Transport on weighted Networks: when correlations are independent of degree

Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.Comment: 8 pages, 8 figure

Combinatorial approach to Modularity

Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard tool in the area of community detection, providing at the same time a way to evaluate partitions and, by maximizing it, a method to find communities. In this work, we study the modularity from a combinatorial point of view. Our analysis (as the modularity definition) relies on the use of the configurational model, a technique that given a graph produces a series of randomized copies keeping the degree sequence invariant. We develop an approach that enumerates the null model partitions and can be used to calculate the probability distribution function of the modularity. Our theory allows for a deep inquiry of several interesting features characterizing modularity such as its resolution limit and the statistics of the partitions that maximize it. Additionally, the study of the probability of extremes of the modularity in the random graph partitions opens the way for a definition of the statistical significance of network partitions.Comment: 8 pages, 4 figure

Social inertia in collaboration networks

This work is a study of the properties of collaboration networks employing the formalism of weighted graphs to represent their one-mode projection. The weight of the edges is directly the number of times that a partnership has been repeated. This representation allows us to define the concept of "social inertia" that measures the tendency of authors to keep on collaborating with previous partners. We use a collection of empirical datasets to analyze several aspects of the social inertia: 1) its probability distribution, 2) its correlation with other properties, and 3) the correlations of the inertia between neighbors in the network. We also contrast these empirical results with the predictions of a recently proposed theoretical model for the growth of collaboration networks.Comment: 7 pages, 5 figure

Percolative phase transition on ferromagnetic insulator manganites: uncorrelated to correlated polaron clusters

In this work, we report an atomic scale study on the ferromagnetic insulator manganite LaMnO$_{3.12}$ using $\gamma-\gamma$ PAC spectroscopy. Data analysis reveals a nanoscopic transition from an undistorted to a Jahn-Teller-distorted local environment upon cooling. The percolation thresholds of the two local environments enclose a macroscopic structural transition (Rhombohedric-Orthorhombic). Two distinct regimes of JT-distortions were found: a high temperature regime where uncorrelated polaron clusters with severe distortions of the Mn$^{3+}$O$_{6}$ octahedra survive up to $T \approx 800 K$ and a low temperature regime where correlated regions have a weaker JT-distorted symmetry.Comment: 4 pages, 4 Figures, submitted to PRL, new version with more data, text reformulate

Statistical significance of communities in networks

Nodes in real-world networks are usually organized in local modules. These groups, called communities, are intuitively defined as sub-graphs with a larger density of internal connections than of external links. In this work, we introduce a new measure aimed at quantifying the statistical significance of single communities. Extreme and Order Statistics are used to predict the statistics associated with individual clusters in random graphs. These distributions allows us to define one community significance as the probability that a generic clustering algorithm finds such a group in a random graph. The method is successfully applied in the case of real-world networks for the evaluation of the significance of their communities.Comment: 9 pages, 8 figures, 2 tables. The software to calculate the C-score can be found at http://filrad.homelinux.org/cscor

Human dynamics revealed through Web analytics

When the World Wide Web was first conceived as a way to facilitate the sharing of scientific information at the CERN (European Center for Nuclear Research) few could have imagined the role it would come to play in the following decades. Since then, the increasing ubiquity of Internet access and the frequency with which people interact with it raise the possibility of using the Web to better observe, understand, and monitor several aspects of human social behavior. Web sites with large numbers of frequently returning users are ideal for this task. If these sites belong to companies or universities, their usage patterns can furnish information about the working habits of entire populations. In this work, we analyze the properly anonymized logs detailing the access history to Emory University's Web site. Emory is a medium size university located in Atlanta, Georgia. We find interesting structure in the activity patterns of the domain and study in a systematic way the main forces behind the dynamics of the traffic. In particular, we show that both linear preferential linking and priority based queuing are essential ingredients to understand the way users navigate the Web.Comment: 7 pages, 8 figure

Langevin theory of absorbing phase transitions with a conserved magnitude

The recently proposed Langevin equation, aimed to capture the relevant critical features of stochastic sandpiles, and other self-organizing systems is studied numerically. This equation is similar to the Reggeon field theory, describing generic systems with absorbing states, but it is coupled linearly to a second conserved and static (non-diffusive) field. It has been claimed to represent a new universality class, including different discrete models: the Manna as well as other sandpiles, reaction-diffusion systems, etc. In order to integrate the equation, and surpass the difficulties associated with its singular noise, we follow a numerical technique introduced by Dickman. Our results coincide remarkably well with those of discrete models claimed to belong to this universality class, in one, two, and three dimensions. This provides a strong backing for the Langevin theory of stochastic sandpiles, and to the very existence of this new, yet meagerly understood, universality class.Comment: 4 pages, 3 eps figs, submitted to PR

Sticky grains do not change the universality class of isotropic sandpiles

We revisit the sandpile model with ``sticky'' grains introduced by Mohanty and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties were claimed to be in the universality class of directed percolation for both isotropic and directed models. Simulations in the so-called fixed-energy ensemble show that this conclusion is not valid for isotropic sandpiles and that this model shares the same critical properties of other stochastic sandpiles, such as the Manna model. %as expected from the existence of an extra %conservation-law, absent in directed percolation. These results are strengthened by the analysis of the Langevin equations proposed by the same authors to account for this problem which we show to converge, upon coarse-graining, to the well-established set of Langevin equations for the Manna class. Therefore, the presence of a conservation law keeps isotropic sandpiles, with or without stickiness, away from the directed percolation class.Comment: 4 pages. 3 Figures. Subm. to PR

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.Comment: 10 pages, 8 figure