  Many real world networks (graphs) are observed to be 'small worlds', i.e.,
the average path length among nodes is small. On the other hand, it is somewhat
unclear what other average path length values networks can produce. In
particular, it is not known what the maximum and the minimum average path
length values are. In this paper we provide a lower estimation for the shortest
average path length (l) values in connected networks, and the largest possible
average path length values in networks with given size and density. To the
latter end, we construct a special family of graphs and calculate their average
path lengths. We also demonstrate the correctness of our estimation by
simulations.
