data structures using in state transition diagramsthe nodes are used to represent states and the edges represent legal moves from one state to the other graphs are also used to draw activity network diagrams these diagrams are extensively used as project management tool to represent the interdependent relationships between groupsstepsand tasks that have significant impact on the project an activity network diagram (andalso known as an arrow diagram or pert (program evaluation review techniqueis used to identify time sequences of events which are pivotal to objectives it is also helpful when project has multiple activities which need simultaneous management ands help the project development team to create realistic project schedule by drawing graphs that exhibitthe total amount of time needed to complete the project the sequence in which activities must be performed the activities that can be performed simultaneously the critical activities that must be monitored on regular basis sample and is shown in fig and may be performed simultaneously must be completed before start end-point of the project starting point of the project end must be completed before but after boxes denote activity arrows denote dependency among activities figure activity network diagram points to remember graph is basically collection of vertices (also called nodesand edges that connect these vertices degree of node is the total number of edges containing the node when the degree of node is zeroit is also called an isolated node path is known as closed path if the edge has the same end-points closed simple path with length or more is known as cycle graph in which there exists path between any two of its nodes is called connected graph an edge that has identical end-points is called loop the size of graph is the total number of edges in it the out-degree of node is the number of edges that originate at the in-degree of node is the number of edges that terminate at node is known as sink if it has positive in-degree but zero out-degree transitive closure of graph is constructed to answer reachability questions since an adjacency matrix contains only and sit is called bit matrix or boolean matrix the memory use of an adjacency matrix is ( )where is the number of nodes in the graph topological sort of directed acyclic graph is defined as linear ordering of its nodes in which each node comes before all the nodes to which it has outbound edges every dag has one or more number of topological sorts vertex of is called an articulation point if removing along with the edges incident to results in graph that has at least two connected components biconnected graph is defined as connected graph that has no articulation vertices