Emmanuel Orsini

6ème conférence sur les Modèles et l’Analyse des Réseaux : Approches Mathématiques et Informatique (MARAMI), Paris, 2015.

L’article qui suit propose de donner un sens à la modularité dans les flots de liens et ainsi de bénéficier de certaines de ses propriétés, et des heuristiques qui l’optimisent. Cette no- tion de modularité aboutira après quelques simplifications à un algorithme capable de calculer une partition sur un jeu de données de 400 000 emails. Pour ce faire on construira une nou- velle modélisation où le temps est complètement continu, sur laquelle la modularité se définit naturellement et de manière pertinente. Cette modélisation apporte une nouvelle interpretation des réseaux dynamiques, qui se veut suffisamment générale pour s’adapter à différents types de données.

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Raphaël Fournier and Matthieu Latapy

International Journal of Internet Science ARTICLE IN PRES S 2015, 10 (1), ISSN 1662-5544

Recent studies have shown that child abuse material is shared through peer-to-peer (P2P) networks, which allow users to exchange files without a central server. Obtaining knowledge on the extent of this activity has major consequences for child protection, policy making and Internet regulation. Previous works have developed tools and analyses to provide overall figures in temporally-limited measurements. Offenders’ behavior is mostly studied through small-scale interviews and there is few information on the times at which they engage in such activity. Here we show that the proportion of search-engine queries for pedophile content gradually has grown by a factor of almost 3 in three years. We also find that during the day, certain hours are, on average, privileged by seekers. Our results demonstrate that P2P networks are actively used to search for pedophile content and we find new and large-scale results on pedophile offenders’ profile, indicating that a substantial proportion is well-integrated into family life and professional work activities.

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Clémence Magnien and Fabien Tarissan.

In proceedings of the International Symposium on Foundations and Applications of Big Data Analytics (FAB), in conjunction with ASONAM, 2015.

For a long time now, researchers have worked on defining different metrics able to characterize the importance of nodes in networks. Among them, centrality measures have proved to be pertinent as they relate the position of a node in the structure to its ability to diffuse an information efficiently. The case of dynamic networks, in which nodes and links appear and disappear over time, led the community to propose extensions of those classical measures. Yet, they do not investigate the fact that the network structure evolves and that node importance may evolve accordingly. In the present paper, we propose temporal extensions of notions of centrality, which take into account the paths existing at any given time, in order to study the time evolution of nodes’ importance in dynamic networks. We apply this to two datasets and show that the importance of nodes does indeed vary greatly with time. We also show that in some cases it might be meaningless to try to identify nodes that are consistently important over time, thus strengthening the interest of temporal extensions of centrality measures.

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Nicolas Dugué, Anthony Perez, Maximilien Danisch, Florian Bridoux, Amélie Daviau, Tennessy Kolubako, Simon Munier and Hugo Durbano.

IEEE/ACM International Conference on Advances in Social Network Analysis and Mining (ASONAM), 2015, Paris. (Demo track paper)

On Twitter, social capitalists use dedicated hashtags and mutual subscriptions to each other in order to gain followers and to be retweeted. Their methods are successful enough to make them appear as influent users. Indeed, applications dedicated to the influence measurement such as Klout and Kred give high scores to most of these users. Meanwhile, their high number of retweets and followers are not due to the relevance of the content they tweet, but to their social capitalism techniques. In order to be able to detect these users, we train a classifier using a dataset of social capitalists and regular users. We then implement this classifier in a web application that we call DDP. DDP allows users to test whether a Twitter account is a social capitalist or not and to visualize the data we use to make the prediction. DDP allows administrator to crawl data from a lot of users automatically. Furthermore, administrators can manually label Twitter accounts as social capitalists or regular users to add them into the dataset. Finally, administrators can train new classifiers in order to take into account the new Twitter accounts added to the dataset, and thus making evolve the classifier with these new recently collected data. The web application is thus a way to collect data, make evolve the knowledge about social capitalists and to keep detecting them efficiently.

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Tiphaine Viard, Matthieu Latapy, Clémence Magnien

First International Workshop on Dynamics in Networks (DyNo), in conjunction with ASONAM, 2015.

Interaction traces between humans are usually rich in information concerning the patterns and habits of individuals. Such datasets have been recently made available, and more and more researchers address the new questions raised by this data. A link stream is a sequence of triplets (t, u, v) indicating that an interaction occurred between u and v at time t, and as such is a natural representation of these data. We generalize the classical notion of cliques in graphs to such link streams: for a given , a -clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least every during this time interval. We proceed to compute the maximal -cliques on a real-world dataset of contact among students, and show how it can bring new interpretation to patterns of contact.

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François Queyroi, Sergey Kirgizov

Information Processing Letters, Volume 115, Issue 9, September 2015, Pages 689–693 http://www.sciencedirect.com/science/article/pii/S0020019015000678

We discuss  the computation  of a  distance between  two hierarchical clusterings of the  same set. It is defined as  the minimum number of  elements that  have to  be removed so  the remaining  clusterings are  equal. The problem of distance  computing was extensively studied for partitions. We prove it can be  solved in polynomial time in the case of hierarchies  as it gives  birth to a  class of perfect  graphs. We  also  propose an  algorithm  based on  recursively computing  maximum assignments.

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Tiphaine Viard, Matthieu Latapy et Clémence Magnien

ALGOTEL 2015 — 17èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, juin 2015, Beaune, France

Un flot de liens est une séquence de triplets (t,u,v), signifiant que u et v ont interagi au temps t. Nous généralisons la notion de cliques à ces flots de liens : pour un delta donné, une delta-clique est un ensemble de nœuds et un intervalle de temps, tels que toutes les paires de nœuds dans cet ensemble interagissent au moins tous les delta sur cet intervalle. Nous proposons un premier algorithme permettant d’énumérer les delta-cliques dans un flot de liens.

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Soumajit Pramanik, Maximilien Danisch, Qinna Wang and Bivas Mitra

[extended abstract] Twitter for Research, 1st International & Interdisciplinary Conference, 2015

We developed a Twitter app to suggest users to mention in a tweet in order to maximise the spread of an information. Users that are popular, active on Twitter and interested in the content of the tweet are targeted. The problem is mapped to the knapsack problem, the length of the screen name of a user being an important variable. Collected data (who retweets among the suggested users and features of these users) will be used to improve the app and theory/models of information spread on Online Social Networks. The application is available at: http://bit.ly/1BKZURE

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Christophe Crespelle, Matthieu Latapy, Ha Duong Phan.

Discrete Applied Mathematics, Volume 195, 20 November 2015, Pages 59–73

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.

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Noé Gaumont, François Queyroi, Clémence Magnien et Matthieu Latapy.

In Complex Networks VI (pp. 57-64). Springer International Publishing. 2015

Many studies use community detection algorithms in order to understand complex networks. Most papers study node communities, i.e. groups of nodes, which may or may not overlap. A widely used measure to evaluate the quality of a community structure is the modularity. However, sometimes it is also relevant to study link partitions rather than node partitions. In order to evaluate a link partition, we propose a new quality function: Expected Nodes. Our function is based on the same inspiration as the modularity and compares, for a given link group, the number of incident nodes to the expected one. In this short note, we discuss the advantages and drawbacks of our quality function compared to other ones on synthetics graphs. We show that Expected Nodes is able to pass some fundamental sanity criteria and is the one that best identifies the most relevant partition in a more realistic context.

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Noé Gaumont, François Queyroi

ALGOTEL 2014 — 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Jun 2014, Le Bois-Plage-en-Ré, France. pp.1-4

La recherche de communautés chevauchantes est un enjeu important pour l’analyse des réseaux complexes. Une piste souvent envisagée est la recherche d’un partitionnement des arêtes du graphe. L’évaluation de cette décomposition tient cependant rarement compte du fait que les communautés recherchées correspondent à des groupes d’arêtes. Nous discutons dans ce papier l’utilisation de nouveaux critères pouvant répondre à ce problème. Nous proposons de comparer le nombre de sommets incidents à un groupe d’arêtes au nombre attendu dans un graphe aléatoire. Un optimum local de la mesure dérivée de ce concept peut être obtenu par un algorithme glouton. Nous présentons les premiers résultats obtenus à travers une analyse de la mesure et des tests empiriques.

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François Queyroi

5ème conférence sur les Modèles et l’Analyse des Réseaux : Approches Mathématiques et Informatique (MARAMI), Paris, 2014.

Nous présentons une transformation de graphes temporels, appelée -duplication, permettant de réduire l’hétérogénéité temporelle dans l’analyse de réseaux dynamiques. Au lieu de construire une séquence d’instantanées à partir d’un découpage global du temps, nous utilisons une approche centrée sur les individus en considérant un sommet sur plusieurs sessions i.e. des périodes durant lesquelles il se connecte au moins tous les . Cette note décrit précisément le concept de -duplication et fournit des pistes quant à son utilisation pour l’analyse de réseaux complexes. En particulier, nous proposons une généralisation du concept de k-cores aux graphes temporels.

Tackx Raphaël, Maximilien Danisch et Fabien Tarissan

In Acte de la 5ème Conférence sur les Modèles et l’Analyse des Réseaux : Approches Mathématiques et Informatique (MARAMI’14), Paris, France, 2014.

De nombreux réseaux rencontrés en pratique se prêtent naturellement à la formalisation sous forme de graphes pour analyser et modéliser leur structure. Cette représentation plate des réseaux s’est montrée cependant peu efficace pour rendre compte de propriétés importantes et non triviales liées à la structure bipartie des réseaux. Des travaux récents ont montré notamment que des propriétés de recouvrements semblaient être présentes dans la plupart des réseaux réels et qu’elles permettaient de mieux expliquer des propriétés observées sur dans les graphes simples. Le présent travail entend poursuivre cette problématique en étudiant les propriétés liées aux recouvrements dans les structures communautaire des réseaux sociaux. Nous conduisons pour cela une étude basée sur le réseau des pages et catégories WIKIPEDIA et nous montrons notamment que parmi les métriques proposées récemment pour rendre compte de ces recouvrements complexes entre communautés, le coefficient de redondance était plus pertinent que le populaire coefficient de clustering biparti étudié généralement en pratique.

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Fabien Tarissan

In ISCS 2014: Interdisciplinary Symposium on Complex Systems, Emergence, Complexity and Computation, 14:309-318, Springer, 2014.

Many real-world networks lend themselves to the use of graphs for analysing and modelling their structure. But such a simple representation has proven to miss some important and non trivial properties hidden in the bipartite structure of the networks. Recent papers have shown that overlapping properties seem to be present in bipartite networks and that it could explain better the properties observed in simple graphs. This work intends to investigate this question by studying two proposed metrics to account for overlapping structures in bipartite networks. The study, conducted on four dataset stemming from very different contexts (computer science, juridical science and social science), shows that the most popular metrics, the clustering coefficient, turns out to be less relevant that the recent redundancy coefficient to analyse intricate overlapping properties of real networks.

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Romain Hollanders, Daniel Bernardes, Bivas Mitra, Raphael Jungers, Jean-Charles Delvenne, Fabien Tarissan.

In Journal of Network Science, 2(3):341-266, Cambridge University Press, 2014.

Peer-to-peer (p2p) systems have driven a lot of attention in the past decade as they have become a major source of Internet traffic. The amount of data flowing through the p2p network is huge and hence challenging both to comprehend and to control. In this work, we take advantage of a new and rich dataset recording p2p activity at a remarkable scale to address these difficult problems. After extracting the relevant and measurable properties of the network from the data, we develop two models that aim to make the link between the low-level properties of the network, such as the proportion of peers that do not share content (i.e., free riders) or the distribution of the files among the peers, and its high-level properties, such as the Quality of Service or the diffusion of content, which are of interest for supervision and control purposes. We observe a significant agreement between the high-level properties measured on the real data and on the synthetic data generated by our models, which is encouraging for our models to be used in practice as large-scale prediction tools. Relying on them, we demonstrate that spending efforts to reduce the amount of free-riders indeed helps to improve the availability of files on the network. We observe however a saturation of this phenomenon after 65% of free-riders.

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Matthieu Latapy, Elie Rotenberg, Christophe Crespelle, Fabien Tarissan

13th IFIP International Conference on Networking – Networking 2014, 2014, Trondheim, Norway. IEEE, pp.1-9

Most current models of the internet rely on knowledge of the degree distribution of its core routers, which plays a key role for simulation purposes. In practice, this distribution is usually observed directly on maps known to be partial, biased and erroneous. This raises serious concerns on the true knowledge one may have of this key property. Here, we design an original measurement approach targeting reliable estimation of the degree distribution of core routers, without resorting to any map. It consists in sampling random core routers and precisely estimate their degree thanks to probes sent from many distributed monitors. We run and assess a large-scale measurement following this approach, carefully controlling and correcting bias and errors encountered in practice. The estimate we obtain is much more reliable than previous knowledge, and it shows that the true degree distribution is very different from all current assumptions.

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Fabien Tarissan, Elie Rotenberg, Matthieu Latapy, Christophe Crespelle

IEEE 22nd International Symposium on Modeling Analysis and Simulation of Computer and Telecomunication Systems (MASCOTS’14), At Paris, France

The classical approach for Internet topology measurement consists in distributively collecting as much data as possible and merging it into one single piece of topology on which are conducted subsequent analysis. Although this approach may seem reasonable, in most cases network measurements performed in this way suffer from some or all of the following limitations: they give only partial views of the networks under concern, these views may be intrinsically biased, and they contain erroneous data due to the measurement tools. Here we present a new tool, named UDP Ping , that relies on a very different approach for the measurement of the Internet topology. Its basic principle is to measure the interface of a given target directed toward a monitor which sends the measurement probe. We demonstrate how to use it to deploy real world-wide measurements that provide reliable (i.e. bias and error free) knowledge of the Internet topology, namely the degree distribution of routers in the core Internet in our example.

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Alice Albano, Jean-Loup Guillaume, and Bénédicte Le Grand

Proceedings of the 8th IEEE International Conference on Research Challenges in Information Science (RCIS 2014)

The analysis of social networks is a challenging research area, in particular because of their dynamic features. In this paper, we study such evolving graphs through the evolution of their community structure. More specifically, we build on existing approaches for the identification of stable communities over time. This paper presents two contributions. We first propose a new way to compute such stable communities, using a different time scale, called intrinsic time. This intrinsic time is related to the dynamics of the graph (e.g., in terms of link appearance or disappearance) and independent from traditional (extrinsic) time units, like the second. We then show how visualization both at intrinsic and extrinsic time scales can help validating and interpreting the obtained communities. Our results are illustrated on a social network made of contacts among the participants of the 2006 edition of the Infocom conference.

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Lionel Tabourier, Anne-Sophie Libert, and Renaud Lambiotte

2014, DyNakII, 2nd International Workshop on Dynamic Networks and Knowledge Discovery (PKDD 2014 workshop)

In this work, we consider the issue of unveiling unknown links in a social network, one of the difficulties of this problem being the small number of unobserved links in comparison of the total number of pairs of nodes. We define a simple supervised learning-to-rank framework, called RankMerging, which aims at combining information provided by various unsupervised rankings. As an illustration, we apply the method to the case of a cell phone service provider, which uses the network among its contractors as a learning set to discover links existing among users of its competitors. We show that our method substantially improves the performance of unsupervised metrics of classification. Finally, we discuss how it can be used with additional sources of data, including temporal or semantic information

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