4.3k citations · 22.3k across the 124 of their papers we have counts for
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Dynamical patterns of epidemic outbreaks in complex heterogeneous networks
Marc Barthelemy, Alain Barrat, Romualdo Pastor-Satorras +1
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the…
Weighted evolving networks: coupling topology and weights dynamics
Alain Barrat, Marc Barthelemy, Alessandro Vespignani
We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple…
Velocity and hierarchical spread of epidemic outbreaks in scale-free networks
Marc Barthelemy, Alain Barrat, Romualdo Pastor-Satorras +1
We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the ne…
On the properties of small-world network models
A. Barrat, M. Weigt
We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometr…
Time scale separation and heterogeneous off-equilibrium dynamics in spin models over random graphs
A. Barrat, R. Zecchina
We study analytically and numerically the statics and the off-equilibrium dynamics of spin models over finitely connected random graphs. We identify a threshold value for the conne…
Temperature evolution and bifurcations of metastable states in mean-field spin glasses, with connections with structural glasses
A. Barrat, S. Franz, G. Parisi
The correlations of the free-energy landscape of mean-field spin glasses at different temperatures are investigated, concentrating on models with a first order freezing transition.…