7 - The Small-World Spectrum: Using Small Worlds to Compare Networks

Summary

Some people appear to learn more slowly. Could they just be learning different things? Suppose two groups of children are learning words – they have growing vocabularies – but one group acquires the list more slowly than the other. Can we use the structure of the information they learn to gain insight into whether or not they are learning different information? Small worlds are one way of measuring the structure of a community. When quantitatively defined, small worlds have a number of useful properties, including that they compare the structure of a network relative to different versions of itself, thereby providing a kind of ‘control’ network against which to benchmark a measurement. In this chapter, I discuss small worlds and several ways to evaluate them, and then use them to answer a simple question: Are children who learn to talk late just slow versions of early talkers? Or are they learning something different about the world? Along the way, I will enumerate three different approaches to explaining where structure comes from: function, formation, and emulation.