Learning Networks Among Swedish Municipalities: Is Sweden a Small World?
Distributed, networked learning processes are widely touted as a basis for superior performance. Yet we know relatively little about how learning networks operate in the aggregate. We explore this issue by utilizing a unique data set on learning among Swedish municipalities. The data indicate that geographic proximity and county are the basic structuring properties of the global network. Municipalities learn from their near neighbors, especially from neighbors in the same county, and these two principles produce a high degree of local clustering in the municipal learning networks. At the same time, we also find evidence that Swedish municipalities are a small world linked together on a national basis. Two mechanisms knit the Swedish municipalities together. First, county seats serve as hubs that link local clusters together. Second, local clusters aggregate into regional clusters. Despite a high degree of local clustering, hubs and regions provide a structural basis for the national diffusion of policy ideas and practices among Swedish municipalities.
KeywordsLearning Social networks Local government Municipalities Counties Sweden Small-world networks Regionalism Hubs Markov clustering Proximity Girvan-Newman Community structure
Distributed, networked learning processes are widely touted as a basis for superior performance. Public and private organizations, cities and regions, and even nations are exhorted to network, to innovate collaboratively, to benchmark, and above all to learn from one another (Agranoff, 2006; Betsill & Bulkeley, 2004; Cooke & Morgan, 1993; Goldsmith & Eggers, 2004; Kraatz, 1998; Lee & van de Meene, 2012; Powell, Koput, & Smith-Doerr, 1996; Slaughter, 2009). From case study research, we know a good deal about local strategies of networking, innovation, and collaboration (e.g., Saxenian, 1996). And from diffusion studies, we also know that the structure of networks shapes the diffusion of information, ideas, innovations, policies, and best practices (Cao, 2010; Davis, 1991; Granovetter, 1973; Gray, 1973; Hedström, Sandell, & Stern, 2000; Lee & Strang, 2006; Mintrom & Vergari, 1998; Stone, 2004). However, we know relatively little about how the local learning choices of individuals, firms, cities, or nations aggregate into global network patterns that may subsequently affect diffusion. In this chapter, we explore this question by examining how the learning strategies of Swedish municipalities aggregate to produce a national intermunicipal learning network.
Interdependence between the policy choices of local governments has attracted growing interest recently (Lee & van de Meene, 2012; Marsden, Frick, May, & Deakin, 2011). It has been argued that subnational governments can act like democratic laboratories (Shipan & Volden, 2012; Volden, 2006) and that they can learn important lessons from each other. Literature on urban policy mobilities (Jacobs, 2012; McCann, 2011) and policy diffusion (Krause, 2011; Lee & van de Meene, 2012) has begun to explore the mechanisms of policy transfer and diffusion between cities. Our research shares this interest in policy mobility and diffusion but approaches the issue from a different angle. Rather than asking why a policy moves from city A to city B, our research is interested in uncovering the relational principles that constitute interurban networks in the first place. We approach the issue from this angle, in part, because of the character of our data, which does not enable us to track the mobility or diffusion of specific policies, but does give us an unusually detailed look at the relationships of learning between Swedish municipalities. Our contribution is therefore not to explain mobility or diffusion per se, but rather to utilize social network analysis to uncover the structuring principles of national learning networks.
Over the last decade or so, economic geographers and economic sociologists have been engaged in a similar exploration of the relational principles that guide learning in interfirm networks. Their research has shown that interfirm learning is often structured by geographical proximity, but that nonlocal networks may be critical pipelines that move knowledge between local clusters of firms (e.g., Amin & Cohendet, 1999; Bathelt, Malmberg, & Maskell, 2004; Bell & Zaheer, 2007; Glückler, 2013; Owen-Smith & Powell, 2004). Although geographical proximity is understood to enhance interactional learning, nonlocal networks are increasingly understood to be important for preventing local learning networks from becoming too parochial (Boschma, 2005; Maskell, 2014). Although research is beginning to reveal variations on this theme, this literature valuably highlights the composite character of learning ecologies, which are produced through the interplay of geography and networks. Our research builds on this literature, but extends this discussion from firms to municipalities. Our research therefore offers a bridge between this literature on interfirm learning and the literature on policy mobility and diffusion. To our knowledge, there has been little cross-fertilization between these two important bodies of literature.
Our exploration of intermunicipal learning networks is based on a unique survey of municipal civil servants conducted in 2010 as part of a wider study of municipal knowledge use in Sweden. In this survey, the senior civil servants in all Swedish municipalities were asked to name other Swedish municipalities from whom they had drawn lessons in a given period. When these choices are aggregated across all Swedish municipalities, the result is a unique glimpse into what an intermunicipal learning network looks like on a national scale. Swedish municipalities provide an interesting context in which to examine learning networks. Much of the fabled Swedish welfare state is actually administered by Sweden’s 290 municipalities varying in size from roughly 3000 inhabitants to 750,000 inhabitants.1 These municipalities have responsibility for a wide range of policy areas, including social services, education, daycare, environmental protection, and planning, and municipal employees compose approximately 25 % of the Swedish workforce (Sveriges Kommuner och Landting, 2014). Although they are organized into 21 counties, the county-municipality relationship is not a hierarchical one and while Swedish municipalities operate within a framework of national law, they have considerable latitude about how to organize and deliver government services and regulation.2 Thus, their extensive and parallel responsibilities create powerful incentives to learn from one another, but their political autonomy means that they are relatively free to decide whom to learn from. We know that the Swedish Association of Local Authorities and Regions (SALAR) actively encourages the municipalities to learn from each other, but we do not know how their choice of whom to learn from aggregates to produce a national learning network.
The chapter is organized as follows: The first section describes our data. In the second section, we provide some basic information about the extent of learning among municipalities and about how municipalities try to learn from each other. In section three, we use social network analysis to explore how municipal clusters of learning are structured. Then, in section four, we examine whether the Swedish municipalities can be described as a small world through which ideas and information may easily diffuse. Section five focuses on what characterizes the municipalities whose nonlocal networks bridge between otherwise disconnected municipalities in the learning network. Section six concludes.
Our data come from a survey of Swedish municipalities conducted in 2010. The survey asked a range of questions about knowledge use in each municipality and was answered by the top civil servant. This manager is in charge of the office responsible for preparing policy proposals for the municipal executive board, which is the most important and powerful local government institution in Sweden (Bäck, 2005). Composed of local politicians appointed in proportion to their party mandate in the municipal assembly, these boards have responsibility for managing and coordinating local administration and also have financial responsibility for the municipality.
The key variable of this study is learningor lesson-drawing (Freeman, 2008, p. 376; see also, Lundin, Öberg, & Josefsson, 2015). Learning is a voluntary activity involving a search for knowledge in order to solve problems. That is, in a learning process actors try to improve the understanding of the relationship between cause and effect by taking advantage of others’ experiences (Lee & Strang, 2006; Lee & van de Meene, 2012; Meseguer, 2005). The survey question used to elicit the municipal learning network was: “What other municipalities have you drawn important lessons from within your field during the last election period (since January 2007)?” In response, municipal managers could mention as many other municipalities as they liked.
A web survey was distributed as a first step, with three follow-up reminders. We then distributed a somewhat shorter version as a postal survey in a second step. This led to a response rate of 78 %. The remaining nonrespondents were telephoned, producing a 100 % response rate on the learning question.3
The information that can be spread among municipal head managers is of a diverse character because a wide range of policy decisions are handled in the municipal executive boards. Overarching issues like budgets, policies, programs, guidelines, and various action plans (e.g., wind power plans and school plans) are within the managers’ purview. Somewhat more limited decisions are also frequently made, such as whether to shut down a certain school or where to locate a recycling station. Moreover, the committees handle minor issues such as what documents should be archived and for how long. We do not know exactly what issues respondents had in mind when answering our question, but they all have equivalent positions within the municipalities and were asked about lessons learned within their field, which includes all issues handled by the municipal executive boards. Furthermore, they were explicitly told to ignore issues that do not reach the political level and “routine matters” concerning individual citizens.
In addition to the key question, we use some other questions from the survey in order to describe learning processes in Swedish municipalities in more detail. Moreover, a series of interviews with municipal officials was conducted in order to develop a more qualitative understanding of how municipalities use knowledge to make policy decisions. Semistructured, open-ended interviews were conducted with 40 politicians and civil servants in six municipalities. These municipalities were strategically selected to maximize variation (two large, two medium-sized, and two small municipalities). For each pair, one municipality had a stable social democratic majority and the other had shifting majorities. The interviews lasted from 45 to 90 min and were recorded. Although we do not report systematically on these interviews in this chapter, they do provide some background information for our interpretation of learning networks.
Local Learning Through Informal Personal Connections
A first step in the analysis is to explore how important information from other municipalities is in municipal decision-making. We also want to know what channels are used to collect information. Table 15.1 provides some basic statistics on learning among municipalities in Sweden according to the survey responses. Of the 290 municipalities surveyed, only 8 % reported they had not learned something important from another municipality during the previous 4 years (since the last election period), whereas 61 % reported learning from between two and nine other municipalities, and the maximum number reported was 26 other municipalities. On average, the municipal managers report that their municipality draws important lessons from about seven other municipalities.
The survey also included a question on how often information from other municipalities is used when issues are prepared before political decision. Table 15.1 reveals that although information from other municipalities is not used in a majority of issues, only 12 % reported that they “never or almost never” use such input in the policy process. Furthermore, we asked how often information produced by the Swedish Association of Local Authorities and Regions (SALAR) is employed in the policy process. Around two percent claim that they “never or almost never” use information from SALAR, whereas 59 % use information from SALAR in at least half of the issues. Thus, SALAR seems to function as an important bridge between local governments. This finding was reinforced in the in-depth interviews.
Learning among Swedish local governments: Various survey responses
Q1. How many other municipalities have been learned from? (“Outdegree”)
Q2. How often is information from (a) other municipalities (b) SALAR used when issues are prepared before political decision?
Number of municipalities mentioned
Other municipalities (%)
Never or almost never
Less than half of the issues
About half of the issues
More than half of the issues
Always or almost always
Q3. Channels used “often” or “very often” in order to get information about activities in other municipalities?
1. Informal personal connections
5. Conferences, seminars etc.
2. Internet homepages
6. Written reports produced by other municipalities
3. Regular meetings with certain municipalities
7. Information in media
4. Written reports produced by SALAR
8. Official visits
Learning Clusters Are Based on County Structure
Above all, it is if you find somebody that is successful in a certain area, somebody that has given thought to something. Primarily it is often among neighbors that we look because they are quite similar and work under roughly the same conditions. (2011 interview with civil servant)
The importance of geographical proximity suggests that municipal learning networks in Sweden might be very parochial. If so, it is reasonable to expect that new knowledge, ideas, and best practices would be quite slow to diffuse to local governments in Sweden. But the dyadic analysis presented above does not account for the possibility of learning indirectly through less proximate networks. To explore this possibility, we employ ideas from social network analysis. The aim is to deepen our understanding of the clustering properties of a potential learning network: How are clusters structured? To find out more about this, we started by using the Girvan-Newman method of detecting community structure (Girvan & Newman, 2002). This method finds clusters by iteratively removing edges with high edge betweenness scores until it reaches some specified minimum number of clusters. A betweenness score summarizes the number of times an actor is a bridge between two other actors in the network (Freeman, 1977).
The analysis is presented in Table 15.2 and it reinforces findings in Lundin et al. (2015): county is a very strong predictor of cluster membership. There are 21 counties in Sweden and when directed to detect 21 clusters, the community structure identified by the Girvan-Newman method is very close to the structure of counties. Although some clusters contain municipalities from more than one county, the county structure is clear. Twenty of the clusters are dominated by municipalities from a single county (cluster 14 is an exception with only one municipality). Municipalities from some counties are divided between clusters (Västra Götaland, Skåne), but a single county still dominates each cluster. Only a few counties have the municipalities distributed across clusters without clearly dominating at least one cluster (Uppsala, Västernorrland). The county structure of clusters remains robust even if the algorithm is told to produce a different number of clusters.5
Girvan-newman clusters by county
Counties (number of municipalities per county)
Stockholm (26); Södermanland (1); Skåne (1)
Södermanland (7); Uppsala (2)
Gävleborg (10); Västernorrland (4); Uppsala (1)
Västmanland (7); Uppsala (4); Södermanland (1); Gotland (1); Örebro (1)
Östergötland (12); Halland (1)
Västra Götland (22); Östergötland (1); Jönköping (1)
Jönköping (12); Halland (4); Blekinge (1)
Jämtland (8); Skåne (1); Västernorrland (1)
Västra Götaland (11); Halland (1)
Västra Götaland (14)
Västerbotten (15); Västmanland (1); Västra Götaland (1); Västernorrland (1); Norbotten (1)
Dalarna (14); Västmanland (2)
Norrbotten (13); Västernorrland (1)
Because the pattern of emergence of the global network works via a principle of local proximity, we might expect local clusters to cluster together on a geographical basis. In other words, we should expect the clusters identified above to cluster into larger regions. To examine this, we wanted a clustering technique that did not require us to assign the number of clusters. We selected Markov clustering, which uses a different strategy of community detection (van Dongen, 2008). The Girvan-Newman community detection procedure used above identifies community structure by removing edges with high betweenness centrality until nonoverlapping groups appear. Markov clustering identifies community clusters by “walking around”; it identifies clusters as places where the algorithm spends a lot of time walking. This strategy intuitively captures the way information might circulate geographically.
The two large clusters are indeed regions in a spatial sense. One of them (Fig. 15.1) represents the northern coast plus the Stockholm region (minus Stockholm itself). The second region (Fig. 15.2) runs spatially east to west in the southern part of Sweden and contains the Göteborg region. We also observe that a distinctive subregion can be detected in the Southern region (Fig. 15.2). This subregion is an extremely tight cluster of municipalities around the city of Göteborg. A possible explanation for this tight clustering is the formal creation of a metropolitan region. The formal association is called the Göteborg Region Association of Local Authorities, and the member municipalities are Ale, Alingsås, Göteborg, Härryda, Kungsbacka, Kungälv, Lerum, Lilla Edet, Mölndal, Partille, Stenungsund, Tjörn, and Öckerö. All these belong to the distinctive subregion visually detected in Fig. 15.2.
The West Sweden region (Västra Götalandsregionen) that includes the Göteborg Region Association of Local Authorities has been studied in prior research. Gren (2002) notes that this is one of the best organized regions in Sweden, partly through support from the European Union. Lidström (2011) found that citizens in the municipal regions of Göteborg (13 municipalities) and Umeå (6 municipalities) adopted more of a city-regionalist attitude (emphasizing the importance of intermunicipal coordination on a regional basis), as opposed to a localist attitude (strong municipal autonomy). The findings of Gren (2002) and Lidström (2011) suggest explanations for the existence of this subregion in the learning network.
A Small World?
The previous analysis has shown that learning networks in Sweden are to a large extent structured by county. However, we want to know more about whether the municipalities are efficiently integrated on a national scale. The literature on small-world networks suggests that networks might be well connected despite highly localizing tendencies (Watts, 1999; Uzzi, Amaral, & Reed-Tsochas, 2007). Small-world networks are more cosmopolitan than expected because of the connections that occur among local clusters. If Swedish municipalities compose a small world, knowledge, ideas, and best practices might be diffused widely and rapidly despite the localism of learning networks.
A small-world network is defined as a graph with high clustering but low path length.7 A random graph typically has low clustering but also short average path lengths. A highly clustered network, by contrast, generally has high path lengths. A small-world network is a network with higher clustering than a random graph but with similar path lengths. A key feature of a small-world network is that despite the high clustering, which is expected to impede communication across the network, links between clusters can greatly shorten the path lengths and hence facilitate more rapid and cosmopolitan communication. In small worlds, path lengths are often reduced through the influence of highly connected hubs that link different clusters together. Well-connected hubs are not a necessary feature of small worlds, but it is reasonable to expect them to be important in networks with high local clustering. A number of scholars have pointed to the potential for small-world networks to diffuse knowledge and enhance innovation. Cowan and Jonard (2004), for example, simulated knowledge diffusion in innovation networks and found that diffusion in small-world networks produces higher knowledge levels (in the network as a whole) than either a more local network or a random network.
Clustering and average path length in municipal learning networks in Sweden
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 innovation. Thus, hubs are expected to fulfill a crucial role in the diffusion of innovations among the clusters. Accordingly, identifying the hubs and finding out what characterizes 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 others. They should stand out from other municipalities in this respect. Our first measure 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 measure 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 network.9 By multiplying integration and radiality we get a second hub measure (Hub B).
A third possible measure (Hub C) is betweennesscentrality (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.
Correlation between Hub measures
Above, in Fig. 15.2, we discovered a tight network in western Sweden consisting of the members of the Göteborg Region Association of Local Authorities. Many of the municipalities belonging to this association also score high on the three hub measures. If we once again use the 75th percentile to separate out more cosmopolitan cities, 54 % of the Associations’ members are hubs if we focus on the most basic hub measure (Hub A). Using the other two hub measures yields 85 % (Hub B) and 31 % (Hub C), respectively.10 At first glance, at least, this region has done an impressive job of promoting regional cooperation and diffusion of information. However, it is of course also possible that the association was formed around municipalities already having a lot of cooperation. If this is true, the causality runs in the opposite direction.
In order to find out more about what characterizes hubs as transit points, we explore the correlation between the three hub measures introduced above and various municipal characteristics. A first idea is that county seats and larger or more urban municipalities could be important. Such cities might function as regional centers where large companies, authorities, universities, and other organizations are located and where infrastructure is more developed. These features might increase the probability that knowledge diffuses through such municipalities. A second idea is that healthy fiscal conditions or a favorable economic climate might characterize the transit points. Cities like this are perhaps more innovative and outward-looking. Lastly, features of the local population could be important—perhaps transit points have a younger and more educated population?
Descriptive statistics: Swedish municipalities
Hub A (indegree × outdegree)
Hub B (integration × radiality)
Hub C (betweenness centrality)
Log population (number of inhabitants)
County seat (1 = Yes; 0 = No)
Unemployment rate (percent)
Tax base (SEK/citizen)
Mean age (in years)
College degree (percent of population)
What characterizes cosmopolitan municipalities?
Internal vs. External learning in county seats
The purpose of this analysis was to better understand how a global learning network emerges from the local learning choices of autonomous Swedish municipalities. We found that the county is a basic structuring property of the global network. Municipalities learn from their near neighbors, especially from neighbors in the same county. Informal personal connections seem to be the main channel through which municipalities learn from one another.
The high degree of clustering in the municipal learning networks prompted us to examine whether the global network met the criteria for a small-world network, and we have shown that it does. This is important because it suggests that ideas, knowledge, and best practices may diffuse through the network of Swedish municipalities despite the relatively parochial learning patterns of many municipalities. One possible mechanism of integration might be regional agglomeration of networks. Using Markov clustering, we found two very large regions in the global network—a northern coast-Stockholm region and a southern east–west region. These regions extend the pattern of local clustering to the regional level and may be an important basis for nonparochial learning.
Another important mechanism for national integration of municipal learning networks is the role of important network hubs—key transit points in the flow of knowledge. We found that the county seats play this transit-point role for knowledge diffusion. County seats are comparatively well networked outside the county and most of the county seats are linked to one another on a national basis. Hence, although the high clustering of a small-world network is explained by geographic proximity and county, the global integration of this small world works through county seats to a substantial extent. Using county seats as transit points in order to spread best practices more rapidly might therefore be a promising avenue to improve policies.
Interviews suggested that municipalities were quite aware that they learned from geographically proximate neighbors, especially from municipalities within their own county. There may be several reasons why learning is structured this way. Spatially proximate governments often share certain policy-relevant problems, conditions and experiences (Karch, 2007). It is also probably easier to develop a closer relationship with neighboring municipalities; the costs of searching for information from these governments might be lower than looking for information elsewhere (Lundin et al., 2015). Anecdotal evidence from our interviews indicates that municipal bureaucrats tend to circulate between positions in municipalities within counties. This could make it easier to establish the necessary personal connections that, according to our findings, are so important for intermunicipal learning.
There are also other potential explanations for the distinct county pattern that emerges in our analysis. A first possibility is that the role of counties reflects a deep historical legacy. The counties are very close to the old Swedish provinces, whose history reaches back to the seventeenth century. These provinces had a fair degree of political and cultural autonomy and this historical legacy may have structured long-term patterns of intermunicipal interaction. Moreover, in each county, there is a national government authority (Länstyrelsen) acting as a representative of national government to help align local and national policy. Länstyrelsen are also charged with promoting cooperation and working in the interest of the municipalities within the county. This role presumably requires them to work closely with the municipalities in the county. The tendency of municipalities to learn from other municipalities in the same county might be a reflection of the Länstyrelsen’s coordinating role.
Our findings suggest that learning networks are likely to aggregate according to a set of factors that systematically shape learning choices. In the Swedish case, these factors include geographical proximity, personal social relations, urban and regional economic and demographic structure, and political-administrative institutions. Although the important role of geographical proximity and county government are not entirely surprising, we have shown that such factors produce clear global patterns of learning—the small world of Swedish municipalities. This global learning pattern is likely to have important consequences for how knowledge, ideas, and best practices spread to and among Swedish municipalities.
Prior research notes significant variation in welfare services across municipalities, leading some scholars to describe Sweden as a multitude of “welfare municipalities” (Trydegård & Thorslund, 2010).
In a comparative perspective, Swedish local governments are considered to have a lot of power (Sellers & Lidström, 2007). Municipalities have taxing power and a constitutionally protected right of self-government. Swedish public agencies are also known to actively support innovation. The 2010 European Innobarometer Survey found that innovation in the Swedish public sector is much more bottom-up (initiated internally) rather than driven by policy mandate (Arundel & Hollanders, 2011).
Note that the other survey questions presented in this chapter are based on a somewhat smaller sample (i.e., about 78 % of the population).
The main research question in Lundin et al. (2015) is whether local governments tend to learn from governments that are more successful than others; the empirical findings support this hypothesis. However, the importance of proximity, similarity, and power is also examined in the study.
With 10 clusters, the method identifies a regional organization that resembles the three old Swedish provinces (Norrland, Svealand, and Götaland). However, municipalities still tend to cluster with other municipalities from their own county. The northern region includes Norrbotten, Västerbotten, and Västernorrland. The center region includes Stockholm, Uppsala, Södermanland, Gävleborg, Dalarna, Västmanland, Gotland, and Jämtland. Then there are seven small regions in the south: (1) Västra Götaland, Halland, and Jönköping; (2) Örebro; (3) Östergötland; (4) Kronoberg and Blekinge; (5) Värmland; (6) Kalmar; and (7) Skåne.
The E-I index for all the municipalities using this clustering was −.271 (the expected E-I index was .893, significant at <.05).
Clustering refers to the density of interconnections in each social network actor’s local neighborhood—the set of other actors with whom the focal actor is directly connected. The overall clustering of a network is the mean clustering across all the actors in the network. Path length is the mean number of steps it takes each actor in the network to reach every other actor in the network when taking the shortest path.
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 algorithm 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 random graph, the random graph algorithm in UCINET VI (subcommand Erdos-Renyi) is used, specifying that the graph should be same size and density as the Swedish network—290-x290; .0237 density).
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.
If hubs were randomly distributed, we would have expected 25 % of the hubs in the Göteborg Region Association of Local Authorities to be hubs.
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