data structures using weakly connected digraph directed graph is said to be weakly connected if it is connected by ignoring the direction of edges that isin such graphit is possible to reach any node from any other node by traversing edges in any direction (may not be in the direction they pointthe nodes in weakly connected directed graph must have either out-degree or in-degree of at least parallel/multiple edges distinct edges which connect the same end-points are called multiple edges that ise (uvand (uvare known as multiple edges of in fig ( ) and are multiple edges connecting nodes and simple directed graph directed graph is said to be simple directed graph if and only if it has no parallel edges howevera simple directed graph may contain cycles with an exception that it cannot have more than one loop at given node the graph given in fig (ais directed graph in which there are four nodes and eight edges note that edges and are parallel ( (bsince they begin at and end at the edge is loop since it originates and terminates at the same node the sequence of nodesfigure (adirected acyclic abdand cdoes not form path because (dcis not an edge graph and (bstrongly although there is path from node to dthere is no way from to connected directed acyclic graph in the graphwe see that there is no path from node to any other node in gso the graph is not strongly connected howeverg is said (ato be unilaterally connected we also observe that node is sink since it has positive in-degree but zero out-degree transitive closure of directed graph transitive closure of graph is constructed to answer reachability figure (aa graph and its questions that isis there path from node to node in one or (btransitive closure more hopsa binary relation indicates only whether the node is gconnected to node bwhether node is connected to node cetc but once the transitive closure is constructed as shown in fig we can easily determine in ( time whether node is reachable from node or not like the adjacency listdiscussed in section transitive closure is also stored as matrix tso if [ ][ then node can be reached from node in one or more hops (bdefinition for directed graph ( , )where is the set of vertices and is the set of edgesthe transitive closure of is graph ( , *in *for every vertex pair vw in there is an edge (vwin eif and only if there is valid path from to in where and why is it neededfinding the transitive closure of directed graph is an important problem in the following computational taskstransitive closure is used to find the reachability analysis of transition networks representing distributed and parallel systems it is used in the construction of parsing automata in compiler construction recentlytransitive closure computation is being used to evaluate recursive database queries (because almost all practical recursive queries are transitive in nature