labelled graph or weighted graph graph is said to be labelled if every edge in the graph is assigned some data in weighted graphthe edges of the graph are assigned some weight or length the weight of an edge denoted by (eis positive value which indicates the cost of traversing the edge figure (cshows weighted graph multiple edges distinct edges which connect the same end-points are called multiple edges that ise (uvand (uvare known as multiple edges of loop an edge that has identical end-points is called loop that ise (uumulti-graph graph with multiple edges and/or loops is called multi-graph figure (ashows multi-graph size of graph the size of graph is the total number of edges in it directed graphs directed graph galso known as digraphis graph in which every edge has direction assigned to it an edge of directed graph is given as an ordered pair (uvof nodes in for an edge (uv)the edge begins at and terminates at is known as the origin or initial point of correspondinglyv is known as the destination or terminal point of is the predecessor of correspondinglyv is the successor of nodes and are adjacent to each other terminology of directed graph out-degree of node the out-degree of node uwritten as outdeg( )is the number of edges that originate at in-degree of node terminate at the in-degree of node uwritten as indeg( )is the number of edges that degree of node the degree of nodewritten as deg( )is equal to the sum of in-degree and out-degree of that node thereforedeg(uindeg(uoutdeg(uisolated vertex vertex with degree zero such vertex is not an end-point of any edge pendant vertex (also known as leaf vertexa vertex with degree one cut vertex vertex which when deleted would disconnect the remaining graph source node is known as source if it has positive out-degree but zero in-degree sink node is known as sink if it has positive in-degree but zero out-degree reachability node is said to be reachable from node uif and only if there exists (directedpath from node to node for exampleif you consider the directed graph given in fig ( )you will observe that node is reachable from node strongly connected directed graph digraph is said to be strongly connected if and only if there exists path between every pair of nodes in that isif there is path from node to vthen there must be path from node to unilaterally connected graph digraph is said to be unilaterally connected if there exists path between any pair of nodes uv in such that there is path from to or path from to ubut not both