performance of the edge list structure the performance of an edge list structure in fulfilling the graph adt is summarized in table we begin by discussing the space usagewhich is ( mfor representing graph with vertices and edges each individual vertex or edge instance uses ( spaceand the additional lists and use space proportional to their number of entries in terms of running timethe edge list structure does as well as one could hope in terms of reporting the number of vertices or edgesor in producing an iteration of those vertices or edges by querying the respective list or ethe vertex count and edge count methods run in ( timeand by iterating through the appropriate listthe methods vertices and edges run respectively in (nand (mtime the most significant limitations of an edge list structureespecially when compared to the other graph representationsare the (mrunning times of methods get edge( , )degree( )and incident edges(vthe problem is that with all edges of the graph in an unordered list ethe only way to answer those queries is through an exhaustive inspection of all edges the other data structures introduced in this section will implement these methods more efficiently finallywe consider the methods that update the graph it is easy to add new vertex or new edge to the graph in ( time for examplea new edge can be added to the graph by creating an edge instance storing the given element as dataadding that instance to the positional list eand recording its resulting position within as an attribute of the edge that stored position can later be used to locate and remove this edge from in ( timeand thus implement the method remove edge(eit is worth discussing why the remove vertex(vmethod has running time of (mas stated in the graph adtwhen vertex is removed from the graphall edges incident to must also be removed (otherwisewe would have contradiction of edges that refer to vertices that are not part of the graphto locate the incident edges to the vertexwe must examine all edges of operation vertex count)edge countverticesedgesget edge( , )degree( )incident edges(vinsert vertex( )insert edge( , , )remove edge(eremove vertex(vrunning time ( (no(mo(mo( (mtable 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