Characterizing the community structure of complex networks is a key challenge in many scientific fields. Very diverse algorithms and methods have been proposed to this end, many working reasonably well in specific situations. However, no consensus has emerged on which of these methods is the best to use in practice. In part, this is due to the fact that testing their performance requires the generation of a comprehensive, standard set of synthetic benchmarks, a goal not yet fully achieved. Here, we present a type of benchmark that we call "closed", in which an initial network of known community structure is progressively converted into a second network whose communities are also known. This approach differs from all previously published ones, in which networks evolve toward randomness. The use of this type of benchmark allows us to monitor the transformation of the community structure of a network. Moreover, we can predict the optimal behavior of the variation of information, a measure of the quality of the partitions obtained, at any moment of the process. This enables us in many cases to determine the best partition among those suggested by different algorithms. Also, since any network can be used as a starting point, extensive studies and comparisons can be performed using a heterogeneous set of structures, including random ones. These properties make our benchmarks a general standard for comparing community detection algorithms.
How can we accurately compare different community detection algorithms? These algorithms cluster nodes in a given network, and their performance is often validated on benchmark networks with explicit ground-truth communities. Given the lack of cluster labels in real-world networks, a model that generates realistic networks is required for accurate evaluation of these algorithm. In this paper, we present a simple, intuitive, and flexible benchmark generator to generate intrinsically modular networks for community validation. We show how the generated networks closely comply with the characteris…
Heterogeneity characterises real-world networks, where nodes show a broad range of different topological features. However, nodes also tend to organise into communities -- subsets of nodes that are sparsely inter-connected but are densely intra-connected (more than the network's average connectivity). This means that nodes belonging to the same community are close to each other by some distance measure, such as the resistance distance, which is the effective distance between any pair of nodes considering all possible paths. In this work, we present automation (i.e., unsupervised) and missing a…
Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit
近年来，复杂网络社区发现算法受到了广泛的关注。已经提出了各种各样的计算几何学，其中一些具有很长的历史，用于识别社区，或者用于识别良好的图分区。在大多数情况下，算法最大限度地提高了一个特定的目标函数，从而找到了“正确的”分裂成社区。尽管仍然缺乏对算法的彻底比较，但已经努力设计基准，即，具有已知社区结构的随机图模型，可以对算法进行评估。然而，流行的社区检测方法和基准通常假设一个隐式的社区概念的基础上，类candle子图，一种形式的社区结构，并不总是真实网络的特征。具体来说，从几何约束中产生的网络可以具有自然的非类cyclo-like子结构，具有大的有效直径，这可以被解释为长距离社区。在这项工作中，我们表明，远程社区逃避检测流行的方法，这是盲目的一个有限的“视野”的限制，一个内在的上限规模上的社区，他们可以检测到。视野限制意味着远距离社区往往被过度分割。我们展示了如何通过对社区检测采用动态视角（Delvenne et al.（2010）PNAS：107：12755-12760; Lambiotte et al.（2008）arXiv：0812.1770），其中图上的马尔可夫过程的演变被用作在所有尺度上的网络结构上的变焦镜头，人们可以检测集团或非集团样社区，而无需对检测施加上限。因此，算法在固有的低直径，类candle基准上的性能可能并不总是表示在具有本地，稀疏连接的真实网络中同样好的结果…
Modularity-based algorithms used for community detection have been increasing in recent years. Modularity and its application have been generating controversy since some authors argue it is not a metric without disadvantages. It has been shown that algorithms that use modularity to detect communities suffer a resolution limit and, therefore, it is unable to identify small communities in some situations. In this work, we try to apply a density optimization of communities found by the label propagation algorithm and study what happens regarding modularity of optimized results. We introduce a met…
We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how the sketch can be used to explicitly identify six key community events which typically occur during network evolution: growth, shrinkage, merging, splitting, birth and death. Based on these detection techniques, we formulate a community detection algorithm which can process a network concurrently exhibiting all processes. One advantage afforded by the sketch…
Univ de Lyon（里昂大学）；CNRS（法国国家科学研究中心）；Université Lyon 1（里昂第一大学）；Université Mohamed Seddik Benyahia de Jijel（吉杰勒穆罕默德·塞迪克·本叶海亚大学）；Italian National Research Council（意大利国家研究委员会）
Many algorithms have been proposed in the last ten years for the discovery of dynamic communities. However, these methods are seldom compared between themselves. In this article, we propose a generator of dynamic graphs with planted evolving community structure, as a benchmark to compare and evaluate such algorithms. Unlike previously proposed benchmarks, it is able to specify any desired evolving community structure through a descriptive language, and then to generate the corresponding progressively evolving network. We empirically evaluate six existing algorithms for dynamic community detect…
Prevention and intervention work done within community settings often face unique analytic challenges for rigorous evaluations. Since community prevention work (often geographically isolated) cannot be controlled in the same way other prevention programs and these communities have an increased level of interpersonal interactions, rigorous evaluations are needed. Even when the `gold standard' randomized control trials are implemented within community intervention work, the threats to internal validity can be called into question given informal social spread of information in closed network sett…
University of Houston（休斯顿大学）；Texas Center for Superconductivity, University of Houston（休斯顿大学德克萨斯超导中心）
We introduce an ensemble learning scheme for community detection in complex networks. The scheme uses a Machine Learning algorithmic paradigm we call Extremal Ensemble Learning. It uses iterative extremal updating of an ensemble of network partitions, which can be found by a conventional base algorithm, to find a node partition that maximizes modularity. At each iteration, core groups of nodes that are in the same community in every ensemble partition are identified and used to form a reduced network. Partitions of the reduced network are then found and used to update the ensemble. The smaller…
Mining community structures from the complex network is an important problem across a variety of fields. Many existing community detection methods detect communities through optimizing a community evaluation function. However, most of these functions even have high values on random graphs and may fail to detect small communities in the large-scale network (the so-called resolution limit problem). In this paper, we introduce two novel node-centric community evaluation functions by connecting correlation analysis with community detection. We will further show that the correlation analysis can pr…
Luddy School of Informatics, Computing and Engineering, Indiana University（印第安纳大学勒迪信息学、计算与工程学院）；King Abdulaziz University（阿卜杜勒阿齐兹国王大学）；Indiana University Network Science Institute (IUNI)（印第安纳大学网络科学研究所）
Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well, because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against t…
Many networks exhibit some community structure. There exists a wide variety of approaches to detect communities in networks, each offering different interpretations and associated algorithms. For large networks, there is the additional requirement of speed. In this context, the so-called label propagation algorithm (LPA) was proposed, which runs in near-linear time. In partitions uncovered by LPA, each node is ensured to have most links to its assigned community. We here propose a fast variant of LPA (FLPA) that is based on processing a queue of nodes whose neighbourhood recently changed. We t…
In this letter, we deal with evolutionary game theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities that is governed by an environmental feedback mechanism, resulting in co-evolutionary dynamics. Through a rigorous analysis of the system of differential equations obtained, we characterize the equilibria of the coupled dynamical system. Moreove…
In this paper, we propose an improved version of an agglomerative hierarchical clustering algorithm that performs disjoint community detection in large-scale complex networks. The improved algorithm is achieved after replacing the local structural similarity used in the original algorithm, with the recently proposed Dynamic Structural Similarity. Additionally, the improved algorithm is extended to detect fuzzy and crisp overlapping community structure. The extended algorithm leverages the disjoint community structure generated by itself and the dynamic structural similarity measures, to comput…
Heritage Institute of Technology（遗产理工学院）；University of Notre Dame（圣母大学）
Finding community structures in social networks is considered to be a challenging task as many of the proposed algorithms are computationally expensive and does not scale well for large graphs. Most of the community detection algorithms proposed till date are unsuitable for applications that would require detection of communities in real-time, especially for massive networks. The Louvain method, which uses modularity maximization to detect clusters, is usually considered to be one of the fastest community detection algorithms even without any provable bound on its running time. We propose a no…
A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community d…
Community detection is a fundamental and important problem in network science, as community structures often reveal both topological and functional relationships between different components of the complex system. In this paper, we first propose a gradient descent framework of modularity optimization called vector-label propagation algorithm (VLPA), where a node is associated with a vector of continuous community labels instead of one label. Retaining weak structural information in vector-label, VLPA outperforms some well-known community detection methods, and particularly improves the perform…
