Tag Archives: dynamics

Papers

Towards realistic modeling of IP-level routing topology dynamics

Clémence Magnien, Amélie Medem, Sergey Kirgizov, Fabien Tarissan

Many works have studied the Internet topology, but few have investigated the question of how it evolves over time. This paper focuses on the Internet routing IP-level topology and proposes a first step towards realistic modeling of its dynamics. We study periodic measurements of routing trees from a single monitor to a fixed destination set and identify invariant properties of its dynamics. Based on those observations, we then propose a model for the underlying mechanisms of the topology dynamics. Our model remains simple as it only incorporates load-balancing phenomena and routing changes. By extensive simulations,  we show that, despite its simplicity, this model effectively captures the observed behaviors, thus providing key insights of relevant mechanisms governing the Internet routing dynamics. Besides, by confronting simulations over different kinds of topology, we also provide insights of which structural properties play a key role to explain the properties of the observed dynamics, which therefore strengthens the relevance of our model.

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Papers

Outskewer: Using Skewness to Spot Outliers in Samples and Time Series

Sébastien Heymann, Matthieu Latapy, Clémence Magnien

Finding outliers in datasets is a classical problem of high interest for (dynamic) social network analysis. However, most methods rely on assumptions which are rarely met in practice, such as prior knowledge of some outliers or about normal behavior. We propose here Outskewer, a new approach based on the notion of skewness (a measure of the symmetry of a distribution) and its evolution when extremal values are removed one by one. Our method is easy to set up, it requires no prior knowledge on the system, and it may be used on-line. We illustrate its performance on two data sets representative of many use-cases: evolution of ego-centered views of the internet topology, and logs of queries entered into a search engine.
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Papers

Extraction hiérarchique de fenêtres de temps basée sur la structure communautaire

Thomas Aynaud and Jean-Loup Guillaume

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.

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Papers

Phénomènes de diffusion dans les réseaux dynamiques : simulation et modélisation

Alice Albano

Les phénomènes de diffusion sont présents dans de nombreux contextes: diffusion d’épidémies, de virus informatiques, d’information dans des réseaux sociaux, etc. Bien que les réseaux où se produit la diffusion soient souvent dynamiques, cette dynamique n’est pas prise en compte dans la plupart des modèles existants. L’objectif de ces travaux est de proposer des modèles de diffusion, et d’étudier l’impact de la dynamique du réseau sur la diffusion.
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Papers

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

Thomas Aynaud and Jean-Loup Guillaume

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.

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Papers

Link prediction in bipartite graphs using internal links and weighted projection

Oussama Allali, Clémence Magnien and Matthieu Latapy

Many real-world complex networks, like client-product or file-provider relations, have a bipartite nature and evolve during time. Predicting links that will appear in them is one of the main approach to understand their dynamics. Only few works address the bipartite case, though, despite its high practical interest and the specific challenges it raises. We define in this paper the notion of internal links in bipartite graphs and propose a link prediction method based on them. We describe the method and experimentally compare it to a basic collaborative filtering approach. We present results obtained for two typical practical cases. We reach the conclusion that our method performs very well, and that internal links play an important role in bipartite graphs and their dynamics.
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Papers

Long range community detection

Thomas Aynaud and Jean-Loup Guillaume

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.

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Papers

Détection de communautés à long terme dans les graphes dynamiques

Thomas Aynaud and Jean-Loup Guillaume

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.

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Videos

Radar Dynamics: Detection of an Event

Radar Dynamics: Detection of an Event

> By Antoine Mazières, Clémence Magnien and Fabien Tarissan Download As part of the “Radar for the Internet” project described in this paper, this video aims at understanding better the dynamics of the Internet’s topology. The dataset used in this experiment is built on an ego-centeric view of the network from one of our monitors, […]

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Papers

Static community detection algorithms for evolving networks

Thomas Aynaud and Jean-Loup Guillaume

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.

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