Information origin

A semi-structured survey was applied to the actors that comprise the hub: farmers, extension agents, teaching and research institutions, input suppliers and government institutions, among others. Four hundred fifty-seven (457) actors were analyzed in 10 agroecological regions (figure 1) in the analyzed hubs (table 1).

Source: Prepared by the authors

Figure 1 Locations of the agroecological regions that comprise the hubs assessed in this study. 

Table 1 Number of actors included in the network and interviewed per agroecological region and hub 

Note: In the case of Bajío, the analysis grouped three agroecological regions that comprise the hub.

Source: Prepared by the authors based on information from surveys conducted between 2015 and 2016

The number of actors interviewed obeys to direct non-probabilistic sampling. Surveys were applied by technical staff at Cimmyt, from October 2015 to October 2016. The survey comprised of two parts: in the first part, the identification of the actor was considered: name, age and the institution to which he/she belongs; in the second part interviewees were asked about their relations to MasAgro, i.e. who they deal with regarding technical aspects on sustainable maize and wheat practices, and year they started doing this. It is worth mentioning that actors interviewed were free to mention all those actors they remembered at the time of the interview.

Information analysis

Social network analysis (sna) was used for data analysis, based on the premise that social actors are independent and that the links established among them have important consequences for each one (^{Freeman, 2004}); moreover, it uses a mathematical technique to analyze relationships between actors, as well as patterns and implications of those relationships (^{Wasserman & Faust, 1994}).

In innovation management processes, sna is a tool that allows studying the structures that are formed before and after an intervention process (Aguilar- Gallegos et al., 2017; ^{Díaz-José, Rendón-Medel, Aguilar-Ávila & Muñoz-Rodríguez, 2013}; Sánchez- Gómez, Rendón-Medel, & Cervantes-Escoto, 2016).

Moreover, to capture relational information a catalog in which unique keys were assigned to each actor was used. The relational file was initially processed in the NetDraw program (^{Borgatti, Everett, & Freeman, 2002}), to obtain the visual representation of the network, and then it was exported to the program Ucinet 6.288 to carry out subsequent indicator analyses.

The analysis considered two moments: 1) before the implementation of the hub in the region (LB) and 2) after its implementation (LF). Taking into account that the hubs began operating in the agroecological regions at different times, the years of analysis vary for each one (table 2).

Table 2 Year (moment) in which the analyses (before (lb) and after (lf) the implementation of the hub) were carried out per agroecological region 

Source: Prepared by the authors, based on information from surveys conducted between 2015 and 2016

Moreover, the relationships that were considered as LB correspond to all those that already existed in the year the hub was implemented in the agroecological region. This means that in each of the analyzed territories there were already a certain number of relationships already established.

Furthermore, the quantity and the quality of the relationships are established with density and diversity indicators, and the local structure where triads, transitivity and proximity censuses were carried out. For a better comprehension, indicators are explained below:

Density

Refers to the proportion of all existing relationships compared to the ones that can possibly occur within a network (^{Wasserman & Faust, 1994}).

Triad census

A triad is a set of three actors with possible relationships between the three (^{Wasserman & Faust, 1994}), and a triad census summarizes the local structure of a network (Faust, 2006). Based on the types of triads defined by ^{Holland and Leinhardt (1970)}, authors as ^{López-Torres (2013)} proposes three progressive levels in rural sector networks in order to favor innovation transfer (figure 2).

Source: ^{Holland and Leinhardt (1970)}, adapted by ^{López-Torres (2013)}

Figure 2 Classification of triads according to their potential to favor the technology transfer and innovation. 

According to ^{López-Torres (2013)}: i) initial triads do not favor communication between actors and are found in widely dispersed networks; ii) triads in evolution are the most common ones found in rural sector local networks, and receive this name because they are in the middle of the technology transfer process. Finally, iii) promoter triads are ideal for transferring technology and innovation.

Transitivity

It is the number of transitive triads divided by the number of triads that meet the conditions to be transitive (^{Faust, 2006}). ^{Holland and Leinhardt (1970)} argued that “interpersonal relationships tend to be transitive if actor A chooses B and B chooses C; then, it is likely that A chooses C”.

Diversity in relationships

A network has mutually exclusive groups with their own characteristics and, therefore, diversity of relationships is an index that is calculated by subtracting the number of internal links from the group to the number of their external links, and dividing it by the total number of links (Krack- hardt & Stern, 1988).

In this case, the variable that was used to divide the groups was the function of each of the actors in the network, i.e. whether they are farmers, extension agents, government, teaching and research institutions, or inputs suppliers, among others.

Figure 3 indicates that values close to -1 represents equality in relationships (homophily), and those that approach 1 represent diversity in relationships between groups (heterophily).

Source: Prepared by authors, based on ^{Krackhardt and Stern (1988)}

Figure 3 Diversity of relationships scale. 

Closeness

Measures the geodetic distance between the actors in the network; in addition, greater closeness values indicate shorter distances and times, as well as lower communication costs (^{Freeman, 1978}).

Once the base was generated, a “t” test was applied in related samples to measure changes in density indicators, diversity of relations, transitivity and closeness. Subsequently, with the values obtained from the indicators of the final lines, a Pearson’s correlation test was applied, in order to evaluate the structures and relational capital of the hubs analyzed. The average closeness indicator was used as a reference to establish quadrants. This analysis was carried out with the SAS program for Windows version 9 (Statistical Analysis System [SAS], 2004).

Results and discussion

Regarding the relational capital of the networks, the diversity value showed a slight decrease (from 0.43 to 0.41) at the time these were analyzed; this implies that they statistically remain as heterophilic networks (table 3). The persistence of heterophilia in the network is because the hub is a space in which a diversity of actors interact, i.e. farmers, extension agents, input suppliers, and governmental, teaching and research institutions.

These actors can be classified as internal or external to the innovation (^{Sánchez-Gómez, Rendón-Medel, Díaz-José, & Sonder, 2016}), since it is based on the fact that in a network there are mutually exclusive groups (^{Krackhardt & Stern, 1988}). Largely, the success of the hub model depends on the links that are made between these actors.

According to ^{Corsaro, Cantù and Tunisini (2012)}, these interactions allow obtaining information regarding new production ways, as well as services support and external backstopping. While we cannot say that hubs have improved the relational capital in the analyzed regions, it has worked perfectly well as a platform in which constant interactions are promoted.

Changes generated in density, proximity and transitivity indicators are shown in table 3. In this sense, mean comparisons show significant differences in indicators in relation to the moments analyzed. Nonetheless, an increase in density value refers to more saturated networks. This result coincides with the work published by Aguilar- Gallegos et al. (2017), who after an intervention in a goat system, found that density values ranged from 1.18 % to 1.82 %. On the other hand, Sánchez- Gómez, Rendón-Medel and Cervantes-Escoto (2016) identified a change from 0.56 % to 1.08 % after an intervention process with sheep farmers.

Table 3 Changes showed by indicators per analysis moment 

Note: The figures identified with * have a p < 0.05. N: Number of observations (per region); lb: before the implementation of the hub in the region; lf: after its implementation.

Source: Prepared by the authors, based on information from surveys conducted between 2015 and 2016

According to ^{Coleman (1988)}, denser networks favor trust and rules among actors, since they facilitate the application of more effective sanctions among them. In addition, density influences transitivity and closeness values.

^{Díaz-José et al. (2013)} mention that the effect of significant transitive triads points out to the existence of a network closure and represents an increase in relationships among actors; thus, promoting a greater information flow in innovation processes, which translates towards the creation of social capital. Likewise, ^{Burt (2000)} mentions that the social capital metaphor refers to the fact, that when people are better connected, the results obtained will also be much better.

Further, according to ^{López-Torres (2013)}, the ideal triads for transfer of technology and innovation would be, in order of importance: the promoters, the ones in evolution, and finally the initial ones. In this sense, figure 4 shows the changes that occurred between the moments analyzed. In this regard, all regions showed a decrease in initial triads and an increase in the ones that are in evolution an in the promoters, although in the latter it was lower.

Source: Prepared by the authors, based on information from surveys conducted between 2015 and 2016

Figure 4 Changes in the proportion of triads according to their potential to contribute to innovation within networks in agroecological regions that comprise hubs. 

Although, the initial triads are still the ones with the highest proportion in the networks (98.9 %), the change that occurred in the ones that are in evolution and the promoters regarding the moments in which they were analyzed is relevant. This is because, as mentioned by ^{Gómez-Carreto, Zarazúa, Ramírez-Valverde, Guillén-Cuevas and Rendón-Medel (2016)}, this type of triads could contribute to information exchange, as well as to the development and strengthening of technological capabilities.

Therefore, these processes are already taking place in the hub networks. In addition, significant increase in transitivity value (table 3) indicates a greater possibility of a transition from the evolving triads into promoter triads. However, ^{Faust (2006)} states that this probability depends on the size and density of the network.

The correlation analysis carried out with the final lines (table 4), shows a link between diversity of relationships and closeness of the network, with a very strong degree of association, a level of significance p < 0.05, and a positive relationship. In other words, the closeness that exists in a network increases as the value of the diversity of relationships is positive or if the networks tend to be heterophilic.

Table 4 Correlation between indicators and level of significance 

Note: *p < 0.05; N = 10

Source: Prepared by the authors, based on information from surveys conducted between 2015 and 2016

The relationships showed in table 4 suggests that in the regions analyzed there have been relations that, as ^{Sánchez-Gómez, Rendón-Medel, Díaz-José et al. (2016)} mention, they offer on one side social support and a motivation source (linkage with internal actors) for innovation, and, on the other side, they provide specialized services needed for production (linkage with external actors).

Similarly, current proximity indicator values show greater accessibility to the relational capital within the network, since, according to ^{Freeman (1978)}, they showed shorter distances and times and lower costs when communicating (table 3).

Figure 5 shows the position of each of the regions that comprise the hubs according to their level of diversity of relationships and closeness within the network. This figure shows that the regions that comprise the high valleys and the north Pacific hubs behave very similar; this suggests a similar way to manage relationships, plus the fact that these have similar conditions, i.e. they are the only hubs that groups several agroecological regions.

Source: Prepared by the authors, based on information from surveys conducted between 2015 and 2016

Figure 5 Position of the agroecological regions that comprise the hubs according to their diversity of relationships and closeness. 

In contrast, the cases of Bajío and Guanajuato are surprising, i.e. regions that until a few years ago comprised the same hub, but that currently show a different way of managing relationships. This difference can be explained by the fact that the Guanajuato hub already had a learning curve, acquired from the time it was part of the Bajío hub.

The south Pacific hub (Oaxaca) showed a network with the lowest closeness values compared to all the others, but this value is due to the large number of actors that comprise this hub (229 actors). Therefore, this value is considered acceptable, since the network has a closeness value that is higher compared to the one showed in the beginning of the intervention. Finally, the Chiapas hub presents a favorable location in terms of structure and relational capital.

For future research, the authors suggest to analyze the socioeconomic and agricultural contexts of the territories, since these can favor or limit the interactions. Likewise, given the importance of relational capital, processes that help improve the diversity of relationships between the actors should be assessed. Finally, the relationships that ceased to exist during the intervention should also be analyzed, given that their absence can influence the way in which innovation is managed.