Appendix B: Social Network Analysis Results

 

The Getty network is a small world, which means that individuals can reach one another through a few steps. Small-world networks are characterized by measuring the clustering coefficient (CC) and the characteristic path length (CPL) and comparing these results to a random network. The CPL measures the number of nodes between any two nodes within a network, also known as “degrees of separation.” The CC measures how many of a node’s contacts are connected to one another. Most random networks have a short CPL, but the CC of random networks is low. Small worlds, however, have both short CPL and very high CC com pared to a random network. In our network, n, number of nodes, is 6,754; k, average degree, is 0.1605. The requirement stated by the hypothesis is, therefore, that Q(CPL) 1 and Q(CC) > 1, where Q is the ratio of the metrics between the studied network and random network (Uzzi et al., 2007). In our network, Q(CPL) = 1.21 and Q(CC) = 4.5. See Jerrold W. Grossman, “The Evolution of the Mathematical Research Collaboration Graph,” 2003, www.oakland.edu/~grossman/eddie.pdf; Stefan Bornholdt and Heinz Georg Schuster, eds., Handbook of Graphs and Networks (Weinheim, Germany: Wiley-VCH, 2003); Uzzi, Amaral, and Reed-Tsochas, “Small-World Networks and Management Science Research” Stanley Wasserman and Katherine Faust, Social Network Analysis (New York: Cambridge University Press, 1994); Watts and Strogatz, “Collective Dynamics of ‘Small-World’ Networks.”

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