Date Published: October 19, 2016
Publisher: Public Library of Science
Author(s): Ana María Hernández-Hernández, Dolores Viga-de Alva, Rodrigo Huerta-Quintanilla, Efrain Canto-Lugo, Hugo Laviada-Molina, Fernanda Molina-Segui, Peter Csermely.
We use complex network theory to study the differences between the friendship concepts in elementary school and university students. Four friendship networks were identified from surveys. Three of these networks are from elementary schools; two are located in the rural area of Yucatán and the other is in the urban area of Mérida, Yucatán. We analyzed the structure and the communities of these friendship networks and found significant differences among those at the elementary schools compared with those at the university. In elementary schools, the students make friends mainly in the same classroom, but there are also links among different classrooms because of the presence of siblings and relatives in the schools. These kinds of links (sibling-friend or relative-friend) are called, in this work, “mixed links”. The classification of the communities is based on their similarity with the classroom composition. If the community is composed principally of students in different classrooms, the community is classified as heterogeneous. These kinds of communities appear in the elementary school friendship networks mainly because of the presence of relatives and siblings. Once the links between siblings and relatives are removed, the communities resembled the classroom composition. On the other hand, the university students are more selective in choosing friends and therefore, even when they have friends in the same classroom, those communities are quite different to the classroom composition. Also, in the university network, we found heterogeneous communities even when the presence of sibling and relatives is negligible. These differences made up a topological structure quite different at different academic levels. We also found differences in the network characteristics. Once these differences are understood, the topological structure of the friendship network and the communities shaped in an elementary school could be predicted if we know the total number of students and the ties between siblings and relatives. However, at the university, we cannot do the same. This discovery implies that friendship is a dynamic concept that produces several changes in the friendship network structure and the way that people make groups of friends; it provides the opportunity to give analytic support to observational studies. Communities were also studied by gender and we found that when the links among relatives and siblings were removed, the number of communities formed by one gender alone increased. At the university, many communities formed by students of the same gender were also found.
Social scientists have been studying the complex relationships among persons using friendship as a linkage parameter [1–4]. Friendship has a different definition over time; at the preschool level, it is reduced to the relationship among children that play with each other. In adolescence it is defined as the basis of activities that are shared with others, and for adults, the friendship definition rests in face-to-face contact and its frequency . Friendship, as a historical phenomenon, which is complex, dynamic, and sensitive to influence, has been studied in different ways [6, 7].
We began by analyzing the survey results reported in which three elementary schools were considered . The networks extracted from the three schools: E1, E2, and E3 are made up of 108, 226, and 419 students, respectively. An elementary school is defined as a school for children between 6 to 12 years old. All the elementary schools consisted of six grades, ranging from 1 to 6. A survey at the Universidad Marista located in Mérida city in Yucatán State was also conducted. This fourth friendship network from the university has 1,891 nodes and the ages of the participants are between 18 and 24 years. Specifically, we asked respondents to name his or her friends from the university population. They had to include only close face-to-face friends that did not include friends from electronic social networks (like Facebook, Twitter, etc.). We obtained written permission from the guardians and students enrolled in the study. In all cases, we have written consent from the relevant ethics committees. The study on the elementary schools was approved by the Comité de Bioética para la Investigación en Seres Humanos (COBISH) from Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. The study at the university was approved by the Comité de Ética e Investigación de la Escuela de Ciencias de la Salud from Universidad Marista de Mérida. It is important to clarify that the surveys, although similar, were not applied in the same form. In the elementary schools, the studies were supervised personally by professionals in the area of human ecology. There was no possibility of using electronic devices because of the remote area the schools are in. In the case of the university, we conducted the survey using the Internet through a platform that we designed for that purpose, after a brief description of the necessary information to do with the research. We were interested in these different academic levels as they represent the initial and final levels of the formal educational system. We choose these particular areas because of the differences between them. In the countryside, the size of the rural communities comprises a population of around 1,000-2,000 people, with big, close families with low-middle incomes. Most of these people have lived there since they were born. On the other hand, Mérida city has a population around 980,000 people, many of them from other parts of the country or even from other nations. The elementary school E3 is located in a zone of the city categorized as middle-high income. This difference in the population size and its composition is interesting with respect to the behavior of the children evaluated, when they are observed from the perspective of a friendship concept evaluation. Even when the structures of the schools are the same (six grades, different classrooms), the number of sibling or relatives is significantly different in the rural areas compared with the urban area of Mérida. This influence of the family ties lets us study the difference in the network owing to those types of links. We chose the university mainly because the difference in age ranges compared with the age ranges in the elementary schools. Table 1 shows all the information concerning the characteristics of the elementary schools and the university. By extracting information from the surveys, we determined the corresponding adjacency matrix (A) for each of the networks. We noticed that the networks were directed, as the adjacency matrix A was not symmetrical.
This study was conducted using the adjacency matrices obtained for each of the networks that are depicted in Table 2. The properties that characterize these social networks are also displayed. The general conditions on which students were at the institutions are shown in Table 1. The three elementary school networks are all connected once the siblings and relatives to the friendship set are incorporated. If we do not consider these links, the networks corresponding to schools 2 and 3 become disconnected. On the other hand, the university network is disconnected, and is formed by 61 components.
In Table 2 one can see that the elementary schools networks and the university network have quite different characteristic values, except for the clustering coefficient. The average degree for the university network is considerably lower than the values found for elementary schools. In Table 3, the probabilities of being linked with a partner in the same classroom (Pin) and the probabilities of being linked to a partner outside the classroom (Pout) are shown. One can observe from these data that the probability of being linked with partners in the same classroom is higher when the mixed links in the network are not included in the elementary schools. On the other hand, in the university network, the probability of being linked to a partner in the same class is lower than the probability of being linked with a partner from another class. That is the reason why 〈k〉 and ρ are larger for elementary school networks than for university networks. Thus we can say that the concept of friendship creates the topological network in a specific way. We consider the way students are linked in a classroom predictable only in the case when they belong to an elementary school. It is clear that for elementary school students, the friendship concept is so wide that siblings and relatives also belong to the category. One can see in Table 4 that school E3, the one urban school, presents a high number of communities classified as CHm, at least when compared to the other two schools (E1 and E2). It should be noted that it is at this school that the number of relatives and siblings is much fewer than at the other two. This means that friendship is really a spatial concept at this stage of education, where there is a high probability that friends are those within the classroom. To test this hypothesis, we eliminated the mixed links in the schools and checked if there was an increase in the CHm communities. The results are shown in Table 2. When compared with the results depicted in Table 4, we concluded that indeed, the CHm and UHm communities are increased in this case. Therefore, according to the results, spatial confinement favors the formation of friends at this level of education. With university students, it is a different situation. These students have a more defined concept of friendship and therefore do not necessarily consider classmates as friends. One may conclude that spatial confinement has no relevance to having a friend at the university. Even though we also find communities that can be large, most students are in different classrooms; therefore, the type of community is UHt. At this level, we do not have mixed links with relatives and siblings, which is opposite to the case of elementary schools. We have also studied the communities and the gender of the nodes that make up part of each one; at all educational levels, a preference exists to be linked with persons of the same gender, especially when the influence of siblings and relatives is not included (see Table 4). One of the limitations of this type of work is the difficulty of obtaining the data, which is a lot of work and is an slow process that does not provide all the information we need. Another limitation is not having all the information about external factors, which implies the need for not only working with students, but also with their families. There are also regulations such as ethics approvals with which we have to comply. However, we are working to construct a robust database with data not only for friendship networks in Yucatán but also in other places and other grades including secondary school and high school. The strengths of the study lie in exploring the friendship networks and understanding the changes in these at each level and also in learning about the internal variations owing to family ties. Understanding these structures will let us model the dispersion of information or diseases in these kinds of populations. The construction of these kinds of networks is relevant to having a better understanding of the development society. These findings let us know how family ties could affect other areas of life, and are a step to understanding the complexity of social interactions at different ages. In Yucatán, children are in the principal groupaffected by diseases such as Chikungunya or the Zika virus, influenza or dengue fever. This knowledge could provide the opportunity to create another kind of work in future, for example, how to model the dispersion of illness in these types of social communities once we know the topology of the network and how children form communities in the network. This work is one step in constructing a robust database to start with directional work into diseases predict not only in Yucatan but also in other areas with similar problems.
From the study of friendship networks presented we can conclude that, in general, the differences in topologies between the elementary school networks and university networks are an effect attributable to the concept of friendship, which changes over a lifetime. However, a bigger effect is visible when communities in the networks are studied as the basis of family ties, friendship ties, and spatial confinement (Tables 2, 3, and 4). We can also conclude, on the basis of the networks analysis that: 1) the concept of friendship is clearly different at both educational levels and this can be observed from the topology characteristics of the networks and the difference in the percentage of mixed links present in the networks, 2) the mixed links produce a social effect in the elementary schools, which changes the distribution of students in the communities; however, the presence of relatives and siblings does not eradicate completely the effect produced by spatial confinement, 3) it could be possible to predict the topology of other elementary schools if we knew the number of students and mixed links between them; however, this is not possible at the university, 4) at the university, a clear difference exists between the kinds of relationships in which the students are involved, and that is why the percentage of mixed links in this network is low, and 5) it is apparent that the friendship concept has a high personal component that produces a low reciprocity in the university network, a disconnected network, and a large number of small components.