TITLE:
Facebook Dynamics: Modelling and Statistical Testing
AUTHORS:
José Bavio, Melina Guardiola, Gonzalo Perera
KEYWORDS:
Markov Chains, Random Graphs, Social Networks
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.4,
April
18,
2018
ABSTRACT: 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.