Dynamics and stability of small social networks

Abstract

The choices and behaviours of individuals in social systems combine in unpredictable ways to create complex, often surprising, social outcomes. The structure of these behaviours, or interactions between individuals, can be represented as a social network. These networks are not static but vary over time as connections are made and broken or change in intensity. Generally these changes are gradual, but in some cases individuals disagree and as a result "fall out" with each other, i.e. , actively end their relationship by ceasing all contact. These "fallouts" have been shown to be capable of fragmenting the social network into disconnected parts. Fragmentation can impair the functioning of social networks and it is thus important to better understand the social processes that have such consequences.

In this thesis we investigate the question of how networks fragment: what mechanism drives the changes that ultimately result in fragmentation? To do so, we also aim to understand the necessary conditions for fragmentation to be possible and identify the connections that are most important for the cohesion of the network. To answer these questions, we need a model of social network dynamics that is stable enough such that fragmentation does not occur spontaneously, but is simultaneously dynamic enough to allow the system to react to perturbations (i.e. , disagreements). We present such a model and show that it is able to grow and maintain networks exhibiting the characteristic properties of social networks, and does so using local behavioural rules inspired by sociological theory.

We then provide a detailed investigation of fragmentation and confirm basic intuitions on the importance of bridges for network cohesion. Furthermore, we show that this topological feature alone does not explain which points of the network are most vulnerable to fragmentation. Rather, we find that dependencies between edges are crucial for understanding subtle differences between stable and vulnerable bridges. This understandingof the vulnerability of different network components is likely to be valuable for preventing fragmentation and limiting the impact of social fallout

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ORCID for Sally Brailsford: orcid.org/0000-0002-6665-8230

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