A Unifying Model for Representing Time-Varying Graphs

Graph-based models form a fundamental aspect of data representation in Data Sciences and play a key role in modeling complex networked systems. In particular, recently there is an ever-increasing interest in modeling dynamic complex networks, i.e. networks in which the topological structure (nodes and edges) may vary over time. In this context, we propose a novel model for representing finite discrete Time-Varying Graphs (TVGs), which are typically used to model dynamic complex networked systems. We analyze the data structures built from our proposed model and demonstrate that, for most practical cases, the asymptotic memory complexity of our model is in the order of the cardinality of the set of edges. Further, we show that our proposal is an unifying model that can represent several previous (classes of) models for dynamic networks found in the recent literature, which in general are unable to represent each other. In contrast to previous models, our proposal is also able to intrinsically model cyclic (i.e. periodic) behavior in dynamic networks. These representation capabilities attest the expressive power of our proposed unifying model for TVGs. We thus believe our unifying model for TVGs is a step forward in the theoretical foundations for data analysis of complex networked systems.Comment: Also appears in the Proc. of the IEEE International Conference on Data Science and Advanced Analytics (IEEE DSAA'2015

Egomunities, Exploring Socially Cohesive Person-based Communities

In the last few years, there has been a great interest in detecting overlapping communities in complex networks, which is understood as dense groups of nodes featuring a low outbound density. To date, most methods used to compute such communities stem from the field of disjoint community detection by either extending the concept of modularity to an overlapping context or by attempting to decompose the whole set of nodes into several possibly overlapping subsets. In this report we take an orthogonal approach by introducing a metric, the cohesion, rooted in sociological considerations. The cohesion quantifies the community-ness of one given set of nodes, based on the notions of triangles - triplets of connected nodes - and weak ties, instead of the classical view using only edge density. A set of nodes has a high cohesion if it features a high density of triangles and intersects few triangles with the rest of the network. As such, we introduce a numerical characterization of communities: sets of nodes featuring a high cohesion. We then present a new approach to the problem of overlapping communities by introducing the concept of ego-munities, which are subjective communities centered around a given node, specifically inside its neighborhood. We build upon the cohesion to construct a heuristic algorithm which outputs a node's ego-munities by attempting to maximize their cohesion. We illustrate the pertinence of our method with a detailed description of one person's ego-munities among Facebook friends. We finally conclude by describing promising applications of ego-munities such as information inference and interest recommendations, and present a possible extension to cohesion in the case of weighted networks

Triangles to Capture Social Cohesion

Although community detection has drawn tremendous amount of attention across the sciences in the past decades, no formal consensus has been reached on the very nature of what qualifies a community as such. In this article we take an orthogonal approach by introducing a novel point of view to the problem of overlapping communities. Instead of quantifying the quality of a set of communities, we choose to focus on the intrinsic community-ness of one given set of nodes. To do so, we propose a general metric on graphs, the cohesion, based on counting triangles and inspired by well established sociological considerations. The model has been validated through a large-scale online experiment called Fellows in which users were able to compute their social groups on Face- book and rate the quality of the obtained groups. By observing those ratings in relation to the cohesion we assess that the cohesion is a strong indicator of users subjective perception of the community-ness of a set of people

GCP: Gossip-based Code Propagation for Large-scale Mobile Wireless Sensor Networks

Wireless sensor networks (WSN) have recently received an increasing interest. They are now expected to be deployed for long periods of time, thus requiring software updates. Updating the software code automatically on a huge number of sensors is a tremendous task, as ''by hand'' updates can obviously not be considered, especially when all participating sensors are embedded on mobile entities. In this paper, we investigate an approach to automatically update software in mobile sensor-based application when no localization mechanism is available. We leverage the peer-to-peer cooperation paradigm to achieve a good trade-off between reliability and scalability of code propagation. More specifically, we present the design and evaluation of GCP ({\emph Gossip-based Code Propagation}), a distributed software update algorithm for mobile wireless sensor networks. GCP relies on two different mechanisms (piggy-backing and forwarding control) to improve significantly the load balance without sacrificing on the propagation speed. We compare GCP against traditional dissemination approaches. Simulation results based on both synthetic and realistic workloads show that GCP achieves a good convergence speed while balancing the load evenly between sensors

Notre environnement s'est peuplé d'objets communicants

National audienceC'est vraiment allé très vite. En 20 ans, notre environnement s'est peuplé d'une multitude d'objets intelligents - étiquettes, capteurs divers et bien sûr téléphones portables - qui détectent, activent et communiquent entre eux via les infrastructures de télécommunication, des réseaux de capteurs voire des mini réseaux personnels. Une révolution qui a su profiter des progrès constants de la microélectronique et des télécommunications sans fil

Maximizing the Cohesion is NP-hard

We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.Comment: No. RR-7734 (2011

Understanding community evolution in Complex systems science

International audienceComplex systems is a new approach in science that studying organized be- haviours in computer science, biology, physics, chemistry, and many other fields. By collecting articles containing topic keywords relevant for the field of complex networks from ISI Web of knowledge during 1985-2009, we construct a science network, which connects ~ 215000 articles according to the proportion of shared references. Moreover, articles' publication time makes it dynamically evolve in time. We here use a two-step approach [3] to explore community evolution and study underlying information behind community changes. We firstly detect com- munities by applying Louvain algorithm [2] on each snapshot graph, and secondly construct relationships between partitions at successive snapshot graphs [1]

Finding cohesive communities with C³

Social communities have drawn a lot of attention in the past decades. We have previously introduced and validated the use of the cohesion, a graph metric which quantitatively captures the community-ness in a social sense of a set of nodes in a graph. Here we show that the problem of maximizing this quantity is NP-Hard. Furthermore, we show that the dual problem of minimizing this quantity, for a fixed set size is also NP-Hard. We then propose a heuristic to optimize the cohesion which we apply to the graph of voting agreement between U.S Senators. Finally we conclude on the validity of the approach by analyzing the resulting agreement communities.Les communautés sociales ont attiré beaucoup d'attention ces dernières années. Nous avions précédemment proposé et validé l'utilisation de la cohésion, une métrique de graphe qui capture quantitativement la qualité communautaire, au sens social, d'un ensemble de sommets d'un graphe. Nous montrons que le problème de trouver un ensemble de cohésion maximum dans un graphe non orienté est NP-dur. Par ailleurs, nous montrons que le problème dual de minimiser cette quantité, pour une taille donnée, est aussi NP-dur. Nous proposons ensuite une heuristique pour optimiser la cohésion que nous appliquons au graph d'agrément de vote entre Sénateurs des États-Unis. Finalement nous concluons sur la validité de l'approche en analysant les communautés résultantes

Translation on Graphs: An Isometric Shift Operator

International audienceIn this letter, we propose a new shift operator for graph signals, enforcing that our operator is isometric. Doing so, we ensure that as many properties of the time shift as possible get carried over. Finally, we show that our operator behaves reasonably for graph signals

Kriging for indirect measurement, with application to flow measurement

International audienceKriging, a technique originating from geostatistics, is employed to build black-box models to be used to predict a quantity of interest based on the values taken by some experimental factors. This attractive alternative to more popular techniques such as neural networks is first presented. It is then applied to the measurement of the flow in a water pipe from the observation of speed at given points of a cross section. A pure black-box model turns out not to be satisfactory, and two approaches are suggested for incorporating prior knowledge. The second one, which is more systematic also turns out to provide much better performance