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.


I. Introduction
Distributed, networked learning processes are widely touted as a basis for superior performance. Public and private organizations are exhorted to network, to innovate collaboratively, and to benchmark. From diffusion studies, we know that ideas, innovations and best practices diffuse through networks. And from case study research, we now know a good deal about local strategies of networking, innovation, and collaboration. Yet we know relatively little about learning networks themselves. If learning is indeed a distributed, networked process, how would we begin to understand these networks on a more global scale? We explore these questions by utilizing a unique data set on Swedish municipalities. As part of a wider study of knowledge use in Sweden, municipal governments were asked to identify other municipalities they learned from. When aggregated to the national level, these survey results provide a unique glimpse of what a distributed learning network looks like at the national level. Our goal in this paper is to understand how the local learning strategies of municipalities aggregate to produce a national network with distinctive global properties.
Swedish municipalities provide an interesting context in which to examine distributed, networked learning processes. Much of the fabled Swedish welfare state is actually administered by Sweden's 290 municipalities, which vary in size from roughly 3000 inhabitants (Sorsele) to 750,000 inhabitants (Stockholm). Scholars note significant variation in welfare services across municipalities, leading some scholars to describe Sweden as a multitude of "welfare municipalities" (Trydegård and Thorslund 2010). In addition to providing social services, Swedish municipalities also have responsibilities for education, environmental protection, and planning and municipal employees compose approximately 25% of the Swedish workforce (Swedish Association of Local Authorities and Regions 2013). Municipalities have taxing power and a constitutionally-protected right of self-government. Although they are organized into 21 counties, the countymunicipality relationship is not a hierarchical one.
Although Swedish municipalities operate within a framework of national law, they have considerable latitude about how to organize and deliver government services and regulation. 1 How they decide to learn from each other is therefore of significant consequence. Policy diffusion among Swedish municipalities is facilitated through a common national organization, the Swedish Association of Local Authorities and Regions (SALAR), that actively encourages the municipalities to learn from each other. Some municipalities also have relatively institutionalized patterns of cooperation with other municipalities. For example, the head of the municipal administration office in Norrköping explained the municipality is part of an old established network with eight other municipalities of roughly the same size (Eskilstuna, Västeras, Örebro, Jonköping, Helsingborg, Borås).
The data for this project come from a survey of Swedish municipalities conducted in 2010 by two of the authors, Per Ola Öberg and Martin Lundin. The survey asked a range of questions about knowledge use in the each municipality and was answered by the top civil servant in each municipality. This civil servant is responsible for preparing policy proposals for municipal executive boards, which are the most important and powerful local government institutions. 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 survey question used to elicit the learning network between municipalities was: What other municipalities have you learnt something important from within your field during the last election period (since January 2007)? The response rate for the entire survey was 78%, but through extensive follow-up a 100% response rate on this learning question. 2 A series of interviews with municipal officials was also conducted in order to develop a more qualitative understanding of how municipalities use knowledge and research to make policy decisions. Semi-structured, open-ended interviews were conducted with 40 politicians and civil servants in 6 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. These interviews lasted from 45-90 minutes. The research project also conducted telephone interviews with 27 heads of administration who were selected using stratified cluster sampling (29 were originally selected, but two were dropped because they were among the 6 municipalities interviewed). These interviews were more structured and lasted for 10-15 minutes. Although we do not report systematically on these interviews in this paper, they do provide some background information for our interpretation of learning networks.

II. Local and Global Learning
Of the 290 municipalities surveyed, only one municipality reported they had not learned something from another municipality during the previous four years (since the last election period). Sixty one per cent of municipalities reported learning from between 2 and 9 other municipalities and the maximum number reported was 26 other municipalities. On average, municipalities reported learning from 7 other municipalities.
One of the strong findings of the study is that municipalities learn from their local neighbors. As one local civil servant reported: "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." A dyadic analysis of the data (84000 pairs of municipalities) conducted by Lundin, Öberg, and Josefsson (2013) finds that geographic proximity greatly increases the probability that two municipalities will learn from one another. In addition, a municipality is more likely to learn from another municipality if it is in the same county and if it is of equal or greater population size (Table 1).  (2013) The importance of geographical proximity suggests the 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 through Sweden. However, we also wondered whether, despite this localism, Swedish municipalities might still be 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, and Reed-Tsochas, 2007). Small world networks are more cosmopolitan than expected because of the connections that occur among clusters. If Swedish municipalities are a "small world," knowledge, ideas, and best practices might be diffuse 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. 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 network is a network with higher clustering than a random graph, but with similar path lengths. A key feature of a small work 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 together different clusters. 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. Two measures have been used to identify whether a network exhibits small world properties--a clustering coefficient (as defined by Watts 1999; labeled cc for clustering coefficient) and a measure of average path length (labeled L). These measures are then compared to a random graph of the same size and density (an Erdos-Renyi random graph). 3 Here are the basic measures: cc Sweden: .293 cc random: .025 L Sweden: 5.080 L random: 3.215 In comparing the results above, we see that the 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 what is sometimes called the small world "quotient". Which is: ccSweden/ccrandom//LSweden/Lrandom.
A small world is defined as having a quotient greater than 1. In this case, the result is: ccSweden/ccrandom = 11.72 LSweden/Lrandom = 1.580 Small world quotient (Q) = 11.72/1.580 = 7.437 The standard is that you have a small world if Q > 1 So by this standard, the learning network of Swedish municipalities is indeed a small world, though the path lengths are a little high (LSweden > Lrandom). The higher path lengths might suggest there are fewer "hubs" in the Swedish network than in an ideal small world. 4

III. Clusters and Hubs
Our small world analysis suggests that we also want to deepen our understanding of the clustering properties of this network. To do this, we started by using the Girvan-Newman method of detecting "community structure" (Girvan and Newman 2002) This method finds clusters by iteratively removing edges with high edge betweenness scores until it reaches some specified minimum number of clusters. The analysis reinforces a finding from the dyadic analysis (Table 1): county is a strong predictor of cluster membership.
There are 21 counties in Sweden and when directed to detect 21 clusters, the community structure detected by Girvan-Newman method was very close to the structure of counties. 5 Municipalities strongly clump together as counties. 6 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 erdosrenyi) is used, specifying that the graph should be same size and density as the Swedish network-290-x290; .0237 density). 5 The one major exception is the municipalities of Skåne, which fall between two communities. 6 The alignment between counties and clusters predicted using the Girvan-Newman method was robust even when we specified different numbers of clusters. While some clusters contain more than one county, the country structure is clear. Nineteen of the clusters are dominated by a single county. 7 Only a few counties seem to be distributed across clusters without clearly dominating at least one cluster (UPP; VNL; VML). The county structure of clusters remains robust even if the algorithm is told to produce a different number of clusters. 8 We can also look at what is called the E-I index for each of these clusters. The E-I index is a measure that varies between -1 and +1. At +1, all ties are external to a group (in this case the cluster); at -1, all ties are internal to the group. 9 We see that most of the E-I indexes for the clusters are negative. Only three of the clusters have a positive E-I. That means that most ties are internal to these clusters.
We can now turn from analyzing the clusters, to analyzing the hubs. 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 non-local networks are particularly crucial for path-breaking innovation, while local networking results in more incremental innovation.
We devised several ways to try to identify hubs. First, based on our view that hubs are transit points for learning, we decided that hubs should not only be "learned from," but they must also "learn from others." They should stand out from other municipalities in this. We decided we could measure this by identifying municipalities that have higher than average "indegree" (the number of other municipalities that reported learning from them) and higher than average "outdegree" (the number of municipalities they learned from). The mean in-degree and outdegree were both 6.89. Therefore, we decided that cities with both indegree and outdegree of 7 or greater would be called hubs.
This definition of hubs produced 27 out of 290 municipalities. As indicated in the table above, the hubs are somewhat unevenly distributed. We found that a number of these hubs were relatively small municipalities clustered together in a clique in the Göteberg region (VGO). A number of counties have no hub at all, as we are defining it here. If this definition of hub is used, it raises some question about whether the Swedish learning network is fully connected as a "small world" (e.g., clusters connected to each other through hubs).
Given our finding about the importance of county as a clustering principle, we were also interested in whether the government seat of each county served as the county hub. One way to further investigate this is to examine the E-I index for county seats (using the Girvan-Newman clusters as partitions). The mean E-I index for all municipalities was -.345, indicating that the ties of most municipalities are local (e.g., within cluster). By contrast, the average E-I index for county seats is .130. This means that in contrast with the localism of most municipalities, county seats have on balance more external than internal ties. Only 3 of 21 county seats have negative E-I indexes.
ORE (Örebro) (density = .655); (3) OST (density = .603); (4) KRO and BLE (Karlskrona) (density = .304); (5) VAR (density = .483); (6) SKA (actually divided between three communities; Malmö is part of the big central region) (density = .475 and .379). 9 The E-I index for the all the municipalities, using this clustering was -.271 (the expected E-I index was .893, significant at <.05). Martin Everett pointed out to us that the E-I index is sensitive to density; there is apparently a fix for this, but we have not gotten around to implementing it. Another approach to identifying hubs is to use the concept of closeness centrality. The closeness centrality measure developed by Valente and Foreman (1998) is appropriate for directed graphs. Valente and Foreman distinguish two concepts, integration and radiality. Integration is a measure of how well others in the network are connected to you. Radiality is a measure of how well you are connected outwards to others. These measures go beyond a local measure of degree by incorporating connectedness to indirect ties as well as direct ties. 10 Malmö, Stockholm, Nacka, Skellefteå, Västerås, Göteborg, Umeå, Södertälje, and Uppsala are at the top in terms of integration. But interestingly, many of these towns are quite low on the radiality score (Stockholm is number 200 and Malmö is 199). This suggests that there is an urban hierarchy at work, where the big municipalities learn less from the smaller municipalities. As we saw in the dyadic analysis (Table 1), municipalities learn from other municipalities of equal or larger size. As this suggests, some municipalities may learn from many other towns (high integration scores) or many other towns may learn from them (high radiality scores). However, our conception of hubs as important transit points for learning suggests that both concepts are important. Therefore, we multiplied radiality and integration scores together to produce an index of the importance of different hubs.
We see from this table that all county seats, with the exception of Gotland (Visby), Luleå, and Nyköping are in the top 25% of municipalities in terms of this closeness index (integration x radiality). Taken together, this evidence suggests that county seats are acting as hubs in the learning network of Swedish municipalities. This conclusion is reinforced by looking at the network connecting county seats ( Figure 1; the figure approximately organizes the county seats geographically). Nyköping and Falun are isolates, but the rest of the county seats are linked together.

V. Regional Clusters
Since 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 local clusters to cluster into 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 identifies community structure by removing edges with high betweenness centrality until nonoverlapping groups appear. Markov clustering identifies community clusters by "walking around" and it identifies clusters as places where it spends a lot of time walking. This strategy intuitively captures the way information might circulate geographically.
The markov clustering identified 22 clusters, which seems to approximate the county structure of Sweden. However, two of these clusters are quite large, while many others are quite small. Therefore, the markov clustering algorithm identifies more of the "regional" as opposed to the local clustering structure of the network. The two large clusters are indeed regions in a spatial sense. One of them represents the northern coast plus the Stockholm region (minus Stockholm itself). The second region runs spatially east to west in the southern part of Sweden and contains the Göteberg region. It is useful to examine each of these regions as networks (Figures 2 and 3).

Figure 3: Southern East-West Region
These larger regional clusters attracted our attention because they suggest one of the ways that the national learning network might be integrated-through larger learning regions. In a study of regional innovation and small world networks, Fleming, King, and Juda (2007) find that "large components" are positively correlated with innovation in patent co-authorship networks. From a small world perspective, the idea is that learning can circulate more widely in these regions.
So these two clusters-out of 22 clusters identified by the markov clustering methodcontain the majority of the hubs. This finding suggests an insight consistent with the small world argument: hubs help to integrate regions.
However, we also need to qualify this statement. A distinctive subregion appears in the Southern region. This subregion is a tight cluster of hubs around the city of Göteberg. These hubs include Lerum, Lilla Edet, Partille, Härryda, Öckerö, Alingsås, Orust, Ale, and Tjörn. This tight clustering of towns around Göteberg is impressive. Some preliminary research suggests that this is the consequence of the formal creation of a metropolitan region around Göteberg. The formal association is called Göteborg Region Association of Local Authorities. The member municipalities are Ale, Alingsås, Göteborg, Härryda, Kungsbacka, Kungälv, Lerum, Lilla Edet, Mölndal, Partille, Stenungsund, Tjörn, and Öckerö. This cluster can be clearly seen in the map above and Ale, Alingsås, Göteborg, Härryda, Lerum, Lilla Edet, Partille, Tjörn, and Öckerö are included in the list of highly connected hubs (≥7 indegree and outdegree).
At first glance, at least, this region has done an impressive job of promoting regional cooperation. As Gren notes, the West Sweden region of Västra Götalandsregionen is one of the best organized in Sweden, partly through the support from the E.U. Lindstrom found that citizens in the municipal region of Göteborg (13 municipalities) and Umea (6 municipalities) adopted more of a "city-regionalist" attitude (emphasizing the importance of inter-municipal coordination on regional basis), as opposed to a "localist" attitude (strong municipal autonomy). 11 While the significance of this "city-regionalist" clustering is worth exploring, it is the larger regions (Figure 2 and 3) that are of primary interest to us in this paper.
To deepen our understanding of whether these regional networks are important in shaping wider learning patterns, we sought to explore whether being part of one of these regions had any discernable effect on the adoption of innovation policy. To do this, we decided analyze municipal adoption of climate change programs.

VI: Regions, Counties, and Climate Change Activity
Sweden has a well established reputation for progressive environmental policy and a strong national commitment to climate change policy. Swedish municipalities are themselves internationally known for their leadership on sustainability issues (Granberg and Elander 2007). Given the policy autonomy of Swedish municipalities, however, there is considerable variation in how climate change policy and practice has been developed at the municipal level. In this section, we exploit this variation to explore 11 One question this raises is whether the region around Göteborg is any more likely to have a high "knowledge use" index score than the average. The average knowledge use index for the municipalities that responded to the survey questions is 1.85 (N=224). The average knowledge for the tightly connected municipalities in the Göteborg region is 2.00. This average is for the cities of Kungsbacka, Härryda, Öckerö, Stenungsund, Tjörn, Orust, Ale, Lerum, Göteborg, Mölndal, Kungval, Alingsås, and Borås. In the northern region, there is a similar cluster of towns that includes Upplands Väsby, Ekerö, Huddinge, Salem, Tyresö, Upplands-Bro, Haninge, Täby, Södertälje, and Botkyrka. All these towns are part of Stockholm county. Their average knowledge use index score is 1.86, nearly exactly the average for all municipalities.
whether inter-municipal learning networks have consequences for climate policy and practice. In particular, we examine whether there is any relationship between the pattern of regional clustering described in the previous section and municipal activity on climate change.
We utilize three different indicators of climate change activity in Swedish municipalities: 1) Signatories to the "Covenant of Mayors." The Covenant of Mayors is a European movement of municipalities pledging to work toward energy sustainability and to exceed the EU's goal of 20% reduction of CO2 emissions by 2020. In Sweden, 45 municipalities signed the covenant. 12 Municipalities that have signed the Covenant are coded 1 and municipalities that have not signed it are coded 0.
2. A research project categorizing Swedish municipalities according to the level and breadth of activity on climate change (Langlais, Francke, Nilsson, and Ernborg 2007). Based on telephone interviews with all 290 municipalities (100% response rate), the researchers identified 48 municipalities with a "noteworthy" level of activity. They identified 43 municipalities that fell in one of two categories of very high activity: a "wide variety of activities at a stable and even rising level" or a "wide variety of activities with exceptional engagement" (Langlais, Francke, Nilsson, and Ernborg 2007, 24). Municipalities that are among the 48 or 43 municipalities are coded 1 and those that are not are coded 0.
3. A national report on climate investment at the municipal level (Naturvårdsverket 2013). Sweden implemented a grant program (known as Klimp) for local and regional climate change investment between 2003 and 2008. The report describes the financial level of investment in the 65 municipalities that received funding under this program. Municipalities that have received investment under this program are coded 1 and those that have not are coded 0.
While we recognize that there may be many factors that influence the level of climate change activity in a municipality, exploring the relationship with municipal learning networks makes sense for at least three reasons. First, "climate change activity" captures a broad set of policies and projects and we can expect this activity to be relevant to some degree across all municipalities (e.g., it is not highly sensitive to specific geographical conditions). Second, we expect that climate change requires a certain degree of technological and institutional innovation, which is likely to create incentives for municipalities to tap their learning networks. From previous research, we know that Swedish municipalities are active in networking on climate change issues (Granberg and Elander 2007).
One way to pose the question of whether learning networks are related to climate change activity is to ask whether any network autocorrelation is exhibited between the learning network and the each of the climate change data sets. Network autocorrelation shows whether there is interdependence among the network nodes in terms of their assignment to a particular group partition-in this case, whether they are part of the active climate change municipalities or not. In this case, we use the relational contingency table analysis in UCINET VI to measure autocorrelation. This analysis produces a Chi-Square statistic to indicate whether an observed distribution departs significantly from an expected distribution. The second column in Table 4 reports this Chi-Square statistic for each of the climate change measures described above and for several combined measures.
For each of the measures and for each of the combined measures, we find a highly statistically significant Chi-Square. This means that the municipal learning network exhibits considerable autocorrelation in relation to climate change activity. In other words, municipalities that learn from each other are interdependent with respect to their engagement in climate change activities.
We then ask whether there is any relationship between the large regional clusters identified in the markov clustering analysis and climate change activity. To evaluate this relationship, we created three data sets: 1) municipalities were coded 1 if they were in the Northern Coast-Stockholm Region ( Figure 2) and 0 if they were not; 2) municipalities were coded 1 if they were in the Southern East-West Region ( Figure 3) and 0 if not; and 3) municipalities were coded 1 if they were in one of the two regions and 0 if they were not. We then did an Analysis of Variance (ANOVA) of the relationship of each of these data sets with the data sets measuring climate change. The results are reported in columns 3-5 of Table 4. The results of the ANOVA analysis show that the Southern East-West Region has a statistically significant number of municipalities with active climate change programs. This varies by the measure of climate change activity. There is a particularly strong relationship between municipalities identified by either the telephone survey as having significant climate change activity or by the report on climate change investment (the relationship with the Covenant of Mayors is not significant). Figure 4 shows that almost all of the municipalities in the "core" of this networked region received climate change investment and only the more "peripheral" municipalities did not. From this analysis, we can conclude that municipalities in this region are particularly likely to be active on climate change. However, we cannot conclude from this analysis that the clustering of municipalities into larger regions per se is responsible for advanced climate change activity: the largest cluster, the Northern Coast-Stockholm Region, does not have a strong statistical relationship with climate change activity. Earlier, we found some evidence suggesting that county seats were critical hubs. Table 5 examines whether county seats are among the municipalities identified as active in addressing climate change. The answer is clearly yes. These 21 municipalities are very clearly overrepresented among the 290 Swedish municipalities. County seats are very active as signatories of the Covenant of Mayors. The relationship is also very strong between county seats and national climate change investment at the municipal level. The relationship is statistically significant, but less strong between county seats and the No Investment Climate Change Investment survey assessment of the municipalities most active on climate change (both for the more expansive and more restrictive assessment).
We also saw earlier that several county seats appear less well connected to other county seats and to the wider network of municipalities. Recall that Gotland (Visby), Luleå, and Nyköping were the county seats that were not among the top 25% of municipalities in terms of their closeness ranking (integration x radiality). Nyköping and Falun are isolates in the network of county seats and Nyköping does not appear to be active on climate change. The lack of activity in several other municipalities is perhaps more surprising given their connectedness to the county seat network. In two of the cases below-Gävle and Härnösand-investment went to the county council (Landstinget Gävleborg and Landstinget Västernorrland) rather than directly to the municipality. So these are arguably exceptions that prove the rule (e.g., county is a critical hub). The lack of activity in Umeå is, however, a clearer exception to our argument.