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As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of the information being communicated. Our approach uses both standard and novel network metrics to characterize how unexpected a network configuration is, and to capture a networks ability to conduct information. We find that networks with a higher conductance in link structure exhibit higher information entropy, while unexpected network configurations can be tied to information novelty. We use a simulation model to explain the observed correspondence between the evolution of a networks structure and the information it carries.
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Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in empirical network science is how to make the best possible estimates of network structure given such unreliable data. In this paper we describe a fully Bayesian method for reconstructing networks from observational data in any format, even when the data contain substantial measurement error and when the nature and magnitude of that error is unknown. The method is introduced through pedagogical case studies using real-world example networks, and specifically tailored to allow straightforward, computationally efficient implementation with a minimum of technical input. Computer code implementing the method is publicly available.
A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local richness of the cyclic structure. In this paper, we introduce renewal non-backtracking random walks (RNBRW) as a way of quantifying this structure. RNBRW gives a weight to each edge equal to the probability that a non-backtracking random walk completes a cycle with that edge. Hence, edges with larger weights may be thought of as more important to the formation of cycles. Of note, since separate random walks can be performed in parallel, RNBRW weights can be estimated very quickly, even for large graphs. We give simulation results showing that pre-weighting edges through RNBRW may substantially improve the performance of common community detection algorithms. Our results suggest that RNBRW is especially efficient for the challenging case of detecting communities in sparse graphs.
The global public sphere has changed dramatically over the past decades: a significant part of public discourse now takes place on algorithmically driven platforms owned by a handful of private companies. Despite its growing importance, there is scant large-scale academic research on the long-term evolution of user behaviour on these platforms, because the data are often proprietary to the platforms. Here, we evaluate the individual behaviour of 600,000 Twitter users between 2012 and 2019 and find empirical evidence for an acceleration of the way Twitter is used on an individual level. This manifests itself in the fact that cohorts of Twitter users behave differently depending on when they joined the platform. Behaviour within a cohort is relatively consistent over time and characterised by strong internal interactions, but over time behaviour from cohort to cohort shifts towards increased activity. Specifically, we measure this in terms of more tweets per user over time, denser interactions with others via retweets, and shorter content horizons, expressed as an individuals decaying autocorrelation of topics over time. Our observations are explained by a growing proportion of active users who not only tweet more actively but also elicit more retweets. These behaviours suggest a collective contribution to an increased flow of information through each cohorts news feed -- an increase that potentially depletes available collective attention over time. Our findings complement recent, empirical work on social acceleration, which has been largely agnostic about individual user activity.
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions -- pro-physical-distancing and anti-physical-distancing -- that compete with each other and have mutual immunity to each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. We develop approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Through numerical simulations, we illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease. We find that lengthening the duration that individuals hold an opinion may help suppress disease transmission, and we demonstrate that increasing the cross-layer correlations or intra-layer correlations of node degrees may lead to fewer individuals becoming infected with the disease.
Much research has been done on studying the diffusion of ideas or technologies on social networks including the textit{Influence Maximization} problem and many of its variations. Here, we investigate a type of inverse problem. Given a snapshot of the diffusion process, we seek to understand if the snapshot is feasible for a given dynamic, i.e., whether there is a limited number of nodes whose initial adoption can result in the snapshot in finite time. While similar questions have been considered for epidemic dynamics, here, we consider this problem for variations of the deterministic Linear Threshold Model, which is more appropriate for modeling strategic agents. Specifically, we consider both sequential and simultaneous dynamics when deactivations are allowed and when they are not. Even though we show hardness results for all variations we consider, we show that the case of sequential dynamics with deactivations allowed is significantly harder than all others. In contrast, sequential dynamics make the problem trivial on cliques even though its complexity for simultaneous dynamics is unknown. We complement our hardness results with structural insights that can help better understand diffusions of social networks under various dynamics.
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