Small world networks are characterized by a network where the the path length to any other node is short (as in random graph) and nearby nodes are likely to be connected (as in a network where nodes are only connected to nearest neighbors).In his Nature paper, Watts demonstrates that social networks, the US power grid and the nervous system of C. Elegans are examples of small world networks. Small world networks have simple properties but tremendously complex emergent properties. Get the paper here
Watts also published a full-length book on the topic. It is extremely interesting and can be enjoyed by people of all backgrounds. Get it at Amazon here
How do small world networks relate to neuroscience? Look at the poster directly to the left of Nancy's office door. Get the full paper on epilepsy in small world networks here
Contributed by Tilman