Ego-centred models of social networks: the social atom

This thesis set out to contribute to the realm of social physics, with a partic- ular focus on human social networks. Our approach, however, is somewhat different from what is typical in disciplines such as complex systems or sta- tistical physics. Rather than simplifying the features of the constituents of our system (people), and stressing their rules of interaction, we focus on better understanding those very same constituents, modelling them as so- cial atoms. Our rationale is that a better understanding of such an atom may shed light on how (and why) it interacts with other atoms to form social collectives. Given its robustness and the evolutionary roots of its premises, we use the Social Brain Hypothesis as our departure point. This theory states that the evolutionary drive behind the development of large brains in humans was the need to process social information and that the limited capacity of our brains imposes a limit to the number of relationships we can manage— the so-called “Dunbar’s number”, roughly 150. Moreover, evidence keeps revealing that these relationships are further organised in a series of hierar- chically inclusive layers with decreasing emotional intensity, whose sizes exhibit a more or less constant scaling. Notwithstanding the empirical ev- idence, neither the presence of scaling in the organisation of personal net- works nor its connection with limited cognitive skills had been explained so far. In Chapter 2 we present a mathematical model that solves this puzzle. The assumptions of the model are quite simple, and well founded on em- pirical evidence. Firstly, the number of relationships we maintain tends to be stable on average. Secondly, these relationships are costly, and our resources are limited. With these two premises, our results show that the hierarchical organisation emerges naturally from the principle of maximum entropy. Not only that, but we also predict a hitherto unnoticed regime of organisation whose existence we prove using several datasets from com- munities of immigrants. The former model considers that relationships can only belong to a discrete set of categories (layers). In Chapter 3 we extend it so that rela- tionships are classified in a continuum. This modification allows us to test the model with data from very different sources such as online communica- tions, face-to-face contacts, and phone calls. Our results show that the two regimes of organisation found in the previous model persist in this vari- ant, and reveal the underlying existence of a (universal) scaling parameter which does not depend on any particular number of layers. To incorporate these ideas into socio-centric models, we build on the so-called Structural Balance Theory. This theory, underpinned by psycho- logical motivations, posits that the structure of social networks of positive and negative relationships are highly interdependent. However, the theory has received little empirical validation, and negative social relationships are poorly understood—both from an ego-centric and a socio-centric per- spective. For that reason, we turn to developing an experimental software in order to gather data within a school. In Chapters 4 and 5 we present results from these experiments. In Chapter 4 we analyse the socio-centric networks using machine learning techniques and find that the structure of positive and negative networks is indeed very much connected. Besides, we study the two types of net- works separately, showing that they exhibit quite distinct features and that gender effects in negative social networks are weak and asymmetrical for boys and girls. In Chapter 5, on the other hand, we focus on the structure of negative personal networks. Remarkably, using data from two differ- ent experimental settings, we show that the structure of personal networks of negative relationships mirrors that of the positive ones and exhibits a similar scaling—albeit their size is significantly smaller. Chapter 6 summarises our results and presents future (and current) lines of investigation. Among them, we outline a model of a social fluid that uses the insights gained with this thesis to build a model of social collec- tives as ensembles of personal networks. This model is compatible, at the micro-level, with the observations of the social brain hypothesis, and, at the macro-level, with the premises of the structural balance theory.