PubMed Health⌕ Search

Biomedical subjects

Marc Barthélemy

Publications and source records attributed to Marc Barthélemy.

10 recordsLinked to original sources
PubMed2006

Resolution limit in community detection.

Detecting community structure is fundamental for uncovering the links between structure and function in complex networks and for practical applications in many disciplines such as biology and sociology. A popular method now widely used relies on the optimization of a quantity called modularity, which is a quality index for a partition of a network into communities. We find that modularity optimization may fail to identify modules smaller than a scale which depends on the total size of the network and on the degree of interconnectedness of the modules, even in cases where modules are unambiguously defined. This finding is confirmed through several examples, both in artificial and in real social, biological, and technological networks, where we show that modularity optimization indeed does not resolve a large number of modules. A check of the modules obtained through modularity optimization is thus necessary, and we provide here key elements for the assessment of the reliability of this community detection method.

Animals↗
PubMed2006

Epidemic variability in complex networks.

We study numerically the variability of the outbreak of diseases on complex networks. We use a susceptible-infected model to simulate the disease spreading at short times in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time of a node on its degree and its distance to the seed. In particular, we show that the infection time of hubs have non-negligible fluctuations which limit their reliability as early detection stations. Finally, we discuss the effect of the multiplicity of paths between two nodes on the infection time. In particular, we demonstrate that the existence of even long paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies.

Journal Article↗
PubMed2006

The role of the airline transportation network in the prediction and predictability of global epidemics.

The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large-scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this article, we present a stochastic computational framework for the forecast of global epidemics that considers the complete worldwide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: (i) we study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; and (ii) we evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. To address these issues we define a set of quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.

Aviation↗
PubMed2005

Dynamical patterns of epidemic outbreaks in complex heterogeneous networks.

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 epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.

Communicable Disease Control↗
PubMed2004

Modeling the evolution of weighted networks.

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 weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scale-free behavior with exponents depending on the microscopic parameters characterizing the coupling rules. Very interestingly, the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices' degree.

Journal Article↗
PubMed2004

Weighted evolving networks: coupling topology and weight dynamics.

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 weight-driven dynamics and generates networks exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scale-free behavior for the weight, strength, and degree distributions.

Ecology↗
PubMed2004

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks.

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 network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.

Disease Outbreaks↗
PubMed2003

Connectivity distribution of spatial networks.

We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of such networks as a functional of the distribution of the nodes. We show that for regular spatial densities, the corresponding spatial network has a connectivity distribution decreasing faster than an exponential. In contrast, we also show that scale-free networks with a power law decreasing connectivity distribution are obtained when a certain information measure of the node distribution (integral of higher powers of the distribution) diverges. We illustrate our results on a simple example for which we present simulation results. Finally, we speculate on the role played by the limiting case P(k) proportional, variant k(-1) which appears empirically to be relevant to spatial networks of biological origin such as the ones constructed from gene expression data.

Journal Article↗
PubMed2002

Large scale cross-correlations in Internet traffic.

The Internet is a complex network of interconnected routers, and the existence of a collective behavior such as congestion suggests that the correlations between the different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network "Renater." We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues-up to a rescaling that exhibits a typical correlation time of the order of 10 min-and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between the connections. The study of the most correlated connections reveals the existence of "active centers" that are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the world-wide web traffic.

Journal Article↗