Applications
In a real network like the World Wide Web, a short average path length facilitates the quick transfer of information and reduces costs. The efficiency of mass transfer in a metabolic network can be judged by studying its average path length. A power grid network will have less losses if its average path length is minimized.
Most real networks have a very short average path length leading to the concept of a small world where everyone is connected to everyone else through a very short path.
As a result, most models of real networks are created with this condition in mind. One of the first models which tried to explain real networks was the random network model. It was later followed by the Watts and Strogatz model, and even later there were the scale-free networks starting with the BA model. All these models had one thing in common: they all predicted very short average path length. The average path lengths of some networks are listed in Table..
The average path length depends on the system size but does not change drastically with it. Small world network theory predicts that the average path length changes proportionally to log n, where n is the number of nodes in the network.
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