arXiv subjects

Renaud Lambiotte

Publications and source records attributed to Renaud Lambiotte.

At least 73 records · Page 4Linked to original sources

arXiv2023

Cross-Relation Characterization of Knowledge Networks

Knowledge networks have become increasingly important as a changing repository of data which can be represented, studied and modeled by using complex networks concepts and methodologies. Here we report a study of knowledge networks corresponding to the areas of Physics and Theology, obtained from the Wikipedia and taken at two different dates separated by 4 years. The respective two versions of these networks were characterized in terms of their respective cross-relation signatures, being summarized in terms of modification indices obtained for each of the nodes that are preserved among the two versions. The proposed methodology is first evaluated on Erdos-Renyi (ER) and Barabasi-Albert model (BA) networks, before being tested on the knowledge networks obtained from the Wikipedia respectively to the areas of Physics and Theology. In the former study, it has been observed that the nodes at the core and periphery of both types of theoretical models yielded similar modification indices within these two groups of nodes, but with distinct values when taken across these two groups. The study of the Physics and Theology networks indicated that these two networks have signatures respectively similar to those of the BA and ER models, as well as that higher modification values being obtained for the periphery nodes, as compared to the respective core nodes.

physics.soc-ph↗

arXiv2023

Safeguarding Physical Sneaker Sale Through a Decentralized Medium

Sneakers were designated as the most counterfeited fashion item online, with three times more risk in a trade than any other fashion purchase. As the market expands, the current sneaker scene displays several vulnerabilities and trust flaws, mostly related to the legitimacy of assets or actors. In this paper, we investigate various blockchain-based mechanisms to address these large-scale trust issues. We argue that (i) pre-certified and tracked assets through the use of non-fungible tokens can ensure the genuine nature of an asset and authenticate its owner more effectively during peer-to-peer trading across a marketplace; (ii) a game-theoretic-based system with economic incentives for participating users can greatly reduce the rate of online fraud and address missed delivery deadlines; (iii) a decentralized dispute resolution system biased in favour of an honest party can solve potential conflicts more reliably.

cs.CR↗

arXiv2023

Between News and History: Identifying Networked Topics of Collective Attention on Wikipedia

The digital information landscape has introduced a new dimension to understanding how we collectively react to new information and preserve it at the societal level. This, together with the emergence of platforms such as Wikipedia, has challenged traditional views on the relationship between current events and historical accounts of events, with an ever-shrinking divide between "news" and "history". Wikipedia's place as the Internet's primary reference work thus poses the question of how it represents both traditional encyclopaedic knowledge and evolving important news stories. In other words, how is information on and attention towards current events integrated into the existing topical structures of Wikipedia? To address this we develop a temporal community detection approach towards topic detection that takes into account both short term dynamics of attention as well as long term article network structures. We apply this method to a dataset of one year of current events on Wikipedia to identify clusters distinct from those that would be found solely from page view time series correlations or static network structure. We are able to resolve the topics that more strongly reflect unfolding current events vs more established knowledge by the relative importance of collective attention dynamics vs link structures. We also offer important developments by identifying and describing the emergent topics on Wikipedia. This work provides a means of distinguishing how these information and attention clusters are related to Wikipedia's twin faces of encyclopaedic knowledge and current events -- crucial to understanding the production and consumption of knowledge in the digital age.

cs.CY↗

arXiv2023

Non-Markovian paths and cycles in NFT trades

Recent years have witnessed the availability of richer and richer datasets in a variety of domains, where signals often have a multi-modal nature, blending temporal, relational and semantic information. Within this context, several works have shown that standard network models are sometimes not sufficient to properly capture the complexity of real-world interacting systems. For this reason, different attempts have been made to enrich the network language, leading to the emerging field of higher-order networks. In this work, we investigate the possibility of applying methods from higher-order networks to extract information from the online trade of Non-fungible tokens (NFTs), leveraging on their intrinsic temporal and non-Markovian nature. While NFTs as a technology open up the realms for many exciting applications, its future is marred by challenges of proof of ownership, scams, wash trading and possible money laundering. We demonstrate that by investigating time-respecting non-Markovian paths exhibited by NFT trades, we provide a practical path-based approach to fraud detection.

cs.SI↗

arXiv2023

Fragmentation from group interactions: A higher-order adaptive voter model

The adaptive voter model allows for studying the interplay between homophily, the tendency of like-minded individuals to attract each other, and social influence, the tendency for connected individuals to influence each other. However, it relies on graphs, and thus, it only considers pairwise interactions. We develop a minimal extension of the adaptive voter model to hypergraphs to study the interactions of groups of arbitrary sizes using a threshold parameter. We study $S$-uniform hypergraphs as initial configurations. With numerical simulations, we find new phenomena not found in the counterpart pairwise models, such as the formation of bands in the magnetization and the lack of an equilibrium state. Finally, we develop an analytical model using a sparse hypergraph approximation that accurately predicts the bands' boundaries and height.

physics.soc-ph↗

arXiv2023

SHEEP: Signed Hamiltonian Eigenvector Embedding for Proximity

We introduce a spectral embedding algorithm for finding proximal relationships between nodes in signed graphs, where edges can take either positive or negative weights. Adopting a physical perspective, we construct a Hamiltonian which is dependent on the distance between nodes, such that relative embedding distance results in a similarity metric between nodes. The Hamiltonian admits a global minimum energy configuration, which can be reconfigured as an eigenvector problem, and therefore is computationally efficient to compute. We use matrix perturbation theory to show that the embedding generates a ground state energy, which can be used as a statistical test for the presence of strong balance, and to develop an energy-based approach for locating the optimal embedding dimension. Finally, we show through a series of experiments on synthetic and empirical networks, that the resulting position in the embedding can be used to recover certain continuous node attributes, and that the distance to the origin in the optimal embedding gives a measure of node extremism.

physics.soc-ph↗

arXiv2023

Exploring QSAR Models for Activity-Cliff Prediction

Pairs of similar compounds that only differ by a small structural modification but exhibit a large difference in their binding affinity for a given target are known as activity cliffs (ACs). It has been hypothesised that quantitative structure-activity relationship (QSAR) models struggle to predict ACs and that ACs thus form a major source of prediction error. However, a study to explore the AC-prediction power of modern QSAR methods and its relationship to general QSAR-prediction performance is lacking. We systematically construct nine distinct QSAR models by combining three molecular representation methods (extended-connectivity fingerprints, physicochemical-descriptor vectors and graph isomorphism networks) with three regression techniques (random forests, k-nearest neighbours and multilayer perceptrons); we then use each resulting model to classify pairs of similar compounds as ACs or non-ACs and to predict the activities of individual molecules in three case studies: dopamine receptor D2, factor Xa, and SARS-CoV-2 main protease. We observe low AC-sensitivity amongst the tested models when the activities of both compounds are unknown, but a substantial increase in AC-sensitivity when the actual activity of one of the compounds is given. Graph isomorphism features are found to be competitive with or superior to classical molecular representations for AC-classification and can thus be employed as baseline AC-prediction models or simple compound-optimisation tools. For general QSAR-prediction, however, extended-connectivity fingerprints still consistently deliver the best performance. Our results provide strong support for the hypothesis that indeed QSAR methods frequently fail to predict ACs. We propose twin-network training for deep learning models as a potential future pathway to increase AC-sensitivity and thus overall QSAR performance.

cs.LG↗

arXiv2022

An Efficient and Decentralized Blockchain-based Commercial Alternative (Full Version)

While online interactions and exchanges have grown exponentially over the past decade, most commercial infrastructures still operate through centralized protocols, and their success essentially depends on trust between different economic actors. Digital advances such as blockchain technology has led to a massive wave of \textit{Decentralized Ledger Technology} (\textit{DLT}) initiatives, protocols and solutions. This advance makes it possible to implement trustless systems in the real world, which, combined with appropriate economic and participatory incentives, would foster the proper functioning and drive the adoption of a decentralized platform among different actors. This paper describes an alternative to current commercial structures and networks by introducing \textit{Lyzis Labs}, which is is an incentive-driven and democratic protocol designed to support a decentralized online marketplace, based on blockchain technology. The proposal, \textit{Lyzis Marketplace}, allows to connect two or more people in a decentralized and secure way without having to rely on a \textit{Trusted Third Party} (\textit{TTP}) in order to perform physical asset exchanges while mainly providing transparent and fully protected data storage. This approach can potentially lead to the creation of a permissionless, efficient, secure and transparent business environment where each user can gain purchasing and decision-making power by supporting the collective welfare while following their personal interests during their various interactions on the network.

cs.GT↗

arXiv2022

Discrete curvature on graphs from the effective resistance

This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably, we find a relation to a number of well-established discrete curvatures (Ollivier, Forman, combinatorial curvature) and show evidence for convergence to continuous curvature in the case of Euclidean random graphs. Being both efficient to calculate and highly amenable to theoretical analysis, these resistance curvatures have the potential to shed new light on the theory of discrete curvature and its many applications in mathematics, network science, data science and physics.

math.DG↗

arXiv2022

Unifying information propagation models on networks and influence maximization

Information propagation on networks is a central theme in social, behavioral, and economic sciences, with important theoretical and practical implications, such as the influence maximization problem for viral marketing. Here, we consider a model that unifies the classical independent cascade models and the linear threshold models, and generalise them by considering continuous variables and allowing feedback in the dynamics. We then formulate its influence maximization as a mixed integer nonlinear programming problem and adopt derivative-free methods. Furthermore, we show that the problem can be exactly solved in the special case of linear dynamics, where the selection criterion is closely related to the Katz centrality, and propose a customized direct search method with local convergence. We then demonstrate the close-to-optimal performance of the customized direct search numerically on both synthetic and real networks.

cs.SI↗

arXiv2022

Flow stability for dynamic community detection

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.

physics.soc-ph↗

arXiv2022

Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multi-scale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and recovers as limits well-known concept such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.

physics.soc-ph↗

arXiv2022

Consensus from group interactions: An adaptive voter model on hypergraphs

We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions $\{0,1\}$ form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can also split and merge (adaptation). In a hypergraph, these groups are represented by hyperedges of different sizes. The heterogeneity of group sizes is controlled by a parameter $β$. To study the impact of $β$ on reaching consensus, we provide extensive computer simulations and compare them with an analytic approach for the dynamics of the average magnetization. We find that group interactions amplify small initial opinion biases, accelerate the formation of consensus and lead to a drift of the average magnetization. The conservation of the initial magnetization, known for basic voter models, is no longer obtained.

physics.soc-ph↗

arXiv2022

Consensus Dynamics and Opinion Formation on Hypergraphs

In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective pairwise node interactions, regardless of the initially underlying multi-way interaction structure. We thus focus on dynamics based on a certain class of non-linear interaction functions, which can model different sociological phenomena such as peer pressure and stubbornness. Unlike for linear consensus dynamics on networks, we show how our nonlinear model dynamics can cause shifts away from the average system state. We examine how these shifts are influenced by the distribution of the initial states, the underlying hypergraph structure and different forms of non-linear scaling of the node interaction function.

physics.soc-ph↗

arXiv2021

Consensus dynamics on temporal hypergraphs

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multi-way interactions. We compare this dynamics with that on appropriate projections of this higher-order network representation that flatten the temporal, the multi-way component, or both. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multi-way interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, the majority in these first-mover groups has a higher influence on the final consensus value - a behaviour that is not observable in this form in projections of the temporal hypergraph.

physics.soc-ph↗

arXiv2021

Extracting Complements and Substitutes from Sales Data: A Network Perspective

The complementarity and substitutability between products are essential concepts in retail and marketing. Qualitatively, two products are said to be substitutable if a customer can replace one product by the other, while they are complementary if they tend to be bought together. In this article, we take a network perspective to help automatically identify complements and substitutes from sales transaction data. Starting from a bipartite product-purchase network representation, with both transaction nodes and product nodes, we develop appropriate null models to infer significant relations, either complements or substitutes, between products, and design measures based on random walks to quantify their importance. The resulting unipartite networks between products are then analysed with community detection methods, in order to find groups of similar products for the different types of relationships. The results are validated by combining observations from a real-world basket dataset with the existing product hierarchy, as well as a large-scale flavour compound and recipe dataset.

cs.SI↗

arXiv2021

Variance and covariance of distributions on graphs

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of weighted graphs and retains many of its intuitive and desired properties. Interestingly, we find that a number of famous concepts in graph theory and network science can be reinterpreted in this setting as variances and covariances of particular distributions. As a particular application, we define the maximum variance problem on graphs with respect to the effective resistance distance, and characterize the solutions to this problem both numerically and theoretically. We show how the maximum variance distribution is concentrated on the boundary of the graph, and illustrate this in the case of random geometric graphs. Our theoretical results are supported by a number of experiments on a network of mathematical concepts, where we use the variance and covariance as analytical tools to study the (co-)occurrence of concepts in scientific papers with respect to the (network) relations between these concepts.

physics.soc-ph↗

arXiv2021

From centre to centres: polycentric structures in individual mobility

The availability of large-scale datasets collected via mobile phones has opened up opportunities to study human mobility at an individual level. The granular nature of these datasets calls for the design of summary statistics that can be used to describe succinctly mobility patterns. In this work, we show that the radius of gyration, a popular summary statistic to quantify the extent of an individual's whereabouts, suffers from a sensitivity to outliers, and is incapable of capturing mobility organised around multiple centres. We propose a natural generalisation of the radius of gyration to a polycentric setting, as well as a novel metric to assess the quality of its description. With these notions, we propose a method to identify the centres in an individual's mobility and apply it to two large mobility datasets with socio-demographic features, showing that a polycentric description can capture features that a monocentric model is incapable of.

physics.soc-ph↗