Multi-scale Modularity in Complex Networks

We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not appropriate to uncover modules in empirical networks, mainly because modularity optimization has an intrinsic bias towards partitions having a characteristic number of modules which might not be compatible with the modular organization of the system. We argue for the use of more flexible quality functions incorporating a resolution parameter that allows us to reveal the natural scales of the system. Different types of multi-resolution quality functions are described and unified by looking at the partitioning problem from a dynamical viewpoint. Finally, significant values of the resolution parameter are selected by using complementary measures of robustness of the uncovered partitions. The methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure

A Systematic Analysis of Community Detection in Complex Networks

Numerous techniques have been proposed by researchers to uncover the hidden patterns of real-world complex networks. Finding a hidden community is one of the crucial tasks for community detection in complex networks. Despite the presence of multiple methods for community detection, identification of the best performing method over different complex networks is still an open research question. In this article, we analyzed eight state-of-the-art community detection algorithms on nine complex networks of varying sizes covering various domains including animal, biomedical, terrorist, social, and human contacts. The objective of this article is to identify the best performing algorithm for community detection in real-world complex networks of various sizes and from different domains. The obtained results over 100 iterations demonstrated that the multi-scale method has outperformed the other techniques in terms of accuracy. Multi-scale method achieved 0.458 average value of modularity metric whereas multiple screening resolution, unfolding fast, greedy, multi-resolution, local fitness optimization, sparse Geosocial community detection algorithm, and spectral clustering, respectively obtained the modularity values 0.455, 0.441, 0.436, 0.421, 0.368, 0.341, and 0.340.

Laplacian Dynamics and Multiscale Modular Structure in Networks

Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time-scale of the process acts as an intrinsic parameter that uncovers community structures at different resolutions. The stability extends and unifies standard notions for community detection: modularity and spectral partitioning can be seen as limiting cases of our dynamic measure. Similarly, recently proposed multi-resolution methods correspond to linearisations of the stability at short times. The connection between community detection and Laplacian dynamics enables us to establish dynamically motivated stability measures linked to distinct null models. We apply our method to find multi-scale partitions for different networks and show that the stability can be computed efficiently for large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and the generalisation of stability to directed network

Post-Processing Hierarchical Community Structures: Quality Improvements and Multi-scale View

Dense sub-graphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Most existing community detection algorithms produce a hierarchical structure of community and seek a partition into communities that optimizes a given quality function. We propose new methods to improve the results of any of these algorithms. First we show how to optimize a general class of additive quality functions (containing the modularity, the performance, and a new similarity based quality function we propose) over a larger set of partitions than the classical methods. Moreover, we define new multi-scale quality functions which make it possible to detect the different scales at which meaningful community structures appear, while classical approaches find only one partition.Comment: 12 Pages, 4 figure

A framework for community detection in heterogeneous multi-relational networks

There has been a surge of interest in community detection in homogeneous single-relational networks which contain only one type of nodes and edges. However, many real-world systems are naturally described as heterogeneous multi-relational networks which contain multiple types of nodes and edges. In this paper, we propose a new method for detecting communities in such networks. Our method is based on optimizing the composite modularity, which is a new modularity proposed for evaluating partitions of a heterogeneous multi-relational network into communities. Our method is parameter-free, scalable, and suitable for various networks with general structure. We demonstrate that it outperforms the state-of-the-art techniques in detecting pre-planted communities in synthetic networks. Applied to a real-world Digg network, it successfully detects meaningful communities.Comment: 27 pages, 10 figure