Social networks 1

Many biological, social, and economic systems evolve over time to exhibit modularity at multiple scales. The current work aims at developing a model of the formation of hierarchically organized modules in originally undifferentiated systems. The specific question addressed by the generative modeling is: can hierarchical modularity emerge from vertices that simply adapt their outgoing edge weights to other vertices so as to increase their relevance within the network?As a concrete example for expository purposes, imagine that there 50 authors who are connected to each other by a directed 50 X 50 matrix of continuously valued weights that can be interpreted as the amount of readership traffic that each author sends to every other author through their citations. The following three steps are taken: 1) Each agent calculates its steady-state readership traffic, 2A) random Gaussian noise is added to each agent's 50-length vector of outgoing weights (e.g. transition probabilities), 3) The steady-state readership traffic is recalculated and if it is greater than it was in Step 1, then the change to outgoing weights is kept, otherwise it is reverted to the old weights.The simulations demonstrate several phenomena related to the emergence of multiscale modules: 1) reciprocal connections (when vertex A connects strongly to B, then B connects strongly to A), 2) densely connected cliques above the dyadic level, 3) increasing modularity and number of communities as the network evolves, and 4) a fine-to-coarse pattern of community formation. Thus, multiscale modularity can arise in networks even without incorporating spatial proximity, explicit collaborations, fields, trust, coalitions, external inputs, or similarity, pointing to possibly widespread applicability to economic trade, social organizations, professional networks, social media structures, and neural circuits.

Human choices are shaped by preferences and often influenced by network effects through social connections. Understanding these network effects helps policymakers design interventions based on behaviour spread, marketers craft campaigns based on peer influence, and electoral planners compare the impact of socioeconomic variables and network influences on voter preferences. In our research, we estimate the extent to which a decision maker’s choice is influenced by their network connections versus their individual attributes. Importantly, we quantify the uncertainty of these estimations, which offers multiple benefits - it prevents over-reliance on potentially inaccurate estimations due to limited or noisy data, and it enables consideration of network-induced uncertainties while evaluating counterfactual scenarios such as altering future choice sets. We achieve this by developing a Bayesian non-parametric model to capture network effects using a Gaussian process over graphs. Within the discrete choice framework, we represent the utility of an item to a decision maker as a sum of this graph-based network effect and a covariate effect based on the individual’s and choice item’s features. The decision maker selects the item with the highest utility in the available choice set. Our Bayesian formulation allows us to quantify the uncertainty of the network effect on utility using the posterior distribution. The graph-based Gaussian process kernel hyperparameters are learned using gradient descent, eliminating the need for manual hyperparameter tuning. We show that smooth graph-based kernels yield well-calibrated network-induced uncertainties and validate them on real-world datasets, including US election results and Android app installation data.

Social categories, such as race, gender, or socioeconomic status, are core driving forces of social tie formation. They shape our identities, determining our social behavior and our connection preferences. Homophily, the preference for connecting with similar others, is one of the most common and widely studied interaction patterns; however, the dynamics driving multidimensional connection preferences remain largely unexplored. Furthermore, while homophily in social networks leads to enhanced trust between individuals, it also exacerbates segregation and breeds inequality. As individuals belong to multiple groups, people can experience marginalization in several dimensions simultaneously, suffering intersectional inequalities.In this work, we develop a network model of homo / heterophilic interactions with multidimensional attribute vectors. We use the model to tackle two crucial questions: How do we integrate information from our multidimensional identities to form connections with each other, and how do multidimensional connection preferences impact intersectional inequalities of social capital?To answer the first question, we systematically model group-preference aggregation mechanisms and compare them using Bayesian model selection. We find that a simple aggregation mechanism consistently outperforms more complex alternatives.We also use the model to operationalize intersectional inequalities of social capital and derive analytical closed-form expressions for the predicted inter-group degree inequalities. We demonstrate that when attributes are uncorrelated, multidimensional degree disparities mirror one-dimensional systems, but attribute correlation induces counterintuitive patterns of emergent intersectionality. For example, for certain population distributions, the parameter regimes where majorities and minorities are advantaged are reversed. We verify the model's predictions with real-world network data, finding a remarkable alignment.

This study explores the impact of social norms and affordances on user attention in a simulated social media environment. By priming with curiosity and manipulating the platform design, participants dwell longer on and spend more time engaging with content from well-informed personas, even without explicitly revealing their defining traits. This finding suggests that subtle modifications to platform design and social norms have the potential to influence user behavior and mitigate the spread of misinformation.

In the past years we have witnessed a vast migration of users from classical social platforms like Twitter to Decentralized Online Social Networks (DOSNs) such as Mastodon. Mastodon operates as a network of independent and decentralized servers, known as instances, that communicate with one another. The rapid growth in the number of users is reshaping Mastodon’s network structure and altering the flow of information among instances and individual users. This growth also presents challenges in identifying and managing harmful servers. To address these issues, Mastodon provides instance administrators with tools for moderating inter-instance interactions.This study examines the interplay between the friendship network of instances and Mastodon’s moderation mechanisms, revealing the main underlying patterns and how they affect the propagation of mis/information. By analyzing structural changes in the network over a year, we observe that the actors of the moderation process change over time. Despite these shifts at the microscopic scale, the analysis of motifs distributions and network balance over time reveals the presence of stable structures at the macroscopic level. In addition, the structure of the banning-banned network unveils two natural sets of instances: a larger group (M)comprising banned instances and a smaller minority group (m) responsible for most bannings. To understand the flowof information we employ an information diffusion model able to reveal the propagation of mis/information. Our findings show that minority group instances share information predominantly within their group, while the majority group exhibits less cohesive communication. Regarding the cross-information spreading, we observe that the nodes in the majority get rapidly isolated while the spreading from the minority to the majority is more resilient under changes of the network. Additionally, an echo-chamber effect emerges, isolating the minority group from untrusted servers.

The dynamics of personal relationships remain largely unexplored due to the inherent difficulties of the longitudinal data collection process. In this paper, we analyze a dataset tracking the temporal evolution of a network of personal relationships among 900 people over the course of four years. We search for evidence that the network is in equilibrium, meaning that all macroscopic properties remain constant, fluctuating around stable values, while the internal microscopic dynamics are active. We find that the probabilities governing the network dynamics are stationary over time and that the degree distributions, as well as edge and triangle abundances match the theoretical equilibrium distributions expected under these dynamics (see Fig. 1). Furthermore, we verify that the system satisfies the detailed balance condition, with only minor point deviations, confirming that it is indeed in equilibrium. Remarkably, this equilibrium persists despite a high turnover in network composition, suggesting that it is an inherent characteristic of human social interactions rather than a trait of the individuals themselves. We argue that this equilibrium may be a general feature of human social networks arising from the competition between different dynamical mechanisms and also from the cognitive and material resources management of individuals. From a practical perspective, the fact that networks are in equilibrium could simplify data collection processes, validate the use of cross-sectional data-based methods like Exponential Random Graph Models, and inform the design of interventions. Our findings advance the understanding of collective human behavior predictability and our ability to describe it using simple mathematical models.

We study fairness in social influence maximization, whereby one seeks to select seeds that spread a given information throughout a network, ensuring balanced outreach among different communities (e.g. demographic groups). In the literature, fairness is often quantified in terms of the expected outreach within individual communities. In this paper, we demonstrate that such fairness metrics can be misleading since they overlook the stochastic nature of information diffusion processes. When information diffusion occurs in a probabilistic manner, multiple outreach scenarios can occur. As such, outcomes such as ``In 50\% of the cases, no one in group 1 gets the information, while everyone in group 2 does, and in the other 50%, it is the opposite'', which always results in largely unfair outcomes, are classified as fair by a variety of fairness metrics in the literature. We tackle this problem by designing a new fairness metric, mutual fairness, that captures variability in outreach through optimal transport theory. We propose a new seed-selection algorithm that optimizes both outreach and mutual fairness, and we show its efficacy on several real datasets. We find that our algorithm increases fairness with only a minor decrease (and at times, even an increase) in efficiency.

Most existing studies assume that the network topology is already known when designing intervention strategies, which is difficult to achieve in practice. We focus on network intervention with sampling information and assume that the nodes are obtained by graph sampling algorithms, where chain-referral sampling methods make it easier to sample nodes with more neighbors. Moreover, we propose a percolation framework to analyze network attacks with such chain-referral sampling data. For a generalized random network with discrete degree distribution, the analytic solution of the relative size of the giant component could be obtained with any given sampling proportion and attack proportion. At the same time, the analysis model is extended by introducing a cutoff proportion to maximize the intervention effect of the sampling information. Experiments in model and empirical networks show that the optimal cutoff proportion estimated by sampling data could effectively improve the attack effect. The intervention effect of sampling partial data could approach that of complete data when selecting the appropriate cutoff degree proportion. This study could provide a reference for effective rumors management and disease prevention in real social networks.