In this chapter, we’ll work with data from an online social network, and use a Watts-Strogatz graph to model it. The WS model has characteristics of a small world network, like the data, but it has low variability in the number of neighbors from node to node, unlike the data.
This discrepancy is the motivation for a network model developed by Barabási and Albert. The BA model captures the observed variability in the number of neighbors, and it has one of the small world properties, short path lengths, but it does not have the high clustering of a small world network.
The chapter ends with a discussion of WS and BA graphs as explanatory models for small world networks.