Modeling, Analysis, and Inference in Social Network Formation

Abstract

Human beings are social creatures that are naturally looking for, and in fact need, social interactions to maintain a healthy life and mindset. In the past couple of decades, the advent of social media platforms has facilitated maintaining relationships with family and friends even across long distances, but it has also affected people's behavior in their social activity, e.g., allowing them to connect with others they do not even know in real life. On the other hand, the growing amount of available data is giving a unique opportunity for the analysis of the social network structures as well as of the underlying human social behavior. Social networks constitute highly complex systems because of their size, the inner complexity of their components (human beings), and the feedback and cascade effects due to the inter-dependency between the individual behavior and the network structure. Furthermore, social networks are strongly coupled with other network systems, e.g., financial markets, technological systems, infrastructures. With the objective of advancing our understanding of such a complex ecosystem, this thesis focuses on the modelling, analysis, and inference of the social network formation process. At a high level, we distinguish between online social networks, based on real-world friendships, and online social networks, corresponding to our virtual identity on the social media platforms. In the fi rst part of the thesis we analyze online social networks, whose topological structure is fundamentally the result of the social behavior of the agents that locally strive to optimize their position in the network. According to a number of socio-economic theories grounded on extensive empirical research, improving one's own network position can increase the individual's social capital in different forms, e.g., in terms of social influence, brokerage opportunities, or social support. Hence, we consider a network formation process in which actors' interest is defi ned as a parametric combination of different socio-strategic incentives based on the network topology. We study this individual networking behavior through the lens of game theory: following a utility maximization principle, actors rationally choose their set of followees. While a more common objective in strategic network formation games is to study the equilibria resulting from predefi ned payoff functions, our goal is to rationalize the observed network structures in terms of the unknown individual behavior of the actors. Our approach proves to be mathematically tractable and statistically robust, and one of its main advantages is that it allows for empirical validations on real-world historical data on well-studied online social networks, as well as for comparison with well-known random networks models. In the second part of the thesis, we turn our attention to today's most popular online social networks. These platforms paved the way for the so-called Web 2.0, giving people the opportunity to build a virtual user profi le and to share different forms of User- Generated Content. Some of these online social networks, e.g., Facebook or LinkedIn, require mutual consent for establishing a friendship, hence they mimic the characteristics of our online social networks. Conversely, Twitter, YouTube, Instagram, TikTok, and many other popular platforms are all directed networks, where social media users can virtually follow real-life strangers. By means of the integrated search engines, they can navigate others' user pro files, and their User-Generated Content, e.g., Tweets or Instagram posts, which is typically catalogued by hashtags that facilitate its discovery to the interested users. While the number of monthly active users in these platforms has dramatically increased in the last decade, the scienti c literature on social network formation models has not considered the User-Generated Content as main driving factor. Our main contribution consists in formulating a network formation model based on the attractiveness of the User-Generated Content. The individual linking decision is rooted in a meritocratic principle that rewards those users that provide higher quality content. The comparison between theoretical results and empirical data from Twitch, a popular platform for online gamers, proves that our quality-based model captures a number of realistic features of User-Generated Content-based online social networks.