Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e., the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering. The results show that the benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

BACKGROUND The increasing availability of digital data on scholarly inputs and outputs—from research funding, productivity, and collaboration to paper citations and scientist mobility—offers unprecedented opportunities to explore the structure and evolution of science. The science of science (SciSci) offers a quantitative understanding of the interactions among scientific agents across diverse geographic and temporal scales: It provides insights into the conditions underlying creativity and the genesis of scientific discovery, with the ultimate goal of developing tools and policies that have the potential to accelerate science. In the past decade, SciSci has benefited from an influx of natural, computational, and social scientists who together have developed big data–based capabilities for empirical analysis and generative modeling that capture the unfolding of science, its institutions, and its workforce. The value proposition of SciSci is that with a deeper understanding of the factors that drive successful science, we can more effectively address environmental, societal, and technological problems. ADVANCES Science can be described as a complex, self-organizing, and evolving network of scholars, projects, papers, and ideas. This representation has unveiled patterns characterizing the emergence of new scientific fields through the study of collaboration networks and the path of impactful discoveries through the study of citation networks. Microscopic models have traced the dynamics of citation accumulation, allowing us to predict the future impact of individual papers. SciSci has revealed choices and trade-offs that scientists face as they advance both their own careers and the scientific horizon. For example, measurements indicate that scholars are risk-averse, preferring to study topics related to their current expertise, which constrains the potential of future discoveries. Those willing to break this pattern engage in riskier careers but become more likely to make major breakthroughs. Overall, the highest-impact science is grounded in conventional combinations of prior work but features unusual combinations. Last, as the locus of research is shifting into teams, SciSci is increasingly focused on the impact of team research, finding that small teams tend to disrupt science and technology with new ideas drawing on older and less prevalent ones. In contrast, large teams tend to develop recent, popular ideas, obtaining high, but often short-lived, impact. OUTLOOK SciSci offers a deep quantitative understanding of the relational structure between scientists, institutions, and ideas because it facilitates the identification of fundamental mechanisms responsible for scientific discovery. These interdisciplinary data-driven efforts complement contributions from related fields such as sciento-metrics and the economics and sociology of science. Although SciSci seeks long-standing universal laws and mechanisms that apply across various fields of science, a fundamental challenge going forward is accounting for un...

Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multi-purpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software (http://www.oslom.org), and we believe it will be a valuable tool in the analysis of networks.