In the 2002 January/February issue of Society, Judith Kleinfeld published an interesting article titled "THE SMALL WORLD PROBLEM." Kleinfeld's article is an excellent review and critique of the small-world problem--the idea that, in very large social networks everyone is connected to everyone else in the world by 6 or fewer links. The reason: networks are not random; instead, they contain weak-ties sufficient to link up everyone.
More important, Kleinfeld's article demonstrates the importance of sociology to complexity science. While physics can be used to study society, it needs sociology. Social systems are not physical systems--for the record, Watts agrees with this point (See Watts 2004).
For example, while a poor, female living in Mexico may be separated by less than six-degrees from a rich male living in Germany, it is very unlikely this poor female can make use of her links the same way someone of a higher socioeconomic status could. Sociology (and social network analysis, specifically, along with the study of kinship networks and health) has a lot to say about the quality of the connections in large social networks--above and beyond such terms as weak and strong ties, triangles, centroids, clusters, etc.
A whole language (all of it sociological, and much of it within social network analysis) awaits to be intersected with the new science of networks. This language includes community health, inequality, social stratification, medical sociology, gender, occupations, etc.
To learn more about the sociological approach to the new science of networks, see Barry Wellman's website and the INTERNATIONAL NETWORK FOR SOCIAL NETWORK ANALYSIS, See also Kleinfeld's COULD IT BE A BIG WORLD?