4.3k citations · 28.3k across the 97 of their papers we have counts for
14 papers · 1 filter
A class of models for random hypergraphs
Marc Barthelemy
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs f…
From one-way streets to percolation on random mixed graphs
Vincent Verbavatz, Marc Barthelemy
In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirica…
The shape of shortest paths in random spatial networks
Alexander P. Kartun-Giles, Marc Barthelemy, Carl P. Dettmann
In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance , geodesics exhibit deviations from their mean length that are of…
Transitions in spatial networks
Marc Barthelemy
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the…
Towards a classification of planar maps
Alexandre Diet, Marc Barthelemy
Planar graphs and their spatial embedding -- planar maps -- are used in many different fields due to their ubiquity in the real world (leaf veins in biology, street patterns in urb…
Spatial Networks
Marc Barthelemy
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networ…
Epidemic variability in complex networks
Pascal Crépey, Fabián P. Alvarez, Marc Barthélemy
We study numerically the variability of the outbreak of diseases on complex networks. We use a SI model to simulate the disease spreading at short times, in homogeneous and in scal…
Characterization and Modeling of weighted networks
Marc Barthelemy, Alain Barrat, Romualdo Pastor-Satorras +1
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific…
Modeling the evolution of weighted networks
Alain Barrat, Marc Barthelemy, Alessandro Vespignani
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple…
The architecture of complex weighted networks
Alain Barrat, Marc Barthelemy, Romualdo Pastor-Satorras +1
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly in…
Truncation of power law behavior in "scale-free" network models due to information filtering
Stefano Mossa, Marc Barthelemy, H. Eugene Stanley +1
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of th…
The Random Fuse Network as a Dipolar Magnet
Marc Barthelemy, Rava da Silveira, Henri Orland
We introduce an approximate mapping between the random fuse network (RFN) and a random field dipolar Ising model (RFDIM). The state of the network damage is associated with a metas…
Classes of behavior of small-world networks
Luis A. Nunes Amaral, Antonio Scala, Marc Barthelemy +1
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the…
Small-world networks: Evidence for a crossover picture
Marc Barthelemy, Luis A. N. Amaral
Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder in the links,…