Page - (000328) - in Knowledge and Networks

326 clustering coefficient) and a measure of average path length (labeled L).8 These measures are then compared to a random graph of the same size and density (an Erdos-Renyi random graph). Table 15.3 shows the basic measures in the Swedish case. In comparing the results in Table 15.3, we see that the Swedish local learning network is much more clustered than the random graph, but the path lengths are also longer. We can take this a step farther by estimating the small-world quotient (Q), which is given by Eq. [15.1]: Q cc cc L L Sweden Random Sweden random = / (15.1) A small world is usually defined as having a quotient greater than 1. In this case, the result is: 1172 158 744. / . .= . So by this standard, the learning network of Swedish municipalities is indeed a small world, though the path lengths are a little high. The higher path lengths might indicate there are fewer hubs in the Swedish network than in an ideal small world. Learning Hubs As noted above, hubs are important in small-world networks because their more cosmopolitan ties allow information to widely and rapidly diffuse. Amin and Cohendet (1999) claim that nonlocal networks are particularly crucial for path- breaking innovation, whereas local networking results in more incremental innova- tion. Thus, hubs are expected to fulfill a crucial role in the diffusion of innovations 8 The clustering coefficient (cc) is measured using the clustering coefficient algorithm in UCINET VI (there are various versions of cc; UCINET uses Watts’s version; see, Watts, 1999). The algo- rithm produces both a weighted and an unweighted coefficient. The unweighted coefficient was used here. (There is a discussion in the literature about the tradeoffs between the two. But it does not make too much difference in this case because the results are similar. The weighted cc is slightly lower than the unweighted cc for the Swedish network; for the random network, weighted and unweighted cc’s are the same). Path length is measured using the geodesic distance algorithm in UCINET VI, which produces a matrix of shortest path lengths between nodes. UCINET VI’s univariate statistics algorithm then calculates mean path length. To produce the Erdos-Renyi ran- dom graph, the random graph algorithm in UCINET VI (subcommand Erdos-Renyi) is used, speci- fying that the graph should be same size and density as the Swedish network—290-x290; .0237 density). Table 15.3 Clustering and average path length in municipal learning networks in Sweden Sweden Random Clustering (cc) 0.293 0.025 Length (L) 5.080 3.215 C. Ansell et al.