You could think of a graph with a number of big clumps of complete graph, then the clumps are connected by long chains. Most vertices will be in a clump, but the average distance will be dominated by the long distance between the clumps.
You could think of a graph with a number of big clumps of complete graph, then the clumps are connected by long chains. Most vertices will be in a clump, but the average distance will be dominated by the long distance between the clumps.