Creating a Small World Graph

Replotting the Data

In the graph below, we've rearranged the data so that clustering coefficient is plotted directly against path length. As alpha increases, the graph measures move from the upper right to the lower left corner of the graph (1). As you can see even more clearly here, there is a set of data points for which the characteristic path length has already fallen near the level of a random graph, but the clustering coefficient is still high, comparable to a caveman graph.

¹ The hook-like feature of the graph is an artifact of the connection algorithm and has no real significance. Watts replots this graphs in terms of a more natural variable, phi, which we will briefly discuss later, and this feature dissappears. For a full discussion of this measure, please refer back to Watts's paper.

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