Community detection is a crucial task to unravel the intricate dynamics of online social networks. The emergence of these networks has dramatically increased the volume and speed of interactions among users, presenting researchers with unprecedented opportunities to explore and analyze the underlying structure of social communities. Despite a growing interest in tracking the evolution of groups of users in real-world social networks, the predominant focus of community detection efforts has been on communities within static networks. In this paper, we introduce a novel framework for tracking communities over time in a dynamic network, where a series of significant events is identified for each community. Our framework adopts a modularity-based strategy and does not require a predefined threshold, leading to a more accurate and robust tracking of dynamic communities. We validated the efficacy of our framework through extensive experiments on synthetic networks featuring embedded events. The results indicate that our framework can outperform the state-of-the-art methods. Furthermore, we utilized the proposed approach on a Twitter network comprising over 60,000 users and 5 million tweets throughout 2020, showcasing its potential in identifying dynamic communities in real-world scenarios. The proposed framework can be applied to different social networks and provides a valuable tool to gain deeper insights into the evolution of communities in dynamic social networks.
Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic …
Heuristic and exact modularity optimization with size-constrained communities
Kellogg School of Management, Northwestern University（西北大学凯洛格管理学院）；Department of Mechanical and Industrial Engineering, University of Toronto（多伦多大学机械与工业工程系）；Centre for Science and Technology Studies (CWTS), Leiden University（莱顿大学科学技术研究中心）；Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University Bloomington（印第安纳大学布鲁明顿分校卢迪信息、计算与工程学院复杂网络与系统研究中心）
We consider two new problems regarding the impact of edge addition or removal on the modularity of partitions (or community structures) in a network. The first problem seeks to add edges to enforce that a desired partition is the partition that maximizes modularity. The second problem seeks to find the sparsest representation of a network that has the same partition with maximum modularity as the original network. We present integer programming formulations, a row generation algorithm, and heuristic algorithms to solve these problems. Further, we demonstrate a counter-intuitive behavior of mod…
Discovering communities in complex networks helps to understand the behaviour of the network. Some works in this promising research area exist, but communities uncovering in time-dependent and/or multiplex networks has not deeply investigated yet. In this paper, we propose a communities detection approach for multislice networks based on modularity optimization. We first present a method to reduce the network size that still preserves modularity. Then we introduce an algorithm that approximates modularity optimization (as usually adopted) for multislice networks, thus finding communities. The …
The maximization of generalized modularity performs well on networks in which the members of all communities are statistically indistinguishable from each other. However, there is no theory bounding the maximization performance in more realistic networks where edges are heterogeneously distributed within and between communities. Using the random graph properties, we establish asymptotic theoretical bounds on the resolution parameter for which the generalized modularity maximization performs well. From this new perspective on random graph model, we find the resolution limit of modularity maximi…
This paper investigates community detection by modularity maximisation on bipartite networks. In particular we are interested in how the operation of projection, using one node set of the bipartite network to infer connections between nodes in the other set, interacts with community detection. We first define a notion of modularity appropriate for a projected bipartite network and outline an algorithm for maximising it in order to partition the network. Using both real and synthetic networks we compare the communities found by five different algorithms, where each algorithm maximises a differe…
Using an intuitive concept of what constitutes a meaningful community, a novel metric is formulated for detecting non-overlapping communities in undirected, weighted heterogeneous networks. This metric, modularity density, is shown to be superior to the versions of modularity density in present literature. Compared to the previous versions of modularity density, maximization of our metric is proven to be free from bias and better detect weakly-separated communities particularly in heterogeneous networks. In addition to these characteristics, the computational running time of our modularity den…
We demonstrate an exact equivalence between two widely used methods of community detection in networks, the method of modularity maximization in its generalized form which incorporates a resolution parameter controlling the size of the communities discovered, and the method of maximum likelihood applied to the special case of the stochastic block model known as the planted partition model, in which all communities in a network are assumed to have statistically similar properties. Among other things, this equivalence provides a mathematically principled derivation of the modularity function, cl…
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…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities over small ones. To solve this problem, we propose to expand the meaning of the edges that are currently used to indicate propensity of nodes for sharing the same community. In our approach this is the role of edges with positive weights while edges with negative weights indicate aversion for putting their end-nodes into one community. We also present a nove…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs exist and no general model allows to both preserve a power-law degree distribution and a high modularity indicating the presence of communities. We present a dynamic preferential attachment hypergraph model which features partition into communities. We prove that its degree distribution follows a power-law and we give theoretical lower bounds for its modularit…
Community detection in networks is the process of identifying unusually well-connected sub-networks and is a central component of many applied network analyses. The paradigm of modularity optimization stipulates a partition of the network's vertices which maximizes the difference between the fraction of edges within groups (communities) and the expected fraction if edges were randomly distributed. The modularity objective function incorporates the network's topology exclusively and has been extensively studied whereas the integration of constraints or external information on community composit…
Imperial College London（帝国理工学院）；University of Cambridge（剑桥大学）；RWTH Aachen University（亚琛工业大学）
Networks are a widely-used tool to investigate the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite size limit of dense networks. The detection of communities or other meso-scale structures is a prominent topic in network science as it allows the identification of functional building blocks in complex systems. When such building blocks may be present in graphons is an open question. In this paper, we define a graphon-modularity and demonstrate that it can be maximised to detect communities in graphons. We then investigate specific synthetic g…
It is of paramount importance to uncover influential nodes to control diffusion phenomena in a network. In recent works, there is a growing trend to investigate the role of the community structure to solve this issue. Up to now, the vast majority of the so-called community-aware centrality measures rely on non-overlapping community structure. However, in many real-world networks, such as social networks, the communities overlap. In other words, a node can belong to multiple communities. To overcome this drawback, we propose and investigate the "Overlapping Modularity Vitality" centrality measu…
Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem - community detection - in multilayer networks are still limited. In this work, we first introduce the multilayer network mode…
Advancing Community Detection with Graph Convolutional Neural Networks: Bridging Topological and Attributive Cohesion
Victoria University of Wellington（维多利亚大学）；Goldenset Collective（Goldenset集体）；School of Computer Science, Beijing University of Posts and Telecommunications（北京邮电大学计算机学院）
Multiple phases in modularity-based community detection
仅基于邻接矩阵来检测网络中的社区是几个科学学科感兴趣的问题。最近，Zhang和Moore在[P. Zhang和C. Moore，Proceedings of the National Academy of Sciences 111，18144（2014）]，称为mod-bp，其通过优化模块度（社区检测中流行的拟合优度度量）和熵（即具有给定模块度的配置的数量）的加权平均来避免过拟合数据。相对权重的调整，即模型的“温度”，对于从mod-bp得到正确的结果至关重要。在这项工作中，我们研究了许多相变，mod-bp可能会通过改变两个参数的算法：温度$T$和最大数量的组$q$。我们引入了一组新的序参量，允许确定实际数量的组$\hat{q}$，我们观察合成和真实的网络上存在的相位与任何$\hat{q} \in \{1,q\}$，这是未知的。我们讨论了如何解释mod-bp的结果，以及如何在发现重要社区的问题上做出最优选择。
In this chapter, we apply the theoretical framework introduced in the previous chapter to study how the modular structure of the social network affects the spreading of complex contagion. In particular, we focus on the notion of optimal modularity, that predicts the occurrence of global cascades when the network exhibits just the right amount of modularity. Here we generalize the findings by assuming the presence of multiple communities and an uniform distribution of seeds across the network. Finally, we offer some insights into the temporal evolution of cascades in the regime of the optimal m…
Cornell University（康奈尔大学）；University of California, Davis（加州大学戴维斯分校）；University of Pennsylvania（宾夕法尼亚大学）
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. This paper proposes a convexified modularity maximization approach for estimating the hidden communities under DCSBM. Our approach is based on a convex programming relaxation of the classical (generalized) modularity max…
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…
Multilayer networks capture pairwise relationships between the components of complex systems across multiple modes or scales of interactions. An important meso-scale feature of these networks is measured though their community structure, which defines groups of strongly connected nodes that exist within and across network layers. Because interlayer edges can describe relationships between different modalities, scales, or time points, it is essential to understand how communities change and evolve across layers. A popular method for detecting communities in multilayer networks consists of maxim…
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。
Modularity, first proposed by [Newman and Girvan, 2004], is one of the most popular ways to quantify the significance of community structure in complex networks. It can serve as both a standard benchmark to compare different community detection algorithms, and an optimization objective to detect communities itself. Previous work on modularity has developed many efficient algorithms for modularity maximization. However, few of researchers considered the interpretation of the modularity function itself. In this paper, we study modularity from an information-theoretical perspective and show that …
Modularity, since its introduction, has remained one of the most widely used metrics to assess the quality of community structure in a complex network. However the resolution limit problem associated with modularity limits its applicability to networks with community sizes smaller than a certain scale. In the past various attempts have been made to solve this problem. More recently a new metric, modularity density, was introduced for the quality of community structure in networks in order to solve some of the known problems with modularity, particularly the resolution limit problem. Modularity…
Understanding community structure in social media is critical due to its broad applications such as friend recommendations, link predictions and collaborative filtering. However, there is no widely accepted definition of community in literature. Existing work use structure related metrics such as modularity and function related metrics such as ground truth to measure the performance of community detection algorithms, while ignoring an important metric, size of the community. [1] suggests that the size of community with strong ties in social media should be limited to 150. As we discovered in t…
