modeling social network topologies in elementary schools

Plosone | Complex networks are widely applied in disciplines as varied as economics [1], biology [2], information technology [3] and sociology [4], [5]. Further development of complex networks theory is therefore a vital research area, with recent efforts focusing on measurements [6], topologies [7], [8] and the way data is disseminated through them [9].

Complex networks are a tool for modeling systems in which elements interrelate. Social networks are systems that describe phenomena in which individuals interact within a society (e.g. people, companies, etc.); nodes represent individuals and links represent the social relationships between them. Recent research has focused on the patterns of face-to-face interaction dynamics. In one study, radio frequency identification devices were used to calculate the proximity and duration of interpersonal interactions, and thus create social networks to understand community behavior and apply diffusion processes for infectious diseases and information [10]. Using the same technology, studies have been done in high schools [11] and elementary schools [12] of the mixing patterns of students in a school environment that describe social network’s temporal evolution and apply infectious disease diffusion processes to identify high-risk situations and establish vaccination strategies.

When studying data dissemination within a social system, an understanding is needed of the network topology that models the interactions produced within it. To this end, the present study objective was to evaluate the properties of friendship and enmity networks representing interactions between elementary school students and develop models that reproduce them. This will facilitate future research into problems such as scholastic performance, disease transmission and evolution of the cultural environment, among other important phenomena occurring in schools which could benefit from the formalism of complex networks [13]–[15].

We describe the methodology used to collect the data and generate the databases used in developing the networks. These data have certain characteristics that are not reproduced by classic models of complex network theory. The tests used to analyze friendship networks are described in section ‘Friendship Networks Analysis’ and implementation of the proposed model is described in section ‘Friendship Network Model’, while the enmity networks are addressed in section ‘Enmity Network Analysis’ and the proposed descriptive model in section ‘Enmity Network Model’. Promising future research emphases are proposed.