Page - (000329) - in Knowledge and Networks

327 among the clusters. Accordingly, identifying the hubs and finding out what charac- terizes these municipalities is important. We devised three ways to measure the extent to which each municipality can be characterized as a learning hub. Based on our view that hubs are transit points for learning, hubs should not only be learned from, but they must also learn from oth- ers. They should stand out from other municipalities in this respect. Our first mea- sure is based on degree centrality, which captures the local connectedness of a municipality. By multiplying together how many other municipalities reported learning from a municipality (indegree) by how many others that municipality learned from (outdegree), we get a simple variable capturing the extent to which a municipality takes on the role as a transit point in the Swedish municipal learning network (Hub A). One problem with this measure is that it does not take indirect ties into account. Potentially, a municipality can have high indegree and high outdegree without being that well connected to distant (in network terms) municipalities. Another approach is therefore to use the concept of closeness centrality developed by Valente and Foreman (1998). Valente and Foreman distinguish two measures, integration and radiality. Integration is a measure of how closely other actors in the network are connected to you via a chain of contacts; a municipality is more integrated if other municipalities must take fewer steps (path lengths) to reach you. Radiality is a mea- sure of how well you are connected outwards to others—that is, how easily you can reach others through direct or indirect networks. These measures go beyond a local measure of degree centrality by incorporating the indirect links to the entire net- work.9 By multiplying integration and radiality we get a second hub measure (Hub B). A third possible measure (Hub C) is betweenness centrality (Freeman, 1977), that is, the number of times a municipality sits on the shortest possible path between all other municipalities in the network. Actors with high betweenness scores may perform brokering roles by connecting otherwise disconnected actors and clusters. Table 15.4 shows positive correlation coefficients between the three hub mea- sures. The correlations are not exceptionally strong, which suggests that they cap- ture somewhat different dimensions of what it means to be a hub. Beyond suggestive interpretations, theoretical arguments for why one of these hub measures might be 9 The Valente-Foreman measures use the reverse of the average distances between nodes. The reversed distance is the diameter minus the geodesic distance. The diameter is the longest path between any two points, whereas the geodesic distance is the shortest path. Basically, they reverse the distance measure, turning it into a closeness measure. Table 15.4 Correlation between Hub measures Hub A Hub B Hub C Hub A 1.00 Hub B .56 1.00 Hub C .78 .43 1.00 15 Learning Networks Among Swedish Municipalities: Is Sweden a Small World?