Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the `right' split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted `field-of-view' limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection (Delvenne et al. (2010) PNAS:107: 12755-12760; Lambiotte et al. (2008) arXiv:0812.1770), in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity.Comment: 20 pages, 6 figure

Application and comparative performance of network modularity algorithms to ecological communities classification

Network modularity is a well-studied large-scale connectivity pattern in networks. The detection of modules in real networks constitutes a crucial step towards a description of the network building blocks and their evolutionary dynamics. The performance of modularity detection algorithms is commonly quantified using simulated networks data. However, a comparison of the modularity algorithms utility for real biological data is scarce. Here we investigate the utility of network modularity algorithms for the classification of ecological plant communities. Plant community classification by the traditional approaches requires prior knowledge about the characteristic and differential species, which are derived from a manual inspection of vegetation tables. Using the raw species abundance data we constructed six different networks that vary in their edge definitions. Four network modularity algorithms were examined for their ability to detect the traditionally recognized plant communities. The use of more restrictive edge definitions significantly increased the accuracy of community detection, that is, the correspondence between network-based and traditional community classification. Random-walk based modularity methods yielded slightly better results than approaches based on the modularity function. For the whole network, the average agreement between the manual classification and the network-based modules is 76% with varying congruence levels for different communities ranging between 11% and 100%. The network-based approach recovered the known ecological gradient from riverside – sand and gravel bank vegetation – to dryer habitats like semidry grassland on dykes. Our results show that networks modularity algorithms offer new avenues of pursuit for the computational analysis of species communities

Statistical inference of assortative community structures

We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant assortative modules in networks, unlike alternatives such as modularity maximization, which systematically overfits both in artificial as well as in empirical examples. In addition, we show that our method is not subject to a resolution limit, and can uncover an arbitrarily large number of communities, as long as there is statistical evidence for them. Our formulation is amenable to model selection procedures, which allow us to compare it to more general approaches based on the stochastic block model, and in this way reveal whether assortativity is in fact the dominating large-scale mixing pattern. We perform this comparison with several empirical networks, and identify numerous cases where the network's assortativity is exaggerated by traditional community detection methods, and we show how a more faithful degree of assortativity can be identified.Comment: 15 pages, 6 figures. Code is available at https://graph-tool.skewed.de and a HOWTO documentation at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm