graphs tasks necessary to complete project in the graphnodes may represent taskswhile directed edges (with an arrow at one endindicate which task must be completed before another in both casesthe shape of the graph arises from the specific realworld situation before going furtherwe must mention thatwhen discussing graphsnodes are traditionally called vertices (the singular is vertexthis is probably because the nomenclature for graphs is older than that for treeshaving arisen in mathematics centuries ago trees are more closely associated with computer science howeverboth terms are used more or less interchangeably definitions figure shows simplified map of the freeways in the vicinity of san josecalifornia figure shows graph that models these freeways in the graphcircles represent freeway interchangesand straight lines connecting the circles represent freeway segments the circles are verticesand the lines are edges the vertices are usually labeled in some way--oftenas shown herewith letters of the alphabet each edge is bounded by the two vertices at its ends the graph doesn' attempt to reflect the geographical positions shown on the mapit shows only the relationships of the vertices and the edges--that iswhich edges are connected to which vertex it doesn' concern itself with physical distances or directions alsoone edge may represent several different route numbersas in the case of the edge from to hwhich involves routes and it' the connectedness (or lack of itof one intersection to another that' importantnot the actual routes adjacency two vertices are said to be adjacent to one another if they are connected by single edge thusin figure vertices and are adjacentbut vertices and are not the vertices adjacent to given vertex are sometimes said to be its neighbors for examplethe neighbors of are ihand paths path is sequence of edges figure shows path from vertex to vertex that passes through vertices and we can call this path baej there can be more than one path between two verticesanother path from to is bcdj connected graphs graph is said to be connected if there is at least one path from every vertex to every other vertexas in the graph in figure howeverif "you can' get there from here(as vermont farmers traditionally tell city slickers who stop to ask for directions)the graph is not connectedas in figure