Finding Statistically Significant Communities in Networks

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

Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

Enhancing community detection using a network weighting strategy

A community within a network is a group of vertices densely connected to each other but less connected to the vertices outside. The problem of detecting communities in large networks plays a key role in a wide range of research areas, e.g. Computer Science, Biology and Sociology. Most of the existing algorithms to find communities count on the topological features of the network and often do not scale well on large, real-life instances. In this article we propose a strategy to enhance existing community detection algorithms by adding a pre-processing step in which edges are weighted according to their centrality w.r.t. the network topology. In our approach, the centrality of an edge reflects its contribute to making arbitrary graph tranversals, i.e., spreading messages over the network, as short as possible. Our strategy is able to effectively complements information about network topology and it can be used as an additional tool to enhance community detection. The computation of edge centralities is carried out by performing multiple random walks of bounded length on the network. Our method makes the computation of edge centralities feasible also on large-scale networks. It has been tested in conjunction with three state-of-the-art community detection algorithms, namely the Louvain method, COPRA and OSLOM. Experimental results show that our method raises the accuracy of existing algorithms both on synthetic and real-life datasets.Comment: 28 pages, 2 figure

A generalised significance test for individual communities in networks

Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks, communities are generally heterogeneous in various aspects such as the size, density of edges, connectivity to other communities and significance. In the present study, we propose a method to statistically test the significance of individual communities in a given network. Compared to the previous methods, the present algorithm is unique in that it accepts different community-detection algorithms and the corresponding quality function for single communities. The present method requires that a quality of each community can be quantified and that community detection is performed as optimisation of such a quality function summed over the communities. Various community detection algorithms including modularity maximisation and graph partitioning meet this criterion. Our method estimates a distribution of the quality function for randomised networks to calculate a likelihood of each community in the given network. We illustrate our algorithm by synthetic and empirical networks.Comment: 20 pages, 4 figures and 4 table

Kantian fractionalization predicts the conflict propensity of the international system

The study of complex social and political phenomena with the perspective and methods of network science has proven fruitful in a variety of areas, including applications in political science and more narrowly the field of international relations. We propose a new line of research in the study of international conflict by showing that the multiplex fractionalization of the international system (which we label Kantian fractionalization) is a powerful predictor of the propensity for violent interstate conflict, a key indicator of the system's stability. In so doing, we also demonstrate the first use of multislice modularity for community detection in a multiplex network application. Even after controlling for established system-level conflict indicators, we find that Kantian fractionalization contributes more to model fit for violent interstate conflict than previously established measures. Moreover, evaluating the influence of each of the constituent networks shows that joint democracy plays little, if any, role in predicting system stability, thus challenging a major empirical finding of the international relations literature. Lastly, a series of Granger causal tests shows that the temporal variability of Kantian fractionalization is consistent with a causal relationship with the prevalence of conflict in the international system. This causal relationship has real-world policy implications as changes in Kantian fractionalization could serve as an early warning sign of international instability.Comment: 17 pages + 17 pages designed as supplementary online materia

Connecting Dream Networks Across Cultures

Many species dream, yet there remain many open research questions in the study of dreams. The symbolism of dreams and their interpretation is present in cultures throughout history. Analysis of online data sources for dream interpretation using network science leads to understanding symbolism in dreams and their associated meaning. In this study, we introduce dream interpretation networks for English, Chinese and Arabic that represent different cultures from various parts of the world. We analyze communities in these networks, finding that symbols within a community are semantically related. The central nodes in communities give insight about cultures and symbols in dreams. The community structure of different networks highlights cultural similarities and differences. Interconnections between different networks are also identified by translating symbols from different languages into English. Structural correlations across networks point out relationships between cultures. Similarities between network communities are also investigated by analysis of sentiment in symbol interpretations. We find that interpretations within a community tend to have similar sentiment. Furthermore, we cluster communities based on their sentiment, yielding three main categories of positive, negative, and neutral dream symbols.Comment: 6 pages, 3 figure