**4. Results**

The bipartite graph from the RECI's two-mode network (Figure 1) shows to what extent cities and corporations are in structural advantage positions when acting as interlocking agents. Bigger nodes have greater betweenness centrality and function as "brokers" in the network. Spanish firms such as Telefónica, Indra, Acciona or Tecnalia have a strong presence in the network, but foreign capital firms such as Philips or Endesa (which was acquired by the Italian group Enel in 2009) with a relevant position can also be found. Among cities, Madrid, Barcelona, Málaga or the association between Palencia and Valladolid have a strong position within the network. A bipartite graph such as the one represented in Figure 1 offers a general approach to a two-mode network, indicating that some companies seem to play a prominent role and that certain cities—mostly big Spanish agglomerations—seem to act as connecting nodes among firms and the rest of the cities. However, it does not fully reflect the internal features of the network, that is, how their presence is structured.

To further explore the multiple dimensions of a two-mode network, the data informing the visualization offers relevant insights about the characteristics of cities' and firms' participation. For instance, according to the number of cities where each corporation is present (shown in Table S1, in the Supplementary Data section) Telefónica is involved in 17 cities, followed by corporations such as Acciona, Indra or Phillips, which are involved in eight cities. This defines a network structure with a strong presence of major companies of Spanish origin. Conversely, over 65% of the corporations

identified were only present in two cities, which indicates that a small number of corporations articulate the core of the Smart City development within the RECI. However, this is not to say multinational companies are absent. It is worth mentioning that multinational companies not based in Spain represent four out of the first 11 companies present in at least five cities. Moreover, when considering the total amount of companies which are at least present in two cities, more than half of them (54.5%) are multinational companies with non-Spanish capital, which suggests that the RECI can be seen as a network that facilitates the entrance into the Spanish market, where these companies benefit from a structural advantage by being associated to Spanish firms. This possibility is consistent with the data displayed in Table S4 (Supplementary Material section), where we find that foreign multinationals are present in nine out of the 14 top pairs of companies with a shared presence in the same city. *Sustainability* **2020**, *12*, x FOR PEER REVIEW 7 of 13 benefit from a structural advantage by being associated to Spanish firms. This possibility is consistent with the data displayed in Table S4 (Supplementary Material section), where we find that foreign multinationals are present in nine out of the 14 top pairs of companies with a shared presence in the same city.

**Figure 1.** Bipartite graph of the two-mode network city-by-firm of the RECI. Font size represents **Figure 1.** Bipartite graph of the two-mode network city-by-firm of the RECI. Font size represents betweenness centrality. Darker color is used to identify firms, while lighter correspond to cities.

betweenness centrality. Darker color is used to identify firms, while lighter correspond to cities. Turning to the cities' presence in the network, we find cities such as Barcelona, Madrid or Valladolid/Palencia, with at least 16 corporations present in two cities of the RECI, taking part in Smart City projects (see Table S2 in the Supplementary Materials). Other important cities in terms of the number of corporations involved are Málaga, with 15, or Pamplona and Santander, with 12 corporations each. A key finding is that a remarkable percentage (29%) of cities belonging to the network—a total of 19—do not participate in Smart City projects despite being institutional members of the RECI, and 13 other cities have a minimal participation, with only one corporation involved in a Smart City project. In most cases, cities in the network that do not participate correspond to less populated cities, even though there are some cases of relatively populated ones with just one participation or not participating at all, such as Las Palmas or Cordoba, both with a population above 300,000. However, the highest concentration of firms in Smart City projects is found among the most populated cities. There are some relative exceptions, such as Palencia, but this can be considered as a Turning to the cities' presence in the network, we find cities such as Barcelona, Madrid or Valladolid/Palencia, with at least 16 corporations present in two cities of the RECI, taking part in Smart City projects (see Table S2 in the Supplementary Materials). Other important cities in terms of the number of corporations involved are Málaga, with 15, or Pamplona and Santander, with 12 corporations each. A key finding is that a remarkable percentage (29%) of cities belonging to the network—a total of 19—do not participate in Smart City projects despite being institutional members of the RECI, and 13 other cities have a minimal participation, with only one corporation involved in a Smart City project. In most cases, cities in the network that do not participate correspond to less populated cities, even though there are some cases of relatively populated ones with just one participation or not participating at all, such as Las Palmas or Cordoba, both with a population above 300,000. However, the highest concentration of firms in Smart City projects is found among the most populated cities. There are some relative exceptions, such as Palencia, but this can be considered as a single case, since it is associated with Valladolid in a joint partnership for Smart City projects.

### single case, since it is associated with Valladolid in a joint partnership for Smart City projects. *4.1. The Cities Network*

*4.1. The Cities Network*  Cities are mapped in a network graph (Figure 2) with label sizes proportional to their betweenness. Barcelona, Málaga or the association between Palencia and Valladolid appear as the main nodes of the network in terms of their brokering capacity. The graph shows that bigger cities not only have a higher presence of corporations and more connections but also tend to be connected Cities are mapped in a network graph (Figure 2) with label sizes proportional to their betweenness. Barcelona, Málaga or the association between Palencia and Valladolid appear as the main nodes of the network in terms of their brokering capacity. The graph shows that bigger cities not only have a higher presence of corporations and more connections but also tend to be connected among them. Furthermore, a closer look also suggests that in some cases these cities may have a neighboring effect, playing a leading role for medium-sized cities in their metropolitan areas.

among them. Furthermore, a closer look also suggests that in some cases these cities may have a

neighboring effect, playing a leading role for medium-sized cities in their metropolitan areas.

*Sustainability* **2020**, *12*, x FOR PEER REVIEW 8 of 13

**Figure 2.** Inter-city networks. Node size is based on betweenness centrality in the network. A tie **Figure 2.** Inter-city networks. Node size is based on betweenness centrality in the network. A tie between nodes means they have at least two corporations in common.

between nodes means they have at least two corporations in common. Table S3 displays pairs of cities that share at least three corporations. This threshold allowed us to focus on those cases where participation in the network would provide a structural advantage for cities offering the possibility of a high level of interaction with companies and other cities. The pairs of cities with the highest number of corporations shared are Valladolid and Palencia, which are the capital of neighboring provinces. However, the reason for their close connection is that they established a platform known as Smart City Valladolid and Palencia to foster public-private collaborations for both joint and individual innovations in relation to Smart City development. As for the rest of cities with high numbers of shared corporations, we find different yet complementary situations. On the one hand, big cities such as Madrid, Barcelona or Malaga are usually well connected among them; on the other hand, they could benefit from a neighboring effect, that is, cities from the same region have more options to share the presence of the same firms. This is the case of cities such as Sabadell (near Barcelona) or Fuengirola (near Malaga), but there are opposite situations such as Madrid, which is in general poorly connected to its metropolitan cities. Table S3 in the Supplementary Materials illustrates these possible relations for cities sharing at least three firms. A total of 11 out of 15 pairs include at least one of the main Spanish cities, while eight cases feature some kind of connection, either top-to-top city, regional or metropolitan—variations that would deserve further research combining a quantitative and qualitative analysis and exploring causal factors such as the socioeconomic structure or the political parties in government. However, while factors such as regional and metropolitan links could help explain the cities' connections, it seems Table S3 displays pairs of cities that share at least three corporations. This threshold allowed us to focus on those cases where participation in the network would provide a structural advantage for cities offering the possibility of a high level of interaction with companies and other cities. The pairs of cities with the highest number of corporations shared are Valladolid and Palencia, which are the capital of neighboring provinces. However, the reason for their close connection is that they established a platform known as Smart City Valladolid and Palencia to foster public-private collaborations for both joint and individual innovations in relation to Smart City development. As for the rest of cities with high numbers of shared corporations, we find different yet complementary situations. On the one hand, big cities such as Madrid, Barcelona or Malaga are usually well connected among them; on the other hand, they could benefit from a neighboring effect, that is, cities from the same region have more options to share the presence of the same firms. This is the case of cities such as Sabadell (near Barcelona) or Fuengirola (near Malaga), but there are opposite situations such as Madrid, which is in general poorly connected to its metropolitan cities. Table S3 in the Supplementary Materials illustrates these possible relations for cities sharing at least three firms. A total of 11 out of 15 pairs include at least one of the main Spanish cities, while eight cases feature some kind of connection, either top-to-top city, regional or metropolitan—variations that would deserve further research combining a quantitative and qualitative analysis and exploring causal factors such as the socioeconomic structure or the political parties in government. However, while factors such as regional and metropolitan links could help explain the cities' connections, it seems that the cities' links seem to follow a hierarchical logic, with bigger cities more often connected among them.

that the cities' links seem to follow a hierarchical logic, with bigger cities more often connected among them. To capture the whole complexity of the data informing the visualization, Table S6 includes individual measures of degree, betweenness and closeness. Moreover, a Gini coefficient is computed for each measure to assess the inequality of the three indicators. These measures reveal two further features of the network as a whole. First, betweenness indicates that even the most successful brokering cities acting as the shortest path between two other cities do not play this role very often: Malaga scores 3.3, followed by Barcelona or Santander, with scores below 3. Accordingly, these cities tend to have low scores of degree and closeness, indicating they are poorly connected to the other cities. Second, although the network is characterized by low centrality levels, there are high To capture the whole complexity of the data informing the visualization, Table S6 includes individual measures of degree, betweenness and closeness. Moreover, a Gini coefficient is computed for each measure to assess the inequality of the three indicators. These measures reveal two further features of the network as a whole. First, betweenness indicates that even the most successful brokering cities acting as the shortest path between two other cities do not play this role very often: Malaga scores 3.3, followed by Barcelona or Santander, with scores below 3. Accordingly, these cities tend to have low scores of degree and closeness, indicating they are poorly connected to the other cities. Second, although the network is characterized by low centrality levels, there are high disparities among cities, as reflected in the high Gini's coefficient on betweenness (0.88) and degree (0.79), given that most cities never act as brokers between another pair of cities and tend to have few connections to other cities.

disparities among cities, as reflected in the high Gini's coefficient on betweenness (0.88) and degree (0.79), given that most cities never act as brokers between another pair of cities and tend to have few A possible explanation for this situation is that firms may feature higher levels of connectivity and brokering capacity, aspects that we explore in the next subsection. connections to other cities. A possible explanation for this situation is that firms may feature higher levels of connectivity and brokering capacity, aspects that we explore in the next subsection.
