Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. Moreover, many machine learning algorithms and tools that are developed for complex networks try to take advantage of the existence of communities to improve their performance or speed. As a result, there are many competing algorithms for detecting communities in large networks. Unfortunately, these algorithms are often quite sensitive and so they cannot be fine-tuned for a given, but a constantly changing, real-world network at hand. It is therefore important to test these algorithms for various scenarios that can only be done using synthetic graphs that have built-in community structure, power-law degree distribution, and other typical properties observed in complex networks. The standard and extensively used method for generating artificial networks is the LFR graph generator. Unfortunately, this model has some scalability limitations and it is challenging to analyze it theoretically. Finally, the mixing parameter $μ$, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally-defined networks. In this paper, we provide an alternative random graph model with community structure and power-law distribution for both degrees and community sizes, the Artificial Benchmark for Community Detection (ABCD). We show that the new model solves the three issues identified above and more. The conclusion is that these models produce comparable graphs but ABCD is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (independent) communities and random graph with no community structure.
Multilayer Artificial Benchmark for Community Detection (mABCD)
Decision Analysis and Support Unit, SGH Warsaw School of Economics（决策分析与支持单位，SGH华沙经济学院）；Department of Artificial Intelligence, Wrocław University of Science and Technology（人工智能系，沃姆扎大学科学与技术学院）；Department of Mathematics, Toronto Metropolitan University（数学系，多伦多 Metropolitan 大学）；Tutte Institute for Mathematics and Computing（图图数学与计算研究所）
SGH Warsaw School of Economics（华沙经济学院）；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）
In this paper, we investigate properties and performance of synthetic random graph models with a built-in community structure. Such models are important for evaluating and tuning community detection algorithms that are unsupervised by nature. We propose ABCDe, a multi-threaded implementation of the ABCD (Artificial Benchmark for Community Detection) graph generator. We discuss the implementation details of the algorithm and compare it with both the previously available sequential version of the ABCD model and with the parallel implementation of the standard and extensively used LFR (Lancichine…
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. …
The Artificial Benchmark for Community Detection with Outliers and Overlapping Communities (ABCD+$o^2$)
Dalhousie University（达尔豪斯大学）；Toronto Metropolitan University（多伦多都会大学）；SGH Warsaw School of Economics（华沙经济大学）；University of Ottawa（渥太华大学）；Tutte Institute for Mathematics and Computing（图特数学与计算研究所）
Graph Data Augmentation via Contrastive Generator Inversion ($\texttt{DCBA}$)
Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）；University of Technology Sydney（悉尼科技大学）；SGH Warsaw School of Economics（华沙经济大学）；Toronto Metropolitan University（多伦多都会大学）
Assessing the partitioning performance of community detection algorithms is one of the most important issues in complex network analysis. Artificially generated networks are often used as benchmarks for this purpose. However, previous studies showed their level of realism have a significant effect on the algorithms performance. In this study, we adopt a thorough experimental approach to tackle this problem and investigate this effect. To assess the level of realism, we use consensual network topological properties. Based on the LFR method, the most realistic generative method to date, we propo…
Many community detection algorithms have been developed to uncover the mesoscopic properties of complex networks. However how good an algorithm is, in terms of accuracy and computing time, remains still open. Testing algorithms on real-world network has certain restrictions which made their insights potentially biased: the networks are usually small, and the underlying communities are not defined objectively. In this study, we employ the Lancichinetti-Fortunato-Radicchi benchmark graph to test eight state-of-the-art algorithms. We quantify the accuracy using complementary measures and algorith…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social network analysis and computational biology. There is a significant amount of literature studying this problem under the assumption that the communities do not overlap. When the communities are allowed to overlap, often a pure nodes assumption is made, i.e. each community has a node that belongs exclusively to that community. This assumption, however, may not a…
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…
It is well-known that community detection methods based on modularity optimization often fails to discover small communities. Several objective functions used for community detection therefore involve a resolution parameter that allows the detection of communities at different scales. We provide an explicit upper bound on the community size of communities resulting from the optimization of several of these functions. We also show with a simple example that the use of the resolution parameter may artificially force the complete disaggregation of large and densely connected communities.
Community detection is a fundamental task in social network analysis. In this paper, first we develop an endorsement filtered user connectivity network by utilizing Heider's structural balance theory and certain Twitter triad patterns. Next, we develop three Nonnegative Matrix Factorization frameworks to investigate the contributions of different types of user connectivity and content information in community detection. We show that user content and endorsement filtered connectivity information are complementary to each other in clustering politically motivated users into pure political commun…
Galatasaray University（加拉塔萨雷大学）；University of Burgundy（勃艮第大学）
Community detection is a very active field in complex networks analysis, consisting in identifying groups of nodes more densely interconnected relatively to the rest of the network. The existing algorithms are usually tested and compared on real-world and artificial networks, their performance being assessed through some partition similarity measure. However, artificial networks realism can be questioned, and the appropriateness of those measures is not obvious. In this study, we take advantage of recent advances concerning the characterization of community structures to tackle these questions…
New crisis response and management approaches that incorporate the latest information technologies are essential in all phases of emergency preparedness and response, including the planning, response, recovery, and assessment phases. Accurate and timely information is as crucial as is rapid and coherent coordination among the responding organizations. We are working towards a multipronged emergency response tool that provide stakeholders timely access to comprehensive, relevant, and reliable information. The faster emergency personnel are able to analyze, disseminate and act on key information…
This paper addresses the task of community detection and proposes a local approach based on a distributed list building, where each vertex broadcasts basic information that only depends on its degree and that of its neighbours. A decentralised external process then unveils the community structure. The relevance of the proposed method is experimentally shown on both artificial and real data.
The quest for a quantitative characterization of community and modular structure of complex networks produced a variety of methods and algorithms to classify different networks. However, it is not clear if such methods provide consistent, robust and meaningful results when considering hierarchies as a whole. Part of the problem is the lack of a similarity measure for the comparison of hierarchical community structures. In this work we give a contribution by introducing the {\it hierarchical mutual information}, which is a generalization of the traditional mutual information, and allows to comp…
Community structure of networks provides comprehensive insight into their organizational structure and functional behavior. LPA is one of the most commonly adopted community detection algorithms with nearly linear time complexity. But it suffers from poor stability and occurrence of monster community due to the introduced randomize. We note that different community-oriented node roles impact the label propagation in different ways. In this paper, we propose a role-based label propagation algorithm (roLPA), in which the heuristics with regard to community-oriented node role were used. We have e…
We propose a one parameter family of random walk processes on hypergraphs, where a parameter biases the dynamics of the walker towards hyperedges of low or high cardinality. We show that for each value of the parameter the resulting process defines its own hypergraph projection on a weighted network. We then explore the differences between them by considering the community structure associated to each random walk process. To do so, we generalise the Markov stability framework to hypergraphs and test it on artificial and real-world hypergraphs.
Community structure discovery in complex networks is a quite challenging problem spanning many applications in various disciplines such as biology, social network and physics. Emerging from various approaches numerous algorithms have been proposed to tackle this problem. Nevertheless little attention has been devoted to compare their efficiency on realistic simulated data. To better understand their relative performances, we evaluate systematically eleven algorithms covering the main approaches. The Normalized Mutual Information (NMI) measure is used to assess the quality of the discovered com…
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…
Identifying vital nodes in networks exhibiting a community structure is a fundamental issue. Indeed, community structure is one of the main properties of real-world networks. Recent works have shown that community-aware centrality measures compare favorably with classical measures agnostic about this ubiquitous property. Nonetheless, there is no clear consensus about how they relate and in which situation it is better to use a classical or a community-aware centrality measure. To this end, in this paper, we perform an extensive investigation to get a better understanding of the relationship be…
Identifying community structure in networks is an issue of particular interest in network science. The modularity introduced by Newman and Girvan [Phys. Rev. E 69, 026113 (2004)] is the most popular quality function for community detection in networks. In this study, we identify a problem in the concept of modularity and suggest a solution to overcome this problem. Specifically, we obtain a new quality function for community detection. We refer to the function as Z-modularity because it measures the Z-score of a given division with respect to the fraction of the number of edges within communit…
Xiamen University（厦门大学）；Columbia University（哥伦比亚大学）；Harvard Medical School（哈佛医学院）；Carnegie Mellon University（卡内基梅隆大学）
Dynamic community detection is the hotspot and basic problem of complex network and artificial intelligence research in recent years. It is necessary to maximize the accuracy of clustering as the network structure changes, but also to minimize the two consecutive clustering differences between the two results. There is a trade-off relationship between these two objectives. In this paper, we propose a Feature Transfer Based Multi-Objective Optimization Genetic Algorithm (TMOGA) based on transfer learning and traditional multi-objective evolutionary algorithm framework. The main idea is to extra…
Local community detection consists of finding a group of nodes closely related to the seeds, a small set of nodes of interest. Such group of nodes are densely connected or have a high probability of being connected internally than their connections to other clusters in the network. Existing local community detection methods focus on finding either one local community that all seeds are most likely to be in or finding a single community for each of the seeds. However, a seed member usually belongs to multiple local overlapping communities. In this work, we present a novel method of detecting mu…
Hierarchical organization is an important, prevalent characteristic of complex systems; in order to understand their organization, the study of the underlying (generally complex) networks that describe the interactions between their constituents plays a central role. Numerous previous works have shown that many real-world networks in social, biologic and technical systems present hierarchical organization, often in the form of a hierarchy of community structures. Many artificial benchmark graphs have been proposed in order to test different community detection methods, but no benchmark has bee…
Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions allowing to reveal the network structure in such cohesive subgroups. Comparative studies reported in the literature usually rely on a performance measure considering the community structure as a partition (Rand Index, Normalized Mutual information, etc.). However, this type of comparison neglects the topological properties of the communities. In this article, we…
Community structure is an important structural property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, but analyzing the behaviors of the methods is also of interest in the theoretical research and real applications. Here, we focus on an important measure for community structure, significance [Sci. Rep. 3 (2013) 2930]. Specifically, we study the effect of various network parameters on this measure in detail, analyze the critical behaviors of it in partition transition, and analytically give the…
To obtain the optimal number of communities is an important problem in detecting community structure. In this paper, we extend the measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic $Ω(c)$ is proposed to detect the optimal number of communities. In general, when $Ω(c)$ reaches its local maximum, especially the first one, the corresponding number of communities \emph{c} is likely to be optimal in community detection. Moreover, the statist…
As recent work demonstrated, the task of identifying communities in networks can be considered analogous to the classical problem of decoding messages transmitted along a noisy channel. We leverage this analogy to develop a community detection method directly inspired by a standard and widely-used decoding technique. We further simplify the algorithm to reduce the time complexity from quadratic to linear. We test the performance of the original and reduced versions of the algorithm on artificial benchmarks with pre-imposed community structure, and on real networks with annotated community stru…
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 formulati…
Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and accurate is a very challenging and open problem. In this manuscript, we introduce a new approach to characterize the node importance to communities. First, a centrality metric is proposed to measure the importance of network nodes to community structure using the spectrum of the adjacency matrix. We define the node importance to communities as the relative change …
Various attempts have been made in recent years to solve the Resolution Limit (RL) problem in community detection by considering variants of the modularity metric in the detection algorithms. These metrics purportedly largely mitigate the RL problem and are preferable to modularity in many realistic scenarios. However, they are not generally suitable for analyzing weighted networks or for detecting hierarchical community structure. Resolution limit problems can be complicated, though, and in particular it can be unclear when it should be considered as problem. In this paper, we introduce a met…
Many real networks that are inferred or collected from data are incomplete due to missing edges. Missing edges can be inherent to the dataset (Facebook friend links will never be complete) or the result of sampling (one may only have access to a portion of the data). The consequence is that downstream analyses that consume the network will often yield less accurate results than if the edges were complete. Community detection algorithms, in particular, often suffer when critical intra-community edges are missing. We propose a novel consensus clustering algorithm to enhance community detection o…
University of Washington（华盛顿大学）；West Virginia University（西弗吉尼亚大学）；Middlebury College（明德学院）；University of Michigan（密歇根大学）；University of Oxford（牛津大学）
A wave of recent scholarship documenting the discriminatory harms of algorithmic systems has spurred widespread interest in algorithmic accountability and regulation. Yet effective accountability and regulation is stymied by a persistent lack of resources supporting public understanding of algorithms and artificial intelligence. Through interactions with a US-based civil rights organization and their coalition of community organizations, we identify a need for (i) heuristics that aid stakeholders in distinguishing between types of analytic and information systems in lay language, and (ii) risk…
Community detection can be considered as a variant of cluster analysis applied to complex networks. For this reason, all existing studies have been using tools derived from this field when evaluating community detection algorithms. However, those are not completely relevant in the context of network analysis, because they ignore an essential part of the available information: the network structure. Therefore, they can lead to incorrect interpretations. In this article, we review these measures, and illustrate this limitation. We propose a modification to solve this problem, and apply it to the…
In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of both links and vertices to construct the key affinity description of the given network, where the direct similarities between graph nodes or nodal features are not available to obtain the classical affinity matrix. Indeed, such calculated network centrality information presents the essential structure of network, hence, the proper measure for detecting netwo…
Community detection in complex networks is a topic of high interest in many fields. Bipartite networks are a special type of complex networks in which nodes are decomposed into two disjoint sets, and only nodes between the two sets can be connected. Bipartite networks represent diverse interaction patterns in many real-world systems, such as predator-prey networks, plant-pollinator networks, and drug-target networks. While community detection in unipartite networks has been extensively studied in the past decade, identification of modules or communities in bipartite networks is still in its ea…
Spectral methods based on the eigenvectors of matrices are widely used in the analysis of network data, particularly for community detection and graph partitioning. Standard methods based on the adjacency matrix and related matrices, however, break down for very sparse networks, which includes many networks of practical interest. As a solution to this problem it has been recently proposed that we focus instead on the spectrum of the non-backtracking matrix, an alternative matrix representation of a network that shows better behavior in the sparse limit. Inspired by this suggestion, we here mak…
The spreading of virus infection is here simulated over artificial human networks. The real-space urban life of people is modeled as a modified scale-free network with constraints. A scale-free network has been adopted in several studies for modeling on-line communities so far but is modified here for the aim to represent peoples' social behaviors where the generated communities are restricted reflecting the spatiotemporal constraints in the real life. Furthermore, the networks have been extended by introducing multiple cliques in the initial step of network construction and enabling people to…
Community detection is the process of assigning nodes and links in significant communities (e.g. clusters, function modules) and its development has led to a better understanding of complex networks. When applied to sizable networks, we argue that most detection algorithms correctly identify prominent communities, but fail to do so across multiple scales. As a result, a significant fraction of the network is left uncharted. We show that this problem stems from larger or denser communities overshadowing smaller or sparser ones, and that this effect accounts for most of the undetected communitie…
Binghamton University, State University of New York（纽约州立大学宾汉姆顿分校）；Waseda University（早稻田大学）；Pypestream, Inc.（Pypestream公司）
Text classification is one of the most critical areas in machine learning and artificial intelligence research. It has been actively adopted in many business applications such as conversational intelligence systems, news articles categorizations, sentiment analysis, emotion detection systems, and many other recommendation systems in our daily life. One of the problems in supervised text classification models is that the models' performance depends heavily on the quality of data labeling that is typically done by humans. In this study, we propose a new network community detection-based approach…
