This is simple attempt to show Directed, Undirected, weighted, Unweighted graph Representation in Adjacency list, matrix. This can be helpful to understand how graph are represented or stored. The 2D adjacency matrix can be stored in 2D array and the adjacency list can be stored in linked list. A large value such as infinity may also mean there is no edge between two vertices. Graph representation in incidence matrix and list is not shown here.
For reference check out 10th chapter of DISCRETE MATHEMATICS AND ITS APPLICATIONS by Kenneth H. Rosen.