structure in ( time can also be implemented in ( time with the adjacency list structureusing essentially the same algorithms in additionbeing able to provide access between vertices and edges in both directions allows us to speed up the performance of number of the graph methods by using an adjacency list structure instead of an edge list structure table summarizes the performance of the adjacency list structure implementation of graphassuming that collections and and the incidence collections of the vertices are all implemented with doubly linked lists for vertex vthe space used by the incidence collection of is proportional to the degree of vthat isit is (deg( )thusby proposition the space requirement of the adjacency list structure is ( mtable running times of the methods of graph implemented with the adjacency list structure the space used is ( )where is the number of vertices and is the number of edges operation time vertices (nedges (mendverticesopposite ( incidentedges(vo(deg( )areadjacent( ,wo(min(deg( ),deg( )replace (