Author(s)

José Bavio¹, Melina Guardiola¹, Gonzalo Perera²

¹Departamento de Matemática, Universidad Nacional del Sur, Buenos Aires, Argentina.
²Universidad de la República, Montevideo, Uruguay.

In this work we study virtual social networks known as Facebook. It is used by millions of people worldwide, gathering a combination of virtual elements and real world components. We suggest a probabilistic model to describe the long-term behavior of Facebook. This model includes different friendship connection between profiles, directly or by suggestion. Due to web’s high interactivity level, we simplify the model assuming Markovian dynamic. After the model is established we propose Complete Transversality (CT) communication concept. CT describes people interaction that reflects profile behaviour and leads to estimators that measure this interaction. Then we introduce a weakness version of CT named Segmental Transversality (ST). Within this framework we develop estimators that allow hypothesis testing of CT and ST. And then, in ST context we propose performance measures to address a priori segmentation’s quality.

Markov Chains, Random Graphs, Social Networks

Bavio, J. , Guardiola, M. and Perera, G. (2018) Facebook Dynamics: Modelling and Statistical Testing. Advances in Pure Mathematics, 8, 380-399. doi: 10.4236/apm.2018.84021.