Unfolding ego-centered community structures with « a similarity approach »

Maximilien Danisch, Jean-Loup Guillaume and Bénédicte Le Grand

CompleNet 2013, Berlin

We propose a framework to unfold the ego-centered community structure of a given node in a network. The framework is not based on the optimization of a quality function, but on the study of the irregularity of the decrease of a similarity measure. It is a practical use of the notion of multi-ego-centered community and we validate the pertinence of the approach on a real-world network of wikipedia pages.


Towards multi-ego-centered communities: a node similarity approach

M. Danisch, J.-L. Guillaume and B. Le Grand

Int. J. of Web Based Communities, Vol. 9, No. 3, pp. 299-322, 2012

The community structure of a graph is defined in various ways in the literature: (i) Partition, where nodes can belong to only one community. This vision is unrealistic and may lead to poor results because most nodes belong to several communities in real-world networks. (ii) Overlapping community structure, which is the most natural view, but is often very difficult to identify in practice due to the complex structure of real-world networks, and the huge number of such possible communities. (iii) Ego-centered community which focuses on individual nodes’ communities and seems to be a good compromise. In this paper we investigate the third vision; we propose a new similarity measure between nodes based on opinion dynamics to unfold ego-centered communities. We call it the carryover opinion. In addition to be parameter-free, the carryover opinion can be calculated in a very time-efficient way and can thus be used in huge graphs. We also go further in the idea of ego-centered communities by introducing the new concept of multi-ego-centered communities, i.e., focusing on the communities of a set of nodes rather than of a single node. A key idea is that, although one node generally belongs to numerous communities, a small set of appropriate nodes can fully characterize a single community.


Diffusion Cascades: Spreading Phenomena in Blog Network Communities

Abdelhamid Salah Brahim, Bénédicte Le Grand and Matthieu Latapy

Parallel Processing Letters 22(1): (2012)

A diffusion cascade occurs when information spreads from one node to the rest of the network through a succession of diffusion events. So far diffusion phenomena have been mostly considered at a macroscopic scale i.e. by studying all nodes of the network. We give a complementary way to analyse network interactions by considering the problem at different scales. To that purpose, we use the community structure of the network to characterize diffusion between nodes (and between communities) and to identify interactions behaviour patterns.


Stable community cores in complex networks

Massoud Seifi, Jean-Loup Guillaume, Ivan Junier, Jean-Baptiste Rouquier and Svilen Iskrov

Proceedings of the 3rd Workshop on Complex Networks (CompleNet 2012), Melbourne, Florida

Complex networks are generally composed of dense sub-networks called communities. Many algorithms have been proposed to automatically detect such communities. However, they are often unstable and behave non-deterministically. We propose here to use this non-determinism in order to compute groups of nodes on which community detection algorithms agree most of the time.We show that these groups of nodes, called community cores, are more similar to Ground Truth than communities in real and artificial networks. Furthermore, we show that in contrary to the classical approaches, we can reveal the absence of community structure in random graphs.


Community Cores in Evolving Networks

Massoud Seifi and Jean-Loup Guillaume

Proceedings of the Mining Social Network Dynamic 2012 Workshop (MSND), Inconjunction with the international conference World Wide Web WWW 2012, Lyon,France, pp. 1173-1180

Community structure is a key property of complex networks.Many algorithms have been proposed to automatically detect communities in static networks but few studies haveconsidered the detection and tracking of communities in anevolving network. Tracking the evolution of a given community over time requires a clustering algorithm that producesstable clusters. However, most community detection algorithms are very unstable and therefore unusable for evolvingnetworks. In this paper, we apply the methodology proposedin [14] to detect what we call community cores in evolvingnetworks. We show that cores are much more stable than »classical » communities and that we can overcome the disadvantages of the stabilized methods.


Citations among blogs in a hierarchy of communities: method and case study

Abdelhamid Salah brahim, Bénédicte Le Grand, Lionel Tabourier, Matthieu Latapy

Journal of Computational Science, Vol 2(3), 2011

How does the structure of a network (e.g. its organization into groups or communities) impact the interaction among its nodes? In this paper we propose a generic methodology to study the correlation between complex networks interactions and their community structure. We illustrate it on a blog network and focus on citation links. We first define a homophily probability evaluating the tendency of blogs to ite blogs from the same communities. We then introduce the notion of community distance to capture if a blog cites (or is cited by) blogs distant or not from its community. We analyze the distribution of distances corresponding to each citation link, and use it to build maps of relevant communities which help interpreting blogs interactions. This community-oriented approach allows to study citation links at various abstraction levels, and conversely, enable us to characterize communities with regard to their citation behaviour.


Extraction hiérarchique de fenêtres de temps basée sur la structure communautaire

Thomas Aynaud and Jean-Loup Guillaume

in Proceedings of MARAMI 2011

Dans cet article nous décrivons une méthode de décomposition du temps en fenêtres de temps dans un graphe dynamique. Une particularité de la méthode est que le résultat est un regroupement hiérarchique : les fenêtres de temps sont elles-mêmes susceptibles d’en contenir. En outre, les fenêtres n’ont pas besoin d’être contiguës ce qui permet par exemple de détecter une structure se répétant. De plus, chaque fenêtre est associée à une décomposition en communautés représentant la structure topologique du réseau durant cette fenêtre. Nous appliquons ensuite cette méthode à trois graphes de terrain dynamiques ayant des caractéristiques différentes pour montrer que les fenêtres identifiées correspondent bien à des phénomènes observables. In this paper, we describe a way to cluster the time in time windows in a dynamic network. The result is a tree and thus time windows can themselves contain smaller ones. Moreover, the windows do not have to be consecutive and this allows for instance to detect repeated structure. Each window is also associated to a community decomposition that represents the topological structure of the network during this window. We then apply the method to three dynamic networks to show that observed time windows correspond to observable phenomena.


Multi-Step Community Detection and Hierarchical Time Segmentation in Evolving Networks

Thomas Aynaud and Jean-Loup Guillaume

proceedings of the Fifth SNA-KDD Workshop Social Network Mining and Analysis, in conjunction with the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 2011)

Many complex systems composed of interacting objects  like social networks or the web can be modeled as graphs. They can usually be divided in dense sub-graphs with few links between them, called communities and detecting this underlying community structure may have a major impact in the understanding of these systems. We focus here on evolving graphs, for which the usual approach is to represent the state of the system at different time steps and to compute communities independently on the graph obtained at each time step. We propose in this paper to use a different framework: instead of detecting communities on each time step, we detect a unique decomposition in communities that is relevant for (almost) every time step during a given period called the time window.  We propose a definition of this new decomposition and two algorithms to detect it quickly. We validate both the approach and the algorithms on three evolving networks of different kinds showing that the quality loss at each time step is very low despite the constraint of maximization on several time steps. Since the time window length is a crucial parameter of our technique, we also propose an unsupervised hierarchical clustering algorithm to build automatically a hierarchical time segmentation into time windows. This clustering relies on a new similarity measure based on community structure. We show that it is very efficient in detecting meaningful windows.


Optimisation locale multi-niveaux de la modularité

Thomas Aynaud, Vincent Blondel, Jean-Loup Guillaume and Renaud Lambiotte

in Partitionnement de graphe : optimisation et applications, Traité IC2, Hermes-Lavoisier 2011

Dans ce chapitre, nous présentons une méthode gloutonne pour optimiser la modularité d’un graphe. Cette méthode de partionnement permet de traiter avec une excellente précision des systèmes de taille inégalée, allant jusqu’à plusieurs milliards de liens. Notre algorithme a de surcroît l’avantage de ne pas être limité à l’optimisation de la modularité puisqu’il peut être généralisé à d’autres fonctions de qualité, et de découvrir des communautés à différentes échelles. Les performances de l’algorithme sont évaluées sur des graphes artificiels pour lesquels la structure communautaire est connue, ainsi que sur des graphes de terrain réels.

Long range community detection

Thomas Aynaud and Jean-Loup Guillaume

Latin-American Workshop on Dynamic Networks (LAWDN), Buenos Aires, 2010

Complex networks can usually be divided in dense subnetworks called communities. In evolving networks, the usual way to detect communities is to find several partitions independently, one for each time step. However, this generally causes troubles when trying to track communities from one time step to the next. We propose here a new method to detect only one decomposition in communities that is good for (almost) every time step. We show that this unique partition can be computed with a modification of the Louvain method and that the loss of quality at each time step is generally low despite the constraint of global maximization. We also show that some specific modifications of the networks topology can be identified using this unique partition in the case of the Internet topology.


Détection de communautés à long terme dans les graphes dynamiques

Thomas Aynaud and Jean-Loup Guillaume

Journée thématique Fouille de grands graphes, en conjonction avec la première conférence sur les Modèles et l’Analyse des Réseaux : Approches Mathématiques et Informatique (MARAMI), Toulouse, France, 2010

La plupart des graphes de terrain peuvent être décomposés en sous graphes denses appelés communautés. Habituellement, dans des graphes dynamiques, les communautés sont détectées pour chaque instant indépendamment ce qui pose de nombreux problèmes tels que la stabilité ou le suivi de des communautés entre deux décompositions successives. Nous proposons ici une méthode pour trouver une partition unique, de qualité, couvrant une longue période. Cette décomposition peut être trouvée efficacement via une adaptation de la méthode de Louvain et la perte de qualité à chaque instant due à la contrainte de détecter des communautés globales s’avère assez faible.


Static community detection algorithms for evolving networks

Thomas Aynaud and Jean-Loup Guillaume

Proceedings of International Workshop on Dynamic Networks (WDN), in conjunction with WiOpt 2010, pages 508-514

Complex networks can often be divided in dense sub-networks called communities. We study, using a partition edit distance, how three community detection algorithms transform their outputs if the input network is sligthly modified. The instabilities appear to be important and we propose a modification of one algorithm to stabilize it and to allow the tracking of the communities in a dynamic network. This modification has one parameter which is a tradeoff between stability and quality. The resulting algorithm appears to be very effective. We finally use it on a dynamic network of blogs.


Structure multi-échelle de grands graphes de terrain

Thomas Aynaud and Jean-Loup Guillaume

in Technique et Science Informatiques, vol. 30/2, pp. 137-154, 2011

Most complex networks can be divided into dense sub-graphs called communities. These communities may also be divided recursively producing a hierarchical structure of communities, summarized in a tree named dendrogram. In this article we analyze this structure extracted from several complex networks. First we study the shape of the tree and, in particular, communities imbrications. Then we show that an excessive decomposition of communities can result in meaningless communities. We propose a couple of approaches to solve this problem.


Interactive multiscale visualization of huge graphs: application to a network of weblogs

Massoud Seifi, Jean-loup Guillaume, Matthieu Latapy and Bénédicte Le Grand

Proceedings of the 8th Workshop on Visualization and Knowledge Extraction (EGC 2010)

De nombreux réseaux du monde réel peuvent être modélisés par des grands graphes. Réduire la complexité d’un graphe de manière à ce qu’il puisse être facilement interprété par l’oeil humain est une aide précieuse pour comprendre et analyser ce type de données. Nous proposons une méthodologie de visualisation interactive multi-échelle de grands graphes basée sur une classification des sommets qui nous permet de représenter ces graphes de manière lisible et interprétable. Nous appliquons notre méthodologie à un réseau de blogs francophones.