We typically represent the vertex-edge relationship of a graph in two ways: an adjacency list or an adjacency matrix.

An adjacency matrix is a table. Across the top, every vertex in the graph appears as a column. Down the side, every vertex appears again as a row. Edges can be bi-directional, so each vertex is listed twice.

To find an edge between B and P, we would look for the B row and then trace across to the P column. The contents of this cell represent a possible edge.

Our diagram uses 1 to mark an edge, 0 for the absence of an edge. In a weighted graph, the cell contains the cost of that edge.

In an adjacency list, each vertex contains a list of the vertices where an edge exists. To find an edge, one looks through the list for the desired vertex.