Obtaining Communities with a Fitness Growth Process

The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for evaluating the community structure and, in the light of them, infer possible explanations for the better performance of local methods compared to global ones in these cases

Community detection algorithms: a comparative analysis

Uncovering the community structure exhibited by real networks is a crucial step towards an understanding of complex systems that goes beyond the local organization of their constituents. Many algorithms have been proposed so far, but none of them has been subjected to strict tests to evaluate their performance. Most of the sporadic tests performed so far involved small networks with known community structure and/or artificial graphs with a simplified structure, which is very uncommon in real systems. Here we test several methods against a recently introduced class of benchmark graphs, with heterogeneous distributions of degree and community size. The methods are also tested against the benchmark by Girvan and Newman and on random graphs. As a result of our analysis, three recent algorithms introduced by Rosvall and Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an excellent performance, with the additional advantage of low computational complexity, which enables one to analyze large systems.Comment: 12 pages, 8 figures. The software to compute the values of our general normalized mutual information is available at http://santo.fortunato.googlepages.com/inthepress

Semi-Supervised Overlapping Community Finding based on Label Propagation with Pairwise Constraints

Algorithms for detecting communities in complex networks are generally unsupervised, relying solely on the structure of the network. However, these methods can often fail to uncover meaningful groupings that reflect the underlying communities in the data, particularly when those structures are highly overlapping. One way to improve the usefulness of these algorithms is by incorporating additional background information, which can be used as a source of constraints to direct the community detection process. In this work, we explore the potential of semi-supervised strategies to improve algorithms for finding overlapping communities in networks. Specifically, we propose a new method, based on label propagation, for finding communities using a limited number of pairwise constraints. Evaluations on synthetic and real-world datasets demonstrate the potential of this approach for uncovering meaningful community structures in cases where each node can potentially belong to more than one community.Comment: Fix table

Modularity functions maximization with nonnegative relaxation facilitates community detection in networks

We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective. With the explicit nonnegative constraint, our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities. The near-orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community. Therefore, the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks. Experimental results show that our new algorithm consistently, sometimes significantly, outperforms the traditional spectral relaxation approaches

Robustness of journal rankings by network flows with different amounts of memory

As the number of scientific journals has multiplied, journal rankings have become increasingly important for scientific decisions. From submissions and subscriptions to grants and hirings, researchers, policy makers, and funding agencies make important decisions with influence from journal rankings such as the ISI journal impact factor. Typically, the rankings are derived from the citation network between a selection of journals and unavoidably depend on this selection. However, little is known about how robust rankings are to the selection of included journals. Here we compare the robustness of three journal rankings based on network flows induced on citation networks. They model pathways of researchers navigating scholarly literature, stepping between journals and remembering their previous steps to different degree: zero-step memory as impact factor, one-step memory as Eigenfactor, and two-step memory, corresponding to zero-, first-, and second-order Markov models of citation flow between journals. We conclude that higher-order Markov models perform better and are more robust to the selection of journals. Whereas our analysis indicates that higher-order models perform better, the performance gain for the second-order Markov model comes at the cost of requiring more citation data over a longer time period.Comment: 9 pages, 5 figure

Mapping bilateral information interests using the activity of Wikipedia editors

We live in a global village where electronic communication has eliminated the geographical barriers of information exchange. The road is now open to worldwide convergence of information interests, shared values, and understanding. Nevertheless, interests still vary between countries around the world. This raises important questions about what today's world map of in- formation interests actually looks like and what factors cause the barriers of information exchange between countries. To quantitatively construct a world map of information interests, we devise a scalable statistical model that identifies countries with similar information interests and measures the countries' bilateral similarities. From the similarities we connect countries in a global network and find that countries can be mapped into 18 clusters with similar information interests. Through regression we find that language and religion best explain the strength of the bilateral ties and formation of clusters. Our findings provide a quantitative basis for further studies to better understand the complex interplay between shared interests and conflict on a global scale. The methodology can also be extended to track changes over time and capture important trends in global information exchange.Comment: 11 pages, 3 figures in Palgrave Communications 1 (2015

Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems

Unveiling the community structure of networks is a powerful methodology to comprehend interconnected systems across the social and natural sciences. To identify different types of functional modules in interaction data aggregated in a single network layer, researchers have developed many powerful methods. For example, flow-based methods have proven useful for identifying modular dynamics in weighted and directed networks that capture constraints on flow in the systems they represent. However, many networked systems consist of agents or components that exhibit multiple layers of interactions. Inevitably, representing this intricate network of networks as a single aggregated network leads to information loss and may obscure the actual organization. Here we propose a method based on compression of network flows that can identify modular flows in non-aggregated multilayer networks. Our numerical experiments on synthetic networks show that the method can accurately identify modules that cannot be identified in aggregated networks or by analyzing the layers separately. We capitalize on our findings and reveal the community structure of two multilayer collaboration networks: scientists affiliated to the Pierre Auger Observatory and scientists publishing works on networks on the arXiv. Compared to conventional aggregated methods, the multilayer method reveals smaller modules with more overlap that better capture the actual organization

Consensus clustering in complex networks

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on the specific random seeds, initial conditions and tie-break rules adopted for their execution. Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Here we show that consensus clustering can be combined with any existing method in a self-consistent way, enhancing considerably both the stability and the accuracy of the resulting partitions. This framework is also particularly suitable to monitor the evolution of community structure in temporal networks. An application of consensus clustering to a large citation network of physics papers demonstrates its capability to keep track of the birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report