Dynamics of cascades on burstiness-controlled temporal networks

Abstract

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.

[Retracted] Information Spreading on Memory Activity‐Driven Temporal Networks

“…For the temporal network, an essential factor is the network memory [38,[40][41][42], which means that edges that existed in the current time step may already occur in previous time steps. Sun et al [43] revealed that network memory inhibits the spreading process for SIR models, in which the epidemic threshold is enlarged while the spreading size decreases.…”

Effect of algorithmic bias and network structure on coexistence, consensus, and polarization of opinions

“…While the role of algorithmic bias has been recently modeled in an array of concrete scenarios [18,22,25], a general theoretical framework systematically linking social dynamics, network structure and algorithmic filtering has been missing so far. Here we have put forward such a formalism by extending previous work on binary-state dynamics [2,24,29,[34][35][36]45] with a notion of bias and applying it to synthetic and real-world social networks. While our formalism applies to any binary-state dynamics, we have showcased its flexibility by focusing on the noisy voter, language, and majority-vote models, which consider a (pairwise or group-based) copying or herding mechanism, alongside random or idiosyncratic changes of opinion.…”

“…Our formalism provides a flexible way to parametrize a combination of algorithmic filters and mechanisms of social interactions in terms of transition rates. As such, it may help identify the features of algorithms that promote dynamical and structural polarization in online platforms arguably driven by a mixture of social processes, from homophily [26,27] to social contagion [28,29]. This will require a validation of our theoretical framework by either fitting observational data with specific models, using automatic model selection [56,57] and statistical inference techniques [58], or uncovering causal relationships with controlled experiments of online social behavior [59,60].…”

“…In the highly connected, infinite network size limit the results of all approximations coincide. Higher-order approximations involve evolution equations for random (uncorrelated) networks with an arbitrary degree distribution P k , with degrees in the range k min k k max , and include: (i) the pair approximation [32,48,51], with k max − k min + 2 variables, and 044312-5 (ii) approximate master equations [2,24,29,[34][35][36]52], with (1 + k max − k min )(2 + k max + k min ) variables. In the case of a homogeneous (single community) network structure, the methods developed in the references above can be directly applied to any binary-state model with effective transition rates F * k,m and R * k,m [see Eqs.…”

“…While these results suggest that polarization arises from a mix of social behavioral patterns and the online algorithms constraining them, we still lack a general theoretical framework systematically linking models of information spreading, network structure, and algorithmic bias. This is particularly relevant given the diversity of mechanisms arguably driving the way people exchange information, including homophily [26,27] and social contagion [28,29], which may in turn lead to radically different patterns of polarization. Here we propose such a formalism by extending the theoretical description of binary-state dynamics, based on mean-field [30,31], pair [32,33], and higher-order [24,[34][35][36] approximations, with a simple but flexible notion of algorithmic bias.…”