Adjacency lists are generally preferred because they efficiently represent sparse graphs. An adjacency matrix is preferred if the graph is dense, that is the number of edges |E | is close to the number of vertices squared, |V |<sup>2</sup>, or if one must be able to quickly look up if there is an edge connecting two vertices. | Adjacency lists are generally preferred because they efficiently represent sparse graphs. An adjacency matrix is preferred if the graph is dense, that is the number of edges |E | is close to the number of vertices squared, |V |<sup>2</sup>, or if one must be able to quickly look up if there is an edge connecting two vertices. |