given start vertex of gcomputingfor every vertex of , path with the minimum number of edges between and vor reporting that no such path exists computing cycle in gor reporting that has no cycles directed graphs in this sectionwe consider issues that are specific to directed graphs recall that directed graph (digraph)is graph whose edges are all directed methods dealing with directed edges when we allow for some or all the edges in graph to be directedwe should add the following two methods to the graph adt in order to deal with edge directions isdirected( )test whether edge is directed insertdirectededge(vwo)insert and return new directed edge with origin and destination and storing element alsoif an edge is directedthe method endvertices(eshould return an array such that [ is the origin of and [ is the destination of the running time for the method isdirected(eshould be ( )and the running time of the method insertdirectededge(vwoshould match that of undirected edge insertion reachability one of the most fundamental issues with directed graphs is the notion of reachabilitywhich deals with determining where we can get to in directed graph traversal in directed graph always goes along directed pathsthat ispaths where all the edges are traversed according to their respective directions given vertices and of digraph we say that reaches (and is reachable from uif has directed path from to we also say that vertex reaches an edge ( ,zif reaches the origin vertex of the edge digraph is strongly connected if for any two vertices and of and reaches directed cycle of reaches is cycle where all the edges are may have cycle traversed according to their respective directions (note that consisting of two edges with opposite direction between the same pair of vertices