increase in space usagehoweverwhich is now ( )and in the running time of other methods for examplemethod incidentedges(vnow requires that we examine an entire row or column of array and thus runs in (ntime moreoverany vertex insertions or deletions now require creating whole new array aof larger or smaller sizerespectivelywhich takes ( time table summarizes the performance of the adjacency matrix structure implementation of graph from this tablewe observe that the adjacency list structure is superior to the adjacency matrix in spaceand is superior in time for all methods except for the areadjacent method table running times for graph implemented with an adjacency matrix operation time vertices (nedges (mendverticesoppositeareadjacent ( incidentedges(vo( deg( )replaceinsertedgeremoveedgeo( insert vertexremove vertex ( historicallyboolean adjacency matrices were the first representations used for graphs (so that [ijtrue if and only if (ijis an edgewe should not find this fact surprisinghoweverfor the adjacency matrix has natural appeal as mathematical structure (for examplean undirected graph has symmetric