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- Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová
- Physical review. E, Statistical, nonlinear, and…
- 2011

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We… (More)

- Florent Krzakala, Marc Mézard, François Sausset, Yifan Sun, Lenka Zdeborová
- ArXiv
- 2012

Florent Krzakala1,∗, Marc Mézard, Francois Sausset, Yifan Sun and Lenka Zdeborová 1 CNRS and ESPCI ParisTech, 10 rue Vauquelin, UMR 7083 Gulliver, Paris 75005, France. 2 Univ. Paris-Sud & CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France. 3 LMIB and School of Mathematics and Systems Science, Beihang University, 100191 Beijing, China. 4 Institut de… (More)

- Florent Krzakala, Marc Mézard, François Sausset, Yifan Sun, Lenka Zdeborová
- ArXiv
- 2011

F. Krzakala , M. Mézard , F. Sausset , Y. F. Sun and L. Zdeborová 4 1 CNRS and ESPCI ParisTech, 10 rue Vauquelin, UMR 7083 Gulliver, Paris 75005, France. 2 Univ. Paris-Sud & CNRS, LPTMS, UMR8626, Bât. 100, 91405 Orsay, France. 3 LMIB and School of Mathematics and Systems Science, Beihang University, 100191 Beijing, China. 4 Institut de Physique Théorique,… (More)

- Florent Krzakala, Andrea Montanari, Federico Ricci-Tersenghi, Guilhem Semerjian, Lenka Zdeborová
- Proceedings of the National Academy of Sciences…
- 2007

An instance of a random constraint satisfaction problem defines a random subset (the set of solutions) of a large product space chiN (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and q-coloring of random regular graphs) and study the uniform measure with support on S. As the number of constraints per… (More)

- Michael Chertkov, Lukas Kroc, Florent Krzakala, Massimo Vergassola, Lenka Zdeborová
- Proceedings of the National Academy of Sciences…
- 2010

Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the trajectories of the particles. However, they become problematic as the motility and/or the density of the particles… (More)

- Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová
- Physical review letters
- 2011

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks generated by stochastic block models. Using the cavity method of statistical physics and its relationship to belief propagation, we unveil a phase transition from a regime where we can infer the correct group assignments of the nodes to one where… (More)

- Lenka Zdeborová, Florent Krzakala
- Physical review. E, Statistical, nonlinear, and…
- 2007

We consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color. Using the cavity method, we present a detailed and systematic analytical study of the space of proper colorings (solutions). We show that for a fixed number of colors and as the average vertex degree… (More)

- Andrey Y. Lokhov, Marc Mézard, Hiroki Ohta, Lenka Zdeborová
- Physical review. E, Statistical, nonlinear, and…
- 2014

We study the problem of estimating the origin of an epidemic outbreak: given a contact network and a snapshot of epidemic spread at a certain time, determine the infection source. This problem is important in different contexts of computer or social networks. Assuming that the epidemic spread follows the usual susceptible-infected-recovered model, we… (More)

- Florent Krzakala, Cristopher Moore, +4 authors Pan Zhang
- Proceedings of the National Academy of Sciences…
- 2013

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here, we present a class of spectral algorithms based on a… (More)

- Lenka Zdeborová, Marc Mézard
- ArXiv
- 2006

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdös-Rényi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a… (More)