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.
