algorithm the algorithm to find the transitive closure of graph is given in fig in order to determine the transitive closure of graphwe define matrix where tkij for ijk if there if (ij is not in when tij exists path in from the vertex to vertex with oo if (ijis intermediate vertices in the set ( kand tikj kv ( ki - kk - when > ij otherwise that isgis constructed by adding an edge (ijinto eif and only if tkij look at fig which shows the relation between and tkij figure relation between and ij transitive_closure(atnstep set = = = step repeat steps and while <= step repeat step while <= step if ( [ ][ set [ ][ else set [ ][jincrement [end of loopincrement [end of loopstep repeat steps to while <= step repeat steps to while <= step repeat steps and while <= step set [ ,jt[ ][jv ( [ ][kl [ ][ ]increment step [end of loopstep increment [end of loopstep increment [end of loopstep end figure algorithm to find the transitive enclosure of graph bi-connected components vertex of is called an articulation pointif removing along with the edges incident on vresults in graph that has at least two connected components bi-connected graph (shown in fig is defined as connected graph that has no articulation vertices that isa bi-connected graph is connected and non-separable in the sense that even if we remove any vertex from the graphthe resultant graph is still connected by definitiona (afigure (bnon bi-connected graph bi-connected undirected graph is connected graph that cannot be broken into disconnected pieces by deleting any single vertex in bi-connected directed graphfor any two vertices and wthere are two directed paths from to which have no vertices in common other than and note that the graph shown in fig (ais not bi-connected graphas deleting vertex from the graph results in two disconnected components of the original graph (fig ( )