The diameter of a graph is the longest distance you can find between two vertices.
When you are measuring distances to determine a graph's diameter, recall that if 2 vertices have many paths of different distances connecting them, you can only count the shortest one.
An interesting problem in graph theory is to draw graphs in which both the degrees of the vertices and the diameter of the graph are small. Drawing the largest graphs possible that meet these criteria is an open problem. (See Three For the Money.)
