arXiv subjects

Renaud Lambiotte

Publications and source records attributed to Renaud Lambiotte.

At least 91 records · Page 5Linked to original sources

arXiv2021

Brexit and bots: characterizing the behaviour of automated accounts on Twitter during the UK election

Online Social Networks represent a novel opportunity for political campaigns, revolutionising the paradigm of political communication. Nevertheless, many studies uncovered the presence of d/misinformation campaigns or of malicious activities by genuine or automated users, putting at severe risk the credibility of online platforms. This phenomenon is particularly evident during crucial political events, as political elections. In the present paper, we provide a comprehensive description of the structure of the networks of interactions among users and bots during the UK elections of 2019. In particular, we focus on the polarised discussion about Brexit on Twitter analysing a data set made of more than 10 million tweets posted for over a month. We found that the presence of automated accounts fostered the debate particularly in the days before the UK national elections, in which we find a steep increase of bots in the discussion; in the days after the election day, their incidence returned to values similar to the ones observed few weeks before the elections. On the other hand, we found that the number of suspended users (i.e. accounts that were removed by the platform for some violation of the Twitter policy) remained constant until the election day, after which it reached significantly higher values. Remarkably, after the TV debate between Boris Johnson and Jeremy Corbyn, we observed the injection of a large number of novel bots whose behaviour is markedly different from that of pre-existing ones. Finally, we explored the bots' stance, finding that their activity is spread across the whole political spectrum, although in different proportions, and we studied the different usage of hashtags by automated accounts and suspended users, thus targeting the formation of common narratives in different sides of the debate.

cs.SI↗

arXiv2021

Modeling Collective Anticipation and Response on Wikipedia

The dynamics of popularity in online media are driven by a combination of endogenous spreading mechanisms and response to exogenous shocks including news and events. However, little is known about the dependence of temporal patterns of popularity on event-related information, e.g. which types of events trigger long-lasting activity. Here we propose a simple model that describes the dynamics around peaks of popularity by incorporating key features, i.e., the anticipatory growth and the decay of collective attention together with circadian rhythms. The proposed model allows us to develop a new method for predicting the future page view activity and for clustering time series. To validate our methodology, we collect a corpus of page view data from Wikipedia associated to a range of planned events, that are events which we know in advance will have a fixed date in the future, such as elections and sport events. Our methodology is superior to existing models in both prediction and clustering tasks. Furthermore, restricting to Wikipedia pages associated to association football, we observe that the specific realization of the event, in our case which team wins a match or the type of the match, has a significant effect on the response dynamics after the event. Our work demonstrates the importance of appropriately modeling all phases of collective attention, as well as the connection between temporal patterns of attention and characteristic underlying information of the events they represent.

cs.SI↗

arXiv2021

Flow-based Community Detection in Hypergraphs

To connect structure, dynamics and function in systems with multibody interactions, network scientists model random walks on hypergraphs and identify communities that confine the walks for a long time. The two flow-based community-detection methods Markov stability and the map equation identify such communities based on different principles and search algorithms. But how similar are the resulting communities? We explain both methods' machinery applied to hypergraphs and compare them on synthetic and real-world hypergraphs using various hyperedge-size biased random walks and time scales. We find that the map equation is more sensitive to time-scale changes and that Markov stability is more sensitive to hyperedge-size biases.

physics.soc-ph↗

arXiv2021

Nonlinear consensus on networks: equilibria, effective resistance and trees of motifs

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the effective resistance of the underlying graph equipped with appropriate weights. Our general results are applied to some specific networks, namely trees, cycles and complete graphs. When a network is formed by the union of two subnetworks joined in a single node, we show that the equilibrium points and stability in the whole network can be found by simply studying the smaller subnetworks instead. Applied recursively, this property opens the possibility to investigate the dynamical behaviour on families of networks made of trees of motifs.

math.DS↗

arXiv2021

Dynamics of Majority Rule on Hypergraphs

A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule, and investigate the possibility to represent and analyse the system by means of hypergraphs. We explore the formation of consensus and restrict our attention to interaction groups of size $3$, in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or degree heterogeneity, and recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

physics.soc-ph↗

arXiv2020

Non-linear network dynamics with consensus-dissensus bifurcation

We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and the dominating behaviour of a general class of non-linear dynamical systems. The equilibrium behaviour of the system exhibits a global bifurcation with respect to the system parameter, with a transition from a single constant stationary state to a large range of possible stationary states. Our main result classifies the stability of (a subset of) these stationary states in terms of the effective resistances of the underlying graph; this classification clearly discerns the influence of the specific topology in which the local pitchfork systems are interconnected. We further describe exact solutions for graphs with external equitable partitions and characterize the basins of attraction on tree graphs. Our technical analysis is supplemented by a study of the system on a number of prototypical networks: tree graphs, complete graphs and barbell graphs. We describe a number of qualitative properties of the dynamics on these networks, with promising modeling consequences.

math.DS↗

arXiv2020

Modelling Non-Linear Consensus Dynamics on Hypergraphs

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models, including hypergraphs. In this paper, we explore the non-linear dynamics of consensus on hypergraphs, allowing for interactions within hyperedges of any cardinality. After discussing the different ways in which non-linearities can be incorporated in the dynamical model, building on different sociological theories, we explore its mathematical properties and perform simulations to investigate them numerically. After focussing on synthetic hypergraphs, namely on block hypergraphs, we investigate the dynamics on real-world structures, and explore in detail the role of involvement and stubbornness on polarisation.

physics.soc-ph↗

arXiv2020

Random walks and community detection in hypergraphs

We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by considering the community structure associated to each random walk process. To do so, we generalise the Markov stability framework to hypergraphs and test it on artificial and real-world hypergraphs.

cond-mat.stat-mech↗

arXiv2020

The anatomy of Reddit: An overview of academic research

Online forums provide rich environments where users may post questions and comments about different topics. Understanding how people behave in online forums may shed light on the fundamental mechanisms by which collective thinking emerges in a group of individuals, but it has also important practical applications, for instance to improve user experience, increase engagement or automatically identify bullying. Importantly, the datasets generated by the activity of the users are often openly available for researchers, in contrast to other sources of data in computational social science. In this survey, we map the main research directions that arose in recent years and focus primarily on the most popular platform, Reddit. We distinguish and categorise research depending on their focus on the posts or on the users, and point to different types of methodologies to extract information from the structure and dynamics of the system. We emphasize the diversity and richness of the research in terms of questions and methods, and suggest future avenues of research.

cs.SI↗

arXiv2020

Modelling structure and predicting dynamics of discussion threads in online boards

Internet boards are platforms for online discussions about a variety of topics. On these boards, individuals may start a new thread on a specific matter, or leave comments in an existing discussion. The resulting collective process leads to the formation of `discussion trees', where nodes represent a post and comments, and an edge represents a `reply-to' relation. The structure of discussion trees has been analysed in previous works, but only from a static perspective. In this paper, we focus on their structural and dynamical properties by modelling their formation as a self-exciting Hawkes process. We first study a Reddit dataset to show that the structure of the trees resemble those produced by a Galton-Watson process with a special root offspring distribution. The dynamical aspect of the model is then used to predict future commenting activity and the final size of a discussion tree. We compare the efficiency of our approach with previous works and show its superiority for the prediction of the dynamics of discussions.

cs.SI↗

arXiv2020

Random walks on dense graphs and graphons

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs, where classical methods would become computationally intractable. Through an approximation procedure, the standard system of coupled ordinary differential equations is replaced by a nonlocal evolution equation on the unit interval. In this work, we adopt this methodology to explore the continuum limit of random walks, a popular model for diffusion on graphs. We focus on two classes of processes on dense weighted graph, in discrete and in continuous time, whose dynamics are encoded in the transition matrix and the random-walk Laplacian. We also show that previous works on the discrete heat equation, associated to the combinatorial Laplacian, fall within the scope of our approach. Finally, we apply the spectral theory of operators to characterize the relaxation time of the process in the continuum limit.

math.PR↗

arXiv2020

Random walks and diffusion on networks

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

physics.soc-ph↗

arXiv2020

Opinion Dynamics with Multi-Body Interactions

We introduce and analyse a three-body consensus model (3CM) for non-linear consensus dynamics on hypergraphs. Our model incorporates reinforcing group effects, which can cause shifts in the average state of the system even in if the underlying graph is complete (corresponding to a mean-field interaction), a phenomena that may be interpreted as a type of peer pressure. We further demonstrate that for systems with two clustered groups, already a small asymmetry in our dynamics can lead to the opinion of one group becoming clearly dominant. We show that the nonlinearity in the model is the essential ingredient to make such group dynamics appear, and demonstrate how our system can otherwise be written as a linear, pairwise interaction system on a rescaled network.

physics.soc-ph↗

arXiv2020

Mobile phone data and COVID-19: Missing an opportunity?

This paper describes how mobile phone data can guide government and public health authorities in determining the best course of action to control the COVID-19 pandemic and in assessing the effectiveness of control measures such as physical distancing. It identifies key gaps and reasons why this kind of data is only scarcely used, although their value in similar epidemics has proven in a number of use cases. It presents ways to overcome these gaps and key recommendations for urgent action, most notably the establishment of mixed expert groups on national and regional level, and the inclusion and support of governments and public authorities early on. It is authored by a group of experienced data scientists, epidemiologists, demographers and representatives of mobile network operators who jointly put their work at the service of the global effort to combat the COVID-19 pandemic.

cs.CY↗

arXiv2020

Community detection in networks without observing edges

We develop a Bayesian hierarchical model to identify communities in networks for which we do not observe the edges directly, but instead observe a series of interdependent signals for each of the nodes. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection as well as the selection of an optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of the S&P100 index as well as climate data from US cities.

cs.SI↗

arXiv2019

Multi-body Interactions and Non-Linear Consensus Dynamics on Networked Systems

Multi-body interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyse models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multi-body dynamical effects that go beyond rescaled pairwise interactions can only appear if the interaction function is non-linear, regardless of the underlying multi-body structure. As a practical application, we introduce a specific non-linear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarised clusters where multi-body interactions make one cluster dominate the other.

physics.soc-ph↗

arXiv2019

Constructing Laplacian matrices with Soules vectors: inverse eigenvalue problem and applications

The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks which sets of numbers (counting multiplicities) can be the eigenvalues of a symmetric matrix with nonnegative entries. While examples of such matrices are abundant in linear algebra and various applications, this question is still open for matrices of dimension $N\geq 5$. One of the approaches to solve the SNIEP was proposed by George W. Soules, relying on a specific type of eigenvectors (Soules vectors) to derive sufficient conditions for this problem. Elsner et al. later showed a canonical way to construct all Soules vectors, based on binary rooted trees. While Soules vectors are typically treated as a totally ordered set of vectors, we propose in this article to consider a relaxed alternative: a partially ordered set of Soules vectors. We show that this perspective enables a more complete characterization of the sufficient conditions for the SNIEP. In particular, we show that the set of eigenvalues that satisfy these sufficient conditions is a convex cone, with symmetries corresponding to the automorphisms of the binary rooted tree from which the Soules vectors were constructed. As a second application, we show how Soules vectors can be used to construct graph Laplacian matrices with a given spectrum and describe a number of interesting connections with the concepts of hierarchical random graphs, equitable partitions and effective resistance.

physics.soc-ph↗

arXiv2019

Classes of random walks on temporal networks with competing timescales

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the co-existence of different timescales in the system. Here, we introduce random walks on general stochastic temporal networks allowing for lasting interactions, with up to three competing timescales. We then compare the mean resting time and stationary state of different models. We also discuss the accuracy of the mathematical analysis depending on the random walk model and the structure of the underlying network, and pay particular attention to the emergence of non-Markovian behaviour, even when all dynamical entities are governed by memoryless distributions.

physics.soc-ph↗