In this paper we present a novel strategy to discover the community structure of (possibly, large) networks. This approach is based on the well-know concept of network modularity optimization. To do so, our algorithm exploits a novel measure of edge centrality, based on the k-paths. This technique allows to efficiently compute a edge ranking in large networks in near linear time. Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network. Finally, it discovers the community structure adopting a strategy inspired by the well-known state-of-the-art Louvain method (henceforth, LM), efficiently maximizing the network modularity. The experiments we carried out show that our algorithm outperforms other techniques and slightly improves results of the original LM, providing reliable results. Another advantage is that its adoption is naturally extended even to unweighted networks, differently with respect to the LM.
我们介绍了一种新的算法的社区发现，动态维护社区结构的大型网络，随着时间的推移。该算法最大限度地提高了模块化指数由于一个随机层次聚类的基础上的蒙特卡罗马尔可夫链（MCMC）方法的建设。有趣的是，它可以被视为Louvain算法的动态化（参见Blondel et Al，2008），其中聚合步骤被分层工具概率取代。
Community detection is often used to understand the structure of large and complex networks. One of the most popular algorithms for uncovering community structure is the so-called Louvain algorithm. We show that this algorithm has a major defect that largely went unnoticed until now: the Louvain algorithm may yield arbitrarily badly connected communities. In the worst case, communities may even be disconnected, especially when running the algorithm iteratively. In our experimental analysis, we observe that up to 25% of the communities are badly connected and up to 16% are disconnected. To addr…
In this paper, we focus on the community detection problem in multiplex networks, i.e., networks with multiple layers having same node sets and no inter-layer connections. In particular, we look for groups of nodes that can be recognized as communities consistently across the layers. To this end, we propose a new approach that generalizes the Louvain method by (a) simultaneously updating average and variance of the modularity scores across the layers, and (b) reformulating the greedy search procedure in terms of a filter-based multiobjective optimization scheme. Unlike many previous modularity…
Faster unfolding of communities: speeding up the Louvain algorithm
许多复杂网络都呈现出密集连接的节点组的模块化结构。通常，这样的模块化结构是通过优化某些质量函数来揭示的。尽管存在缺陷，但模块化仍然是最受欢迎的质量功能之一。Louvain算法最初是为了优化模块化而开发的，但已应用于各种方法。因此，加速Louvain算法，使更大的图在更短的时间内分析各种方法。我们建议考虑将节点移动到随机邻居社区，而不是最佳邻居社区。虽然非常简单，但它在具有清晰社区结构的网络中将理论上的运行时复杂度从$\mathcal{O}(m)$降低到了$\mathcal{O}(n \log \langle k \rangle)$。在基准网络中，它将算法加速了大约2-3倍，而在一些真实网络中，它甚至达到了10倍的运行速度。这种改进是由于两个因素：（1）随机邻居可能处于“好”社区;（2）随机邻居可能是枢纽，有助于收敛。最后，性能增益仅略微降低质量，特别是对于模块化，从而提供良好的质量性能比。然而，对于其他一些指标，如显著性或意外性，这些收益不太明显，甚至消失。
Community detection is a key aspect of network analysis, as it allows for the identification of groups and patterns within a network. With the ever-increasing size of networks, it is crucial to have fast algorithms to analyze them efficiently. It is a modularity-based greedy algorithm that divides a network into disconnected communities better over several iterations. Even in big, dense networks, it is renowned for establishing high-quality communities. However it can be at least a factor of ten slower than community discovery techniques that rely on label-propagation, which are generally extr…
In this work, we explore four common algorithms for community detection in networks, namely Agglomerative Hierarchical Clustering, Divisive Hierarchical Clustering (Girvan-Newman), Fastgreedy and the Louvain Method. We investigate their mechanics and compare their differences in terms of implementation and results of the clustering behavior on a standard dataset. We further propose some enhancements to these algorithms that show promising results in our evaluations, such as self-neighboring for Neighbor Matrix constructions, a deterministic slightly faster version of the Louvain Method that fa…
In this paper we introduce and develop the concept of Interval-Weighted Networks (IWN), a novel approach in Social Network Analysis, where the edge weights are represented by closed intervals composed with precise information, comprehending intrinsic variability. We extend IWN for both Newman's modularity and modularity gain and the Louvain algorithm (LA), considering a tabular representation of networks by contingency tables. We apply our methodology in a real-world commuter network in mainland Portugal between the twenty three NUTS 3 regions. The optimal partition of regions is developed and…
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…
The computational demands of community detection algorithms such as Louvain and spectral optimization can be prohibitive for large networks. Eigenvector centrality and Katz centrality are two network statistics commonly used to describe the relative importance of nodes; and their calculation can be closely approximated on large networks by scalable iterative methods. In this paper, we present and leverage a surprising relationship between Katz centrality and eigenvector centrality to detect communities. Beyond the computational gains, we demonstrate that our approach identifies communities tha…
Modularity Based Community Detection in Hypergraphs
SGH Warsaw School of Economics（华沙经济学院）；Poznan University of Technology（波兹南理工大学）；Toronto Metropolitan University（多伦多都会大学）；Tutte Institute for Mathematics and Computing（塔特数学与计算研究所）
A Community Detection and Graph Neural Network Based Link Prediction Approach for Scientific Literature
Chengdu Library and Information Center, Chinese Academy of Sciences（中国科学院成都文献情报中心）；University of Michigan（密歇根大学）；Shandong University of Technology（山东理工大学）；Kunming University of Science and Technology（昆明理工大学）；Macau University of Science and Technology（澳门科技大学）；Purdue University（普渡大学）
Communities in social networks often reflect close social ties between their members and their evolution through time. We propose an approach that tracks two aspects of community evolution in retweet networks: flow of the members in, out and between the communities, and their influence. We start with high resolution time windows, and then select several timepoints which exhibit large differences between the communities. For community detection, we propose a two-stage approach. In the first stage, we apply an enhanced Louvain algorithm, called Ensemble Louvain, to find stable communities. In th…
This paper studies community formation in OSS collaboration networks. While most current work examines the emergence of small-scale OSS projects, our approach draws on a large-scale historical dataset of 1.8 million GitHub users and their repository contributions. OSS collaborations are characterized by small groups of users that work closely together, leading to the presence of communities defined by short cycles in the underlying network structure. To understand the impact of this phenomenon, we apply a pre-processing step that accounts for the cyclic network structure by using Renewal-Nonba…
Community detection is of great importance for online social network analysis. The volume, variety and velocity of data generated by today's online social networks are advancing the way researchers analyze those networks. For instance, real-world networks, such as Facebook, LinkedIn and Twitter, are inherently growing rapidly and expanding aggressively over time. However, most of the studies so far have been focusing on detecting communities on the static networks. It is computationally expensive to directly employ a well-studied static algorithm repeatedly on the network snapshots of the dyna…
Community detection, aiming to group nodes based on their connections, plays an important role in network analysis, since communities, treated as meta-nodes, allow us to create a large-scale map of a network to simplify its analysis. However, for privacy reasons, we may want to prevent communities from being discovered in certain cases, leading to the topics on community deception. In this paper, we formalize this community detection attack problem in three scales, including global attack (macroscale), target community attack (mesoscale) and target node attack (microscale). We treat this as an…
Heterogeneous networks are networks consisting of different types of nodes and multiple types of edges linking such nodes. While community detection has been extensively developed as a useful technique for analyzing networks that contain only one type of nodes, very few community detection techniques have been developed for heterogeneous networks. In this paper, we propose a modularity based community detection framework for heterogeneous networks. Unlike existing methods, the proposed approach has the flexibility to treat the number of communities as an unknown quantity. We describe a Louvain…
Centrality in Collaboration: A Novel Algorithm for Social Partitioning Gradients in Community Detection for Multiple Oncology Clinical Trial Enrollments
University of Toronto（多伦多大学）；University Health Network（大学健康网络）
The graph-theoretical task of determining most likely inter-community edges based on disconnected subgraphs' intra-community connectivity is proposed. An algorithm is developed for this edge augmentation task, based on elevating the zero eigenvalues of graph's spectrum. Upper bounds for eigenvalue elevation amplitude and for the corresponding augmented edge density are derived and are authenticated with simulation on random graphs. The algorithm works consistently across synthetic and real networks, yielding desirable performance at connecting graph components. Edge augmentation reverse-engine…
Deezer Research（Deezer研究院）；École Polytechnique, IP Paris（巴黎综合理工学院，巴黎理工学院）；Harvard University（哈佛大学）
Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction (LP). Their performances are less impressive on community detection (CD), where they are often outperformed by simpler alternatives such as the Louvain method. It is still unclear to what extent one can improve CD with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on LP in a multi-task setting. In this workshop paper, summarizing results from our journal publication (Salh…
Center For Urban Science+Progress, New York University（纽约大学城市科学与进步中心）
Network community detection often relies on optimizing partition quality functions, like modularity. This optimization appears to be a complex problem traditionally relying on discrete heuristics. And although the problem could be reformulated as continuous optimization, direct application of the standard optimization methods has limited efficiency in overcoming the numerous local extrema. However, the rise of deep learning and its applications to graphs offers new opportunities. And while graph neural networks have been used for supervised and unsupervised learning on networks, their applicat…
SGH Warsaw School of Economics（华沙经济学院）；Ryerson University（瑞尔森大学）；Tutte Institute for Mathematics and Computing（塔特数学与计算研究所）
The Artificial Benchmark for Community Detection (ABCD) graph is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter $ξ$ can be tuned to mimic its counterpart in the LFR model, the mixing parameter $μ$. In this paper, we investigate various theoretical asymptotic properties of the ABCD model. In particular, we analyze the modularity function, arguably, the most important graph property of networks in the context of community detection. …
Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods such as Infomap and Louvain. Yet, all these studies agreed that the crucial problem is to convert the unweighted network topology in a 'smart-enough' node dissimilarity matrix that is able to properly address the message passing procedure behind affinity propagation clustering. He…
Federal University of São Paulo（圣保罗联邦大学）；National Institute for Space Research（国家空间研究所）；Institute of Computing, University of Campinas（坎皮纳斯大学计算机学院）
The study and comprehension of complex systems are crucial intellectual and scientific challenges of the 21st century. In this scenario, network science has emerged as a mathematical tool to support the study of such systems. Examples include environmental processes such as wildfires, which are known for their considerable impact on human life. However, there is a considerable lack of studies of wildfire from a network science perspective. Here, employing the chronological network concept -- a temporal network where nodes are linked if two consecutive events occur between them -- we investigat…
