v][i]==1)

       {

          if(state[i]==initial)

              {

              cout<<"Tree Edge :"<<v<<" "<<i<<"\n";

              DFS(i);

               }

            else if(state[i]==visited)

               { 

                   cout<<"Back Edge :"<<v<<" "<<i<<"\n";    

                }

              else if(d[v]<d[i])

                  cout<<"Forward Edge :"<<v<<" "<<i<<"\n";

                else

                  cout<<"Cross Edge :"<<v" "<<i<<"\n";

              }

     }

state[v]=finished;

  f[v]=++time;

return ;

}