replace ( insertvertexinsert edgeremoveedgeo( removevertex (mdetails for selected methods of the graph adt are as followsmethods vertices(and edges(are implemented by calling iterator(and iterator()respectively methods incidentedges and areadjacent all take (mtimesince to determine which edges are incident upon vertex we must inspect all edges since the collections and are lists implemented with doubly linked listwe can insert verticesand insert and remove edgesin ( time the update method removevertex(vtakes (mtimesince it requires that we inspect all the edges to find and remove those incident upon thusthe edge list representation is simple but has significant limitations the adjacency list structure the adjacency list structure for graph adds extra information to the edge list structure that supports direct access to the incident edges (and thus to the adjacent verticesof each vertex this approach allows us to use the adjacency list structure to implement several methods of the graph adt much faster than what is possible with the edge list structureeven though both of these two representations use an amount of space proportional to the number of vertices and edges in the graph the adjacency list structure includes all the structural components of the edge list structure plus the followinga vertex object holds reference to collection ( )called the incidence collection of vwhose elements store references to the edges incident on