Le séminaire de l'équipe ComplexNetworks est un rendez-vous bi-mensuel organisé au sein du laboratoire LIP6. Des indications sur l'accès au site de Jussieu sont disponibles ici.
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Marthe Bonamy, LaBRI, Université de Bordeaux
Kempe equivalence of colourings
Vendredi 3 juin 2016 à 11h, salle 24-25/405
Given a colouring of a graph, a Kempe change is the operation of picking a maximal bichromatic subgraph and switching the two colours in it. Two colourings are Kempe equivalent if they can be obtained from each other through a series of Kempe changes. Kempe changes were first introduced in a failed attempt to prove the Four Colour Theorem, but they proved to be a powerful tool for other colouring problems. They are also relevant for more applied questions, most notably in theoretical physics. Consider a graph with no vertex of degree more than some integer D. In 2007, Mohar conjectured that all its D-colourings are Kempe-equivalent. Feghali, Johnson and Paulusma proved in 2015 that this is true for D=3, with the exception of one single graph which disproves the conjecture in its generality. We settle the remaining cases by proving the conjecture holds for every integer D at least 4. This is a joint work with Nicolas Bousquet (LIRIS, Ecole Centrale Lyon, France), Carl Feghali (Durham University, UK) and Matthew Johnson (Durham University, UK).

Argyris Kalogeratos, MLMDA, CMLA, ENS Cachan
Suppressing diffusion processes on arbitrary networks using treatment resources of limited efficiency
Lundi 13 juin 2016 à 11h, salle 26-00/332
In many real-life situations, it is critical to dynamically suppress or remove an undesired diffusion process (viruses, information, behaviors, etc.). The talk will present a framework for Dynamic Resource Allocation (DRA) assuming a continuous-time SIS epidemic model, and that a budget of treatment resources of limited efficiency are at the disposal of authorities. Special emphasis will be given on the macro- and microscopic (or local) properties of the network structure for the problem and two strategies will be presented that fall in this framework: a) a simple yet effective greedy approach, and b) a more sophisticated one that uses a precomputed priority plan of how the healing strategy should proceed on a specific network. Additionally, extensions in competitive scenarios will be discussed.

Sergey Kirgizov, Le2i, Université de Bourgogne
Temporal density of complex networks and ego-community dynamics
Lundi 04 julliet 2016 à 11h, salle 24-25/405
At first, we say that a ego-community structure is a probability measure defined on the set of network nodes. Any subset of nodes may engender its own ego-community structure around. Many community detection algorithms can be modified to yield a result of this type, for instance, the personalized pagerank. We also recall that community detection algorithms (including personalized pagerank) can be viewed from different perspectives: random walks, convergence of markov chain, spectral clustering, optimization, mincut(s), discrete cheeger inequality(ies), etc. Next, we present a continuous version of Viard-Latapy-Magnien link streams, that we call "temporal density". Classical kernel density estimation is used to move from discrete link streams towards their continuous counterparts. Using matrix perturbation theory we can prove that ego-community structure changes smoothly when the network evolves smoothly. This is very important, for example, for visualization purposes. Combining the temporal density and personalized pagerank methods, we are able to visualize and study the evolution of the ego-community structures of complex networks with a large number of temporal links in order to extract interacting information. For example, we can detect events, trace the evolution of (ego-)community structure, etc. We illustrate and validate our approach using "Primary school temporal network data" provided by sociopatterns.org, and we show how the temporal density can be applied to the study of very large datasets, such as a collection of tweets written by European Parliament candidates during European Parliament election in 2014.