Introduction

In Mexico, there is a marked tendency to promote technological innovation projects in rural areas, where it is assumed that it is sufficient to develop the technology in research centers, whether domestic or foreign, to subsequently transfer knowledge in a "mechanical" to users, inertia refers to the linear model of technological innovation with two characteristics: (i) not always the technology supply matches the demand; and (ii) not properly value the tacit knowledge (^{Hernandez et al., 2005}; ^{Zarazua, 2007}; ^{Muñoz and Santoyo, 2010}). In this context various ideas ranging from the introduction of machinery to new crops to increase productivity, efficiency and profitability of the field in Mexico are registered; this ultimately reflects the interest in improving the conditions of social and economic welfare of the inhabitants, especially those that are embedded in local production systems located in rural areas.

However, there is abundant empirical evidence that accounts for the limited impact of programs and projects doomed to invest in technology, where the supply of inputs and marketing of equipment for agricultural activities particularly prevalent favoring private initiative (inputs, genetic among others) and even contributing to technological dependence, which would not be an alert if it were not for two reasons: 1) it does not appear that improve the competitive positioning of agribusinesses; and 2) it neglects the incorporation of innovative practices that contribute to sustainable management of natural resources: increasing organic matter in soils, rational use of agrochemicals, optimal water use, integrated pest management, and others (^{FAO, 2005}; ^{FAO- SAGARPA, 2007}).

This, due to a reductionist view of innovation in the sense that it is limited to encourage the adoption and incorporation of tangible tools or machinery to produce a product (hard technology), inertia to which ^{Swanson (1997)} categorizes as a material technology : tools and equipment, among others, belittling technology knowledge: know-how, leading largely to improvements made do not impact on improving the competitiveness of the sector and companies alike by generating wealth through jobs and income. This allows question the logic and direction of public policy in Mexico and highlights the discussions on the various aspects related to innovation and multi-causal and multi-nodal nature (more than one actor) (^{Koschatzky, 2002}) field of study of regional environments and innovation networks, which recognizes innovation as a social process (^{Cimoli, 2000}; ^{Caravaca et al,. 2003}; ^{Formichella, 2005}).

This study struggle for the analysis of innovation as a result of interactions between actors sharing a territorial context with their social, cultural, institutional, political and other nuances. I.e. producing goods and services and economic activity, it is an act that is not separated from social reproduction as a whole (^{Becattini and Rullani, 1996}), meaning that economic activity provides a means for reproducing values, knowledge, institutions and physical environment to provide continuity. In this perspective, not enough efforts of mechanical transfer of technology, it is important to explore under the social approach who are the people who manage to incorporate practices and routines to solving problems and meeting needs (^{Gonzalez, 1994}; ^{Long, 2007}).

Based on the above, bursts onto the scene an explanatory concept of the relationship between the quality of the links established within various networks and economic welfare (^{Knack and Keefer, 1997}), called capital, conceived as confidence , norms and networks of social organization that can improve the efficiency of society by facilitating coordinated actions (^{Putman, 1993}, ^{Putman and Goss, 2002}), which favor the presence of nodes that are organized into subnets and act as important catalysts of innovation with influence in regions, production systems, products or sectors of the economy (^{Morales, 2004}; ^{Robles, 2004}; ^{FAO, 2005}; ^{Valdiviezo, 2006}). These actors are the critical mass of the innovation process, about, ^{Dutrénit et al. (2011)} indicate that the critical mass is the main mechanism to promote co- evolutionary processes necessary for the implementation of development processes and induce economic growth and development.

^{Ambriz et al. (2013)} state that all collective actions depend on the mass of individuals "who behave differently from the rest of the group, are this small segment of the population who choose to make great contributions to carry out collective action, are these few individuals who also they diverge from the average". Therefore, the heterogeneity of the group makes it possible to reach a critical mass, it is precisely their diverse interests, resources and disposal elements that will enhance the formation of it, to the point that, at some point in their development process, critical mass could be sufficient to stimulate or "spread" to other players in the social system through certain communication channels in a precise time period (^{Granovetter, 1978}; ^{Valente, 1999}; ^{Olivier et al., 1985}).

The sociological theory of diffusion of innovations poses a proposed by ^{Rogers (1995)} model that relates the existence of a pattern that takes the form of S, as a growth curve or a logistic function (^{Rogers, 1995}), where the speed of adoption It deserves attention, since it is considered to estimate the degree of diffusion of innovations, and also presents a classic normal behavior (bell-shaped), in which it is possible to identify various actors: innovative (2.5% of adopters); early adopters (13.5%); first majority (34%); late majority (34%) and laggards (16%), all subject to the following determinants: (i) comparative advantage; (Ii) compatibility; (Iii) complexity; (Iv) propensity to trial; and (v) propensity to show the benefits and impacts arising from their use.

^{Dutrénit et al. (2011)} give a glimpse of the extent of critical mass by identifying three stages with a view to contributing to economic development within the framework of the trajectories of science, technology and innovation: (i) determination of the preconditions (governance, physical, human, infrastructure, etc.) to integrate critical mass; (ii) strengthening the interaction of the academic sector with the productive sector and creating the critical financial and technical infrastructure; and (iii) continuity of generalized systemic interactions and trading systems financial and technical support to foster new critical mass and improved capabilities in emerging areas. In this exhibition the critical masses as a prelude to the integration of regional environments requirement recognized.

The critical masses, while, promoting learning and knowledge are vital in organizing production processes in a given territory. The presence and local clustering of these actors creates an environment or innovative means, or what is the same: a regional environment for innovation. This implies the presence of actors interacting, and its nature of producers, users, suppliers, customers (^{Rozga, 2003}), and others who meet a key role in the framework of local action and incubating innovative activities. The environment for innovation "refers to the specific social and cultural heritage linked to the development of territorial production systems" (^{Morales, 2004}).

In this regard, the importance of the concept is that seen as vital research activities and development, and also the involvement and participation of companies, institutions and other organizations that generate, disseminate and use new knowledge and economically useful activities production (^{Fisher, 2001}), recognizing the links between the actors involved, from those set out in formal structures and considered essential regulations and contracts, until the minimum personal contacts where the territorial closeness and trust relationships are fundamental, plus the material aspects (enterprises and infrastructure), intangible (know-how, rules), specific institutional learning and logic (^{Maillat and Grosjean, 1999}).

^{Maillat and Grosjean (1999)}; ^{Fischer (2001)}, emphasize the concept of networks of actors, with details of their importance in the regional environment for innovation. ^{Zuluaga et al. (2012)} incorporate elements that combine aspects found in macroeconomic and microeconomic structure, "the characteristics of the regional environment [are] gross domestic product per capita, total exports from the region, the regional government investment in research and development, the number of graduates with undergraduate degree, the number of active researchers and the number of institutions of higher education in the region", dimensions that help explain the so-called economic growth and development.

Rózga (2013) mentions that a peculiarity of the systems [environments] regional is in focus "bottom-up" because right in the micro space, where it is possible to focus on internal interactions between agents and institutional arrangements; thus, it was analyzed in an exploratory manner the innovation network of tomato production system of the Plateau Comiteca, Chiapas, Mexico, using the census triads based on input from ^{Holland and Leinhardt (1970}, ¹⁹⁸¹⁾ in order to glimpse the potential of an analysis algorithm with methodological rigor that helps support public policy decisions about improving the process of diffusion of agricultural innovations into local production systems.

The hypothesis considers that the critical mass is a fundamental concept in the context of regional innovation environments in order to contribute to economic development and growth of Chiapas, based tomato production system; however, given the complexity to assess the stage of development of critical mass, based on input from ^{Holland and Leinhardt (1970}, ¹⁹⁸¹⁾; ^{Faust (2006)} from the perspective of social networks and the theoretical model approach is proposed Everett Rogers (sociological theory of diffusion of innovations), which refers to the existence of a pattern that takes the form of growth curve, and the participation of so-called innovative (approximately 2.5% of the adopters) that could be identified critical mass.

According to data for the period 1999-2012 (^{FAO- FAOSTAT, 2013}) the main tomato producers in the world were China (average production 34.45 million tons), USA (12.83 million tons), India (10.22 million tons), Turkey (9.93 million tons) and Egypt (7.89 million tons), while Mexico ranked tenth (2.87 million tons). The main states with the greatest contribution to the production of tomato are Sinaloa, Baja California and Michoacan, while Chiapas contributes about 1.15% (average 1999-2012 production 30 198.82 t).

Particularly the development of tomato cultivation in the state of Chiapas has been very singular, for example, in the period 1980-1998, production was based primarily on intensive growth. The determination of the factors affecting the growth of production were determined based on input from ^{Contreras (2000)}, using the equation:

P_t= A₀(Y_t - Y₀) + Y₀(A_t - A₀) + (Y_t - Y₀) + Y₀(A_t - A₀)

Where: "P_t"= refers to the total increase in production for the period of analysis, "A₀(Y_t-Y₀)"= quantifies the contribution by performance, "Y₀(A_t-A₀)"= quantifies the contribution by surface “(Y_t-Y₀) + Y₀(A_t-A₀)”= quantifies the combined effect of performance and area," A₀ and A_t"= is the harvested area at the beginning and end of the period analyzed, respectively, "Y₀ y Y_t"= is the performance at the beginning and at the end of the reporting period respectively.

The formula used was:

Where: "n"= number of years of the series, "V_f"= final value of the series and "V_i"= initial value; i.e. through increased income attributable to an improvement in the technological level, which is supported by an average annual growth rate. The formula used was:

Where "n"= number of years of the series, "V_f"= final value of the series and "V_i" initial value. (TMCA) of 8.34% in yield (average 15.56 t ha^-1) and TMCA= -3.85% on the average (782.75 ha) harvested area; meanwhile, the production of tomatoes for the period 1999-2012 was based on a combined (average 31.36 t growth refers to increased area and yield equally (^{Contreras, 2000}) and supported by an TMCA= 1.93% yield (average 31.36 t ha^-1) and TMCA= 2.23% in the harvested acreage (948.30 ha) (^{SAGARPA, 2013}).

Materials and methods

The study was conducted from February to September 2012 and January to march 2013 in 45 jitomateras locations in the municipalities of Comitan, La Trinitaria, Independencia and Las Margaritas, seated in the third district of rural development in Chiapas, with interviews 52 social actors of tomato production system identified through the snow ball technique under the mapping of major players described by ^{Zarazúa et al. (2009)}, a situation that allowed integrating a network of 218 nodes, stopping data collection when references provided us little information.

Additionally, two control measures were observed at the time of data collection: a) the first interview an actor had to be identified by sampling in four municipalities and recognized activity; b) frame referencing actors with whom the respondent establish some kind of strictly related link with their role in the production and marketing of tomato but also showed a tendency to share information that would improve various tasks of cultivation and sale of the vegetable.

Agricultural entrepreneurs interviewed have an average age of 47.16 years and 15.88 years of experience in growing; 6.95 years of years of study. Predominant ejido tenure (1.6 ha and 1.3 ha irrigation temporary). The marketers have on average 16 years developing this task, your age corresponds to 37.5 years with completed primary, and capture around 1,072 t per month.

The collection instrument used integrated three sections: a) identification of the respondent, respondent's name, municipality, years in the region, date and other general data; b) main problems in the production of tomato; and c) related stakeholders. The data obtained in the first and second sections were captured in Microsoft Office Excel 2007. The section of stakeholders, was captured in notebook, employing the DL protocol, which is a flexible language to describe the data in this case they refer to a list of nodes, and the format edge list (^{Borgatti, 2002}). The information captured in notepad was subsequently analyzed in Ucinet 6 498 (^{Borgatti et al., 2002}) by the algorithm called census triads (^{Holland and Leinhardt, 1970}; ^{Faust, 2006}), as the basis of the study of regional environments innovation.

The triads are a group of three actors or nodes and possible relationships or links between them, which could refer to economic "realities", technological, social, among others, to identify the degree of development of critical mass, and therefore, prospects of regional environments for innovation in Chiapas. A focal element in this approach, it is the property of transitivity of real numbers, which, applied to the field of networks, it means that if the node A is linked to B and B is linked to C, then the actor A might be it linked to C. Behind the property, there is the tendency to "balance" and "reciprocity" between the triadic relations (when there are relationships between the actors). A special form of this idea is known as the "equilibrium theory" that especially works with relationships positive or negative effect. It is assumed that if A likes B and B loves C, then to A you should like C, or also, if A likes B and B does not like C, then to A should not like him C (^{Hanneman, 1999}; ^{Holland and Leinhardt, 1970}).

^{Granovetter (1973)} reports that transitivity is closely related to the strength of ties due to (i) the combination over time, referring to the transitivity and behavior of the triads (described below); (ii) emotional intensity; (iii) level of intimacy (mutual trust); and (iv) the reciprocal services that characterize the bonds, and to a lesser extent, linked to the social structure within a particular context in converging interests, actors and rules (formal and informal regulatory framework). Also, Granovetter argues that social network analysis (ARS) is suggested as a tool to link the micro and macro levels of sociological theory, can relate the ARS with a variety of macro phenomena such as social mobility, political, social cohesion and obviously the process of technological diffusion, based on the strength and/or weakness of the links established nodes.

In this scenario, ^{Holland and Leinhardt (1970)} conducted the census of triads with the formula:

Where: n= size of the individual network, k!= represents the factorial value of a triad group of three nodes, and (n-k)!= number of combinations or groups of triads in a network under a triad, considering base element of regional environments for innovation, by quantifying the possible combinations of all players taken in threes (triads), identifying 16 types triads which are based on coded linear combinations with three or four digits. The first digit refers to the number of reciprocal or mutual pairs, the second digit is indicates to asymmetric pairs, the third digit to zero or even unattached pairs, and the fourth digit refers to the orientation of asymmetric pairs. You can sort the codes set forth by Holland and Leinhardt into three groups: a) triads initials, made up of codes 003, 012, 102, and which are recognized as those core groups that make up the critical mass described by various authors under the sociological theory of diffusion of innovations; b) triads in evolution, which groups the codes 021D, 021U, 021C, 111D, 111U, 030C, 201; and c) promoting triads, which includes codes 030T, 120D, 120U, 120C, 210, 300 (^{Holland and Leinhardt, 1970}; ¹⁹⁸¹), same that would constitute the critical mass required by regional environments for innovation.

In the present work the following indicators were calculated to defect to glimpse macro level parameters Network:

Size of individual network. His expression was as follows:

Where: T_n= size of the individual network node n, and A_n= are those directly related to actor n. A larger network suggests that actors or nodes are mostly connected (^{Borgatti et al., 1992}).

Density. It is the percentage of relations between those possible. High densities extensive exchange manifest information available. The mathematical expression is:

Where: D= density, L= number of relationships and g(g-1)= number of possible relations. The density is expressed as a percentage: a density of 100% indicates that all actors are related; one of 0% indicates that all are loose (^{Wasserman and Faust, 1999}).

Index of centralization. It is the ratio of the sum of the differences in the degree of all nodes (d) the gross value of unipolarity (D), and the sum of the degrees of all players if one of them was the maximum possible (n-1), and the other minimum (1). The centralization index is calculated as follows:

Where: d= degree of each actor; D= maximum degree of an actor in the graph, and n= total number of actors. The index values range between 0 and 100%, with 0 being the value for the graph more centralized characterized in that a single actor n_i occupies the center and is connected to everyone else, while among these there is no connection, except with ni (^{Wasserman and Faust, 1999}).

The identifiers used for each of the actors and proportions of each type located, were as follows: AA= administrative assistant, 0.46%; AD= collection and distribution center, 5.97%; CF= final consumer, 1.84%; CI= buyer broker, 5.97%; ER= rural company with legal figure, 4.13%; FM= multiple functions, 16%; IE= research and teaching institution, 2.30%; IG= government institution, 6.88%; OR= rural-social organization, 4.13%; PF= provider of financial services, 1.84%; PI= input supplier for cultivation, 10.10%; PR= producer, 33.95%; PSP= provider of professional services, 5.97% and WE= nuclear family, 0.46%.

Results and discussion

The number of actors that integrates the system network is 218, it presented a low density (1.00%) with a remarkably high rate centralization (17.17%) compared to the density. Something similar happens in other intensive agricultural system in labor as is the strawberry system Michoacan which reached a density of 1.58% and an index of centralization of 18.16% (^{Zarazúa et al., 2011}), however, the density of jitomate system was greater than the density of the East the same (0.46%) guava system, observing similar behavior in the case of centralization index (10.2%) (^{Zarazua, 2007}). Regarding the values obtained in the indicators set out, it is worth mentioning that could be considered "normal" in the context of the formation and consolidation of innovation networks, suggesting the existence of a lot of work to be done in the sense of favoring the relational links between actors in the system.

On the other hand, the values reached in the index of centralization, above 10%, it helps to demonstrate the absence of an actor who is able to integrate all the interests of other actors involved with the system and network innovation, view to achieving a common goal. Similarly, these values also reflect that the network is in a stage of maturity chronological without this necessarily reflected in benefits for its members, which can be regarded as simply dispersed; i.e. where the sum of the individual innovation efforts are not significant.

Evidence of the above, are also the results of the algorithm developed by ^{Holland and Leinhardt (1970}, ¹⁹⁸¹⁾, which relate the existence of a total of 1 703 016 triads (100%), classified into three types: a) triads initials code 003 (1 611 641 triads), code 012 (83 537 triads), code 102 (3 559 triads); b) triads in evolution: code 021D (1 853 triads), 021U code (802 triads), code 021C (944 triads), code 111D (139 triads), code 111U (281 triads), code 030C (5 triads), code 201 (10 triads); and c) promoting triads: code 030T (155 triads), code 120D (35 triads), 120U code (25 triads), code 120C (17 triads), code 210 (11 triads), code 300 (2 triads).

Particularly the promoters triads represent 0.014386% of the total, which are the basis that would constitute the critical mass required by regional environments for innovation within the theoretical model of ^{Rogers (1995)}, which considers the existence of innovative adopter (2.5% of adopters and 13.5% of early adopters). The main attribute of the promoters triads is that given the links established by the participating nodes within the property of transitivity, could significantly contribute to the exchange of information, and gradually, the development and strengthening of technological capabilities.

However, the evidence found is possible to notice that the tomato production system is in a limited position regarding the technological learning process is concerned, in particular, by the number of promoters triads (245). In order to size from a quantitative perspective to the so-called critical mass in the context of sociological theory of diffusion of ^{Rogers (1995)}, without which the innovation diffusion process had no chance of realization, a minimum number of expect 42 575 promoters triads equivalent to 2.5% of triads obtained in the census (^{Holland and Leinhardt, 1970}; ¹⁹⁸¹⁾, Rogers located precisely as key to the process of adoption of innovations. At the moment, there is no evidence of 2.5% of innovators in the jitomate system, however, we must make clear that there is a process of diffusion of innovations, although with certain characteristics that limit the rate of adoption of innovations since no it has the context of support of innovative activity.

Within these peculiarities, it is the recognition of an inherent structure to the subject that enables learning, and in which knowledge is not spontaneous and supported by social relations with the consequent exchange of information and knowledge, but of course, with links differently intensity, to the point that at some point the trust, as an element of capital, could facilitate relations and exchanges with a lower cost of transaction favoring the so-called generalized reciprocity strongly marked with the tacit component, which fosters learning den by creative imitation and subsequently introducing innovations or incremental improvements in the territory-system, under the informal nature of social networks and innovation that show levels of articulation and dissemination based on relevant qualitative information (^{Lara and Diaz-Berrio, 2003}; ^{Zarazua et al., 2009}; ^{Putnam, 2011}).

The evidence found show that producer associations tend to be organized or simulate organized in companies, in order to obtain financial support, unveiling a strategy that is confirmed by analyzing the composition of the company, having in the background as explanation cultural dimension reflected when they express that they do so because "it has always been better learn and work alone," which is not pleasant to deal with different ways of doing things, then leaving the company with a strong family structure. ^{Rogers (1995)} mentions that the values, beliefs and experience are important factors in making innovations.

Thus, it follows that several of these interrelationships to communicate information with others, where those others are not family and are expressed during the collection of field data, may not be entirely true. However, these entrepreneurs are in the process of innovation, with other features of interrelation certainly, but ultimately interrelated because as productive system, now with a little over 51 years after the introduction of the tomato, is itself a regional environment which catalyzes the introduction of innovations, though with limited speed of adoption of innovations, for example, the same adoption of greenhouses or even other vegetable cultivation.

Another angle of reflection we want to use here, reside in the possibility that as it is a social network that is evolutionary process, the critical mass still rests on those actors who have managed to centralize a number of relationships, in fact a hypothesis derived of census results triads to find two of them code 300, it is that these involve those actors with the highest degree of mention, as the first to introduce pavilions and greenhouses in the territory of study. It is the actors who folios FM01, FM02, FM03 and FM04, who happen to be married and are part of so-called key players in the system, identified by ^{Corona (2005)} as propellers nodes of the innovation process is assigned, since steadily they occupy positions where they can influence from public administration and private enterprise, to promote particular projects related to agriculture protected in the territory.

^{Rogers (1995)} has extensively addressed the discussion in this document, by the relationship established between heterophily and dissemination. A principle of human communication, is that the transfer of ideas takes place between individuals who are quite similar (homophilia). The opposite is precisely the need or facility that exists to interact with strangers, are the points of social distance, cultural, instructional, racial and as many (heterophily); such concepts were evidenced in the field; for example, social actors introducers pavilions and greenhouses (native of Puebla) in the system are still perceived as foreign by a series of cultural differences, and this has limited the development of the network and effective communication systems; consequently, the poblano have strengthened their family ties (homophiliac group) as a means to help create and sustain a critical mass of innovation; however, recognize that without the strong involvement of local agribusinesses, is at risk in the medium and long term, the innovative dynamics of the system itself, given the limited ability to adhere to processes of change and improvement.

Conclusions

The innovation network of tomato production system in Chiapas integrates 218 actors and considering the combinations proposed by ^{Holland and Leinhardt (1970}, ¹⁹⁸¹⁾ algorithm, were calculated a total of 1 703 016 triads (100%), of which, 245 are triads promoters that could contribute to the development and strengthening technological capabilities, while not reaching the number of 42 575, equivalent to 2.5% of innovators in the jitomate system, based on the proposals of the theoretical model of ^{Rogers (1995)} and adopter categorization.

The evidence found glimpses a multifactorial aspect of the innovation process, where the singular presence of regional environments for innovation is crucial, given the nature of the productive system and territory (standards, links, cultural aspects and even dogmas surrounding the technological user). In this scenario, innovation networks of tomato production system plays an important role considering the size of the population, power relations established between the actors involved, the influence of key players and the mass media.

Thus, the main contribution of the study is the integration of a methodological proposal that could help to support decision-making of public policy regarding the optimization process of diffusion of agricultural innovations, particularly in the diagnostic stage, to determine whether the conditions for the implementation of projects. It is in short, not to initiate innovation processes sustained substantial investments from public spending without recognizing and strengthen a number of actors that could become critical mass.

Identify potential critical mass for the diffusion of innovations, it is a desirable measure before committing resources to obtain the best possible results. Thus, it would work more with guidance to improve the competitive position of production systems established in rural areas.