edges to the vertices they are incident upon this allows us to define simple algorithms for methods endvertices(eand opposite(veperformance of the edge list structure one method that is inefficient for the edge list structurehoweveris that of accessing the edges that are incident upon vertex determining this set of vertices requires an exhaustive inspection of all the edge objects in the collection that isin order to determine which edges are incident to vertex vwe must examine all the edges in the edge list and checkfor each oneif it happens to be incident to thusmethod incidentedges(vruns in time proportional to the number of edges in the graphnot in time proportional to the degree of vertex in facteven to check if two vertices and are adjacent by the areadjacent( ,wmethodrequires that we search the entire edge collection looking for an edge with end vertices and moreoversince removing vertex involves removing all of its incident edgesmethod removevertex also requires complete search of the edge collection table summarizes the performance of the edge list structure implementation of graph under the assumption that collections and are realized with doubly linked lists (section table running times of the methods of graph implemented with the edge list structure the space used is ( )where is the number of vertices and is the number of edges operation time vertices (nedges (mendverticesopposite ( incidentedgesareadjacent