arXiv subjects

Matthieu Latapy

Publications and source records attributed to Matthieu Latapy.

At least 19 recordsLinked to original sources

arXiv2026

Trivial Graph Features and Classical Learning are Enough to Detect Random Anomalies

Detecting anomalies in link streams that represent various kinds of interactions is an important research topic with crucial applications. Because of the lack of ground truth data, proposed methods are mostly evaluated through their ability to detect randomly injected links. In contrast with most proposed methods, that rely on complex approaches raising computational and/or interpretability issues, we show here that trivial graph features and classical learning techniques are sufficient to detect such anomalies extremely well. This basic approach has very low computational costs and it leads to easily interpretable results. It also has many other desirable properties that we study through an extensive set of experiments. We conclude that detection methods should now target more complex kinds of anomalies.

cs.LG↗

arXiv2025

Improving flocking behaviors in street networks with vision

We improve a flocking model on street networks introduced in a previous paper. We expand the field of vision of walkers, making the model more realistic. Under such conditions, we obtain groups of walkers whose gathering times and robustness to break ups are better than previous results. We explain such improvements because the alignment rule with vision guaranties walkers do not split into divergent directions at intersections anymore, and because the attraction rule with vision gathers distant groups. This paves the way to a better understanding of events where walkers have collective decentralized goals, like protests.

physics.soc-ph↗

arXiv2024

Fast and Robust Flocking of Protesters on Street Networks

We present a simple model of protesters scattered throughout a city who want to gather into large and mobile groups. This model relies on random walkers on a street network that follow tactics built from a set of basic rules. Our goal is to identify the most important rules for fast and robust flocking of walkers. We explore a wide set of tactics and show the central importance of a specific rule based on alignment. Other rules alone perform poorly, but our experiments show that combining alignment with them enhances flocking, and that obtained groups are then remarkably robust.

cs.MA↗

arXiv2024

Mapping low-resolution edges to high-resolution paths: the case of traffic measurements in cities

We consider the following problem : we have a high-resolution street network of a given city, and low-resolution measurements of traffic within this city. We want to associate to each measurement the set of streets corresponding to the observed traffic. To do so, we take benefit of specific properties of these data to match measured links to links in the street network. We propose several success criteria for the obtained matching. They show that the matching algorithm generally performs very well, and they give complementary ways to detect data discrepancies that makes any matching highly dubious.

cs.SI↗

arXiv2023

Link Streams as a Generalization of Graphs and Time Series

A link stream is a set of possibly weighted triplets (t, u, v) modeling that u and v interacted at time t. Link streams offer an effective model for datasets containing both temporal and relational information, making their proper analysis crucial in many applications. They are commonly regarded as sequences of graphs or collections of time series. Yet, a recent seminal work demonstrated that link streams are more general objects of which graphs are only particular cases. It therefore started the construction of a dedicated formalism for link streams by extending graph theory. In this work, we contribute to the development of this formalism by showing that link streams also generalize time series. In particular, we show that a link stream corresponds to a time-series extended to a relational dimension, which opens the door to also extend the framework of signal processing to link streams. We therefore develop extensions of numerous signal concepts to link streams: from elementary ones like energy, correlation, and differentiation, to more advanced ones like Fourier transform and filters.

eess.SP↗

arXiv2023

Temporal Betweenness Centrality on Shortest Paths

Betweenness centrality measure assesses the importance of nodes in a graph and has been used in a variety of contexts. Betweenness centrality has also been extended to temporal graphs. Temporal graphs have edges that bear labels according to the time of the interactions between the nodes. Betweenness centrality has been extended to the temporal graph settings, and the notion of paths has been extended to temporal paths. Recent results by Bu{\ss} et al. and Rymar et al. showed that the betweenness centrality of all nodes in a temporal graph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of time units, m the number of temporal edges and n the number of nodes. In this paper, we improve the running time analysis of these previous approaches to compute the betweenness centrality of all nodes in a temporal graph. We give an algorithm that runs in O(n m T + n^2 T ).

cs.DS↗

arXiv2022

A Frequency-Structure Approach for Link Stream Analysis

A link stream is a set of triplets $(t, u, v)$ indicating that $u$ and $v$ interacted at time $t$. Link streams model numerous datasets and their proper study is crucial in many applications. In practice, raw link streams are often aggregated or transformed into time series or graphs where decisions are made. Yet, it remains unclear how the dynamical and structural information of a raw link stream carries into the transformed object. This work shows that it is possible to shed light into this question by studying link streams via algebraically linear graph and signal operators, for which we introduce a novel linear matrix framework for the analysis of link streams. We show that, due to their linearity, most methods in signal processing can be easily adopted by our framework to analyze the time/frequency information of link streams. However, the availability of linear graph methods to analyze relational/structural information is limited. We address this limitation by developing (i) a new basis for graphs that allow us to decompose them into structures at different resolution levels; and (ii) filters for graphs that allow us to change their structural information in a controlled manner. By plugging-in these developments and their time-domain counterpart into our framework, we are able to (i) obtain a new basis for link streams that allow us to represent them in a frequency-structure domain; and (ii) show that many interesting transformations to link streams, like the aggregation of interactions or their embedding into a euclidean space, can be seen as simple filters in our frequency-structure domain.

eess.SP↗

arXiv2021

A Local Updating Algorithm for Personalized PageRank via Chebyshev Polynomials

The personalized PageRank algorithm is one of the most versatile tools for the analysis of networks. In spite of its ubiquity, maintaining personalized PageRank vectors when the underlying network constantly evolves is still a challenging task. To address this limitation, this work proposes a novel distributed algorithm to locally update personalized PageRank vectors when the graph topology changes. The proposed algorithm is based on the use of Chebyshev polynomials and a novel update equation that encompasses a large family of PageRank-based methods. In particular, the algorithm has the following advantages: (i) it has faster convergence speed than state-of-the-art alternatives for local PageRank updating; and (ii) it can update the solution of recent generalizations of PageRank for which no updating algorithms have been developed. Experiments in a real-world temporal network of an autonomous system validate the effectiveness of the proposed algorithm.

cs.SI↗

arXiv2021

A logical approach for temporal and multiplex networks analysis

Many systems generate data as a set of triplets (a, b, c): they may represent that user a called b at time c or that customer a purchased product b in store c. These datasets are traditionally studied as networks with an extra dimension (time or layer), for which the fields of temporal and multiplex networks have extended graph theory to account for the new dimension. However, such frameworks detach one variable from the others and allow to extend one same concept in many ways, making it hard to capture patterns across all dimensions and to identify the best definitions for a given dataset. This extended abstract overrides this vision and proposes a direct processing of the set of triplets. In particular, our work shows that a more general analysis is possible by partitioning the data and building categorical propositions that encode informative patterns. We show that several concepts from graph theory can be framed under this formalism and leverage such insights to extend the concepts to data triplets. Lastly, we propose an algorithm to list propositions satisfying specific constraints and apply it to a real world dataset.

cs.SI↗

arXiv2021

Full Bitcoin Blockchain Data Made Easy

Despite the fact that it is publicly available, collecting and processing the full bitcoin blockchain data is not trivial. Its mere size, history, and other features indeed raise quite specific challenges, that we address in this paper. The strengths of our approach are the following: it relies on very basic and standard tools, which makes the procedure reliable and easily reproducible; it is a purely lossless procedure ensuring that we catch and preserve all existing data; it provides additional indexing that makes it easy to further process the whole data and select appropriate subsets of it. We present our procedure in details and illustrate its added value on large-scale use cases, like address clustering. We provide an implementation online, as well as the obtained dataset.

cs.SI↗

arXiv2021

Termination of Multipartite Graph Series Arising from Complex Network Modelling

An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs. However, this approach has, until now, severe limitations resulting from its incapacity to reproduce a key property of this object: the overlapping nature of cliques in complex networks. In order to get rid of these limitations we propose to encode the structure of clique overlaps in a network thanks to a process consisting in iteratively factorising the maximal bicliques between the upper level and the other levels of a multipartite graph. We show that the most natural definition of this factorising process leads to infinite series for some instances. Our main result is to design a restriction of this process that terminates for any arbitrary graph. Moreover, we show that the resulting multipartite graph has remarkable combinatorial properties and is closely related to another fundamental combinatorial object. Finally, we show that, in practice, this multipartite graph is computationally tractable and has a size that makes it suitable for complex network modelling.

cs.DM↗

arXiv2021

On the Termination of Some Biclique Operators on Multipartite Graphs

We define a new graph operator, called the weak-factor graph, which comes from the context of complex network modelling. The weak-factor operator is close to the well-known clique-graph operator but it rather operates in terms of bicliques in a multipartite graph. We address the problem of the termination of the series of graphs obtained by iteratively applying the weak-factor operator starting from a given input graph. As for the clique-graph operator, it turns out that some graphs give rise to series that do not terminate. Therefore, we design a slight variation of the weak-factor operator, called clean-factor, and prove that its associated series terminates for all input graphs. In addition, we show that the multipartite graph on which the series terminates has a very nice combinatorial structure: we exhibit a bijection between its vertices and the chains of the inclusion order on the intersections of the maximal cliques of the input graph.

cs.DM↗

arXiv2021

Computing Betweenness Centrality in Link Streams

Betweeness centrality is one of the most important concepts in graph analysis. It was recently extended to link streams, a graph generalization where links arrive over time. However, its computation raises non-trivial issues, due in particular to the fact that time is considered as continuous. We provide here the first algorithms to compute this generalized betweenness centrality, as well as several companion algorithms that have their own interest. They work in polynomial time and space, we illustrate them on typical examples, and we provide an implementation.

cs.DS↗

arXiv2021

Partitions of an Integer into Powers

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In particular, we show that the set of these partitions can be ordered in a natural way which gives the distributive lattice structure to this set. We also give a tree structure which allow efficient and simple enumeration of the partitions of an integer.

math.CO↗

arXiv2021

Generalized Tilings with Height Functions

In this paper, we introduce a generalization of a class of tilings which appear in the literature: the tilings over which a height function can be defined (for example, the famous tilings of polyominoes with dominoes). We show that many properties of these tilings can be seen as the consequences of properties of the generalized tilings we introduce. In particular, we show that any tiling problem which can be modelized in our generalized framework has the following properties: the tilability of a region can be constructively decided in polynomial time, the number of connected components in the undirected flip-accessibility graph can be determined, and the directed flip-accessibility graph induces a distributive lattice structure. Finally, we give a few examples of known tiling problems which can be viewed as particular cases of the new notions we introduce.

math.CO↗

arXiv2020

Strongly Connected Components in Stream Graphs: Computation and Experimentations

Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here several solutions with polynomial time and space complexities, each with its own strengths and weaknesses. We provide an implementation and experimentally compare the algorithms in a wide variety of practical cases. In addition, we propose an approximation scheme that significantly reduces computation costs, and gives even more insight on the dataset.

cs.SI↗

arXiv2019

Do you trade with your friends or become friends with your trading partners? A case study in the G1 cryptocurrency

We study the interplay between social ties and financial transactions made through a recent cryptocurrency called $\breve{G}1$. It has the particularity of combining the usual transaction record with a reliable network of identified users. This gives the opportunity to observe exactly who sent money to whom over a social network. This social network is a key piece of this cryptocurrency, which therefore puts much effort in ensuring that nodes correspond to unique, well identified, real living human users, linked together only if they met at least once in real world. Using this data, we study how social ties impact the structure of transactions and conversely. We show that users make transactions almost exclusively with people they are connected with in the social network. Instead, they tend to build social connections with people they will never make transactions with.

cs.SI↗

arXiv2019

Weighted, Bipartite, or Directed Stream Graphs for the Modeling of Temporal Networks

We recently introduced a formalism for the modeling of temporal networks, that we call stream graphs. It emphasizes the streaming nature of data and allows rigorous definitions of many important concepts generalizing classical graphs. This includes in particular size, density, clique, neighborhood, degree, clustering coefficient, and transitivity. In this contribution, we show that, like graphs, stream graphs may be extended to cope with bipartite structures, with node and link weights, or with link directions. We review the main bipartite, weighted or directed graph concepts proposed in the literature, we generalize them to the cases of bipartite, weighted, or directed stream graphs, and we show that obtained concepts are consistent with graph and stream graph ones. This provides a formal ground for an accurate modeling of the many temporal networks that have one or several of these features.

cs.SI↗