Finding network communities using modularity density

This is the author's accepted manuscript. The final published version is available from IOP Publishing via the DOI in this recordMany real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.Engineering and Physical Sciences Research Council (EPSRC

Analysis of the communities of an urban mobile phone network

This is the final version. Available from Public Library of Science via the DOI in this record. Data Availability: Data available at: Telecom Italia Big Data Challenge 2014, https://dandelion.eu/datamine/open-big-data/.Being able to characterise the patterns of communications between individuals across different time scales is of great importance in understanding people's social interactions. Here, we present a detailed analysis of the community structure of the network of mobile phone calls in the metropolitan area of Milan revealing temporal patterns of communications between people. We show that circadian and weekly patterns can be found in the evolution of communities, presenting evidence that these cycles arise not only at the individual level but also at that of social groups. Our findings suggest that these trends are present across a range of time scales, from hours to days and weeks, and can be used to detect socially relevant events.EPSRCEuropean Commissio

Synchronization in dynamical networks with unconstrained structure switching

We provide a rigorous solution to the problem of constructing a structural evolution for a network of coupled identical dynamical units that switches between specified topologies without constraints on their structure. The evolution of the structure is determined indirectly, from a carefully built transformation of the eigenvector matrices of the coupling Laplacians, which are guaranteed to change smoothly in time. In turn, this allows to extend the Master Stability Function formalism, which can be used to assess the stability of a synchronized state. This approach is independent from the particular topologies that the network visits, and is not restricted to commuting structures. Also, it does not depend on the time scale of the evolution, which can be faster than, comparable to, or even secular with respect to the the dynamics of the units.Comment: 8 pages, 3 figures. arXiv admin note: text overlap with arXiv:1407.074

Depth-dependent critical behavior in V2H

Using X-ray diffuse scattering, we investigate the critical behavior of an order-disorder phase transition in a defective "skin-layer" of V2H. In the skin-layer, there exist walls of dislocation lines oriented normal to the surface. The density of dislocation lines within a wall decreases continuously with depth. We find that, because of this inhomogeneous distribution of defects, the transition effectively occurs at a depth-dependent local critical temperature. A depth-dependent scaling law is proposed to describe the corresponding critical ordering behavior.Comment: 5 pages, 4 figure

Degree correlations in directed scale-free networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between~2 and~3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.Comment: 10 pages, 5 figure

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

A-Train Based Observational Metrics for Model Evaluation in Extratropical Cyclones

Extratropical cyclones contribute most of the precipitation in the midlatitudes, i.e. up to 70 during winter in the northern hemisphere, and can generate flooding, extreme winds, blizzards and have large socio-economic impacts. As such, it is important that general circulation models (GCMs) accurately represent these systems so their evolution in a warming climate can be understood. However, there are still uncertainties on whether warming will increase their frequency of occurrence, their intensity and how much rain or snow they bring. Part of the issue is that models have trouble representing their strength, but models also have biases in the amount of clouds and precipitation they produce. This is caused by potential issues in various aspects of the models: convection, boundary layer, and cloud scheme to only mention a few. In order to pinpoint which aspects of the models need improvement for a better representation of extratropical cyclone precipitation and cloudiness, we will present A-train based observational metrics: cyclone-centered, warm and cold frontal composites of cloud amount and type, precipitation rate and frequency of occurrence. Using the same method to extract similar fields from the model, we will present an evaluation of the GISS-ModelE2 and the IPSL-LMDZ-5B models, based on their AR5 and more recent versions. The AR5 version of the GISS model underestimates cloud cover in extratropical cyclones while the IPSL AR5 version overestimates it. In addition, we will show how the observed CloudSat-CALIPSO cloud vertical distribution across cold fronts changes with moisture amount and cyclone strength, and test if the two models successfully represent these changes. We will also show how CloudSat-CALIPSO derived cloud type (i.e. convective vs. stratiform) evolves across warm fronts as cyclones age, and again how this is represented in the models. Our third process-based analysis concerns cumulus clouds in the post-cold frontal region and how their amount relates to the stability of the boundary layer. This test uses Aqua cloud and vertical atmospheric profiles and when applied to the model output can help assess the accuracy of the convection, boundary layer and cloud scheme