We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.

We propose a novel method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature. We present the results of the algorithm for computer simulated and real networks and compare them with other approaches. The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks. PACS numbers:The description of the structure of complex networks has been one of the focus of attention of the physicist's community in the recent years. The levels of description range from the microscopic (degree, clustering coefficient, centrality measures, etc., of individual nodes) to the macroscopic description in terms of statistical properties of the whole network (degree distribution, total clustering coefficient, degree-degree correlations, etc.) [1,2,3,4]. Between these two extremes there is a "mesoscopic" description of networks that tries to explain its community structure. The general notion of community structure in complex networks was first pointed out in the physics literature by Girvan and Newman [5], and refers to the fact that nodes in many real networks appear to group in subgraphs in which the density of internal connections is larger than the connections with the rest of nodes in the network.The community structure has been empirically found in many real technological, biological and social networks [6,7,8,9, 10] and its emergence seems to be at the heart of the network formation process [11].The existing methods intended to devise the community structure in complex networks have been recently reviewed in [10]. All these methods require a definition of community that imposes the limit up to which a group should be considered a community. However, the concept of community itself is qualitative: nodes must be more connected within its community than with the rest of the network, and its quantification is still a subject of debate. Some quantitative definitions that came from sociology have been used in recent studies [12], but in general, the physics community has widely accepted a recent measure for the community structure based on the concept of modularity Q introduced by Newman and Girvan [13]:where e rr are the fraction of links that connect two nodes inside the community r, a r the fraction of links that have one or both vertices inside of the community r, and the sum extends to all communities r in a given network. Note that this measure provides a way to determine if a certain mesoscopic description of the graph in terms of communities is more or less accurate. The larger the values of Q the most accurate a partition into communities is.The search for the optimal (largest) modularity value is a NP-hard problem due to the fact that the space of possible partitions grows faster than any power of the system size. For this reason, a heuristic search strategy is mandatory to restrict th...

BackgroundTeamwork is a fundamental aspect of many human activities, from business to art and from sports to science. Recent research suggest that team work is of crucial importance to cutting-edge scientific research, but little is known about how teamwork leads to greater creativity. Indeed, for many team activities, it is not even clear how to assign credit to individual team members. Remarkably, at least in the context of sports, there is usually a broad consensus on who are the top performers and on what qualifies as an outstanding performance.Methodology/Principal FindingsIn order to determine how individual features can be quantified, and as a test bed for other team-based human activities, we analyze the performance of players in the European Cup 2008 soccer tournament. We develop a network approach that provides a powerful quantification of the contributions of individual players and of overall team performance.Conclusions/SignificanceWe hypothesize that generalizations of our approach could be useful in other contexts where quantification of the contributions of individual team members is important.

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.

Many studies demonstrate that there is still a significant gender bias, especially at higher career levels, in many areas including science, technology, engineering, and mathematics (STEM). We investigated field-dependent, gender-specific effects of the selective pressures individuals experience as they pursue a career in academia within seven STEM disciplines. We built a unique database that comprises 437,787 publications authored by 4,292 faculty members at top United States research universities. Our analyses reveal that gender differences in publication rate and impact are discipline-specific. Our results also support two hypotheses. First, the widely-reported lower publication rates of female faculty are correlated with the amount of research resources typically needed in the discipline considered, and thus may be explained by the lower level of institutional support historically received by females. Second, in disciplines where pursuing an academic position incurs greater career risk, female faculty tend to have a greater fraction of higher impact publications than males. Our findings have significant, field-specific, policy implications for achieving diversity at the faculty level within the STEM disciplines.

Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.

We study the scaling of fluctuations with the mean of traffic in complex networks using a model where the arrival and departure of "packets" follow exponential distributions, and the processing capability of nodes is either unlimited or finite. The model presents a wide variety of exponents between 1/2 and 1 for this scaling, revealing their dependence on the few parameters considered, and questioning the existence of universality classes. We also report the experimental scaling of the fluctuations in the Internet for the Abilene backbone network. We found scaling exponents between 0.71 and 0.86 that do not fit with the exponent 1/2 reported in the literature.

Lab-in-the-field experiment reveals that humans display a reduced set of consistent behavioral phenotypes in dyadic games.