Detecting communities or the modular structure of real-life networks (e.g. a social network or a product purchase network) is an important task because the way a network functions is often determined by its communities. Traditional approaches to community detection involve modularity-based algorithms, which generally speaking, construct partitions based on heuristics that seek to maximize the ratio of the edges within the partitions to those between them. On the other hand, node embedding approaches represent each node in a graph as a real-valued vector and is thereby able to transform the problem of community detection in a graph to that of clustering a set of vectors. Existing node embedding approaches are primarily based on, first, initiating random walks from each node to construct a context of a node, and then make the vector representation of a node close to its context. However, standard node embedding approaches do not directly take into account the community structure of a network while constructing the context around each node. To alleviate this, we explore two different threads of work. First, we investigate the use of maximum entropy-based random walks to obtain more centrality preserving embedding of nodes, which may lead to more effective clusters in the embedded space. Second, we propose a community structure-aware node embedding approach, where we incorporate modularity-based partitioning heuristics into the objective function of node embedding. We demonstrate that our proposed combination of the combinatorial and the embedding approaches for community detection outperforms a number of modularity-based baselines and K-means clustering on a standard node-embedded (node2vec) vector space on a wide range of real-life and synthetic networks of different sizes and densities.
Community detection algorithms are fundamental tools that allow us to uncover organizational principles in networks. When detecting communities, there are two possible sources of information one can use: the network structure, and the features and attributes of nodes. Even though communities form around nodes that have common edges and common attributes, typically, algorithms have only focused on one of these two data modalities: community detection algorithms traditionally focus only on the network structure, while clustering algorithms mostly consider only node attributes. In this paper, we …
This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where nodes in the network core are seen to be essential in terms of network flow and global structure. Additionally, the connected components in the periphery give information about the community structure of the network, aiding in community detection. A number of explicit results are derived, relating the core and periphery to network flow, community structure …
We propose a new local community detection algorithm that finds communities by identifying borderlines between them using boundary nodes. Our method performs label propagation for community detection, where nodes decide their labels based on the largest "benefit score" exhibited by their immediate neighbors as an attractor to their communities. We try different metrics and find that using the number of common neighbors as benefit scores leads to better decisions for community structure. The proposed algorithm has a local approach and focuses only on boundary nodes during iterations of label pr…
The problem of node-centric, or local, community detection in information networks refers to the identification of a community for a given input node, having limited information about the network topology. Existing methods for solving this problem, however, are not conceived to work on complex networks. In this paper, we propose a novel framework for local community detection based on the multilayer network model. Our approach relies on the maximization of the ratio between the community internal connection density and the external connection density, according to multilayer similarity-based c…
In community detection, datasets often suffer a sampling bias for which nodes which would normally have a high affinity appear to have zero affinity. This happens for example when two affine users of a social network were not exposed to one another. Community detection on this kind of data suffers then from considering affine nodes as not affine. To solve this problem, we explicitly model the (non-)exposure mechanism in a Bayesian community detection framework, by introducing a set of additional hidden variables. Compared to approaches which do not model exposure, our method is able to better …
Community detection is the task of identifying clusters or groups of nodes in a network where nodes within the same group are more connected with each other than with nodes in different groups. It has practical uses in identifying similar functions or roles of nodes in many biological, social and computer networks. With the availability of very large networks in recent years, performance and scalability of community detection algorithms become crucial, i.e. if time complexity of an algorithm is high, it can not run on large networks. In this paper, we propose a new community detection algorith…
The identification of modular structures is essential for characterizing real networks formed by a mesoscopic level of organization where clusters contain nodes with a high internal degree of connectivity. Many methods have been developed to unveil community structures, but only a few studies have probed their suitability in incomplete networks. Here we assess the accuracy of community detection techniques in incomplete networks generated in sampling processes. We show that the walktrap and fast greedy algorithms are highly accurate for detecting the modular structure of incomplete complex net…
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 …
Community detection is a commonly used technique for identifying groups in a network based on similarities in connectivity patterns. To facilitate community detection in large networks, we recast the network to be partitioned into a smaller network of 'super nodes', each super node comprising one or more nodes in the original network. To define the seeds of our super nodes, we apply the 'CoreHD' ranking from dismantling and decycling. We test our approach through the analysis of two common methods for community detection: modularity maximization with the Louvain algorithm and maximum likelihoo…
Detecting communities has long been popular in the research on networks. It is usually modeled as an unsupervised clustering problem on graphs, based on heuristic assumptions about community characteristics, such as edge density and node homogeneity. In this work, we doubt the universality of these widely adopted assumptions and compare human labeled communities with machine predicted ones obtained via various mainstream algorithms. Based on supportive results, we argue that communities are defined by various social patterns and unsupervised learning based on heuristics is incapable of capturi…
Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in graphs. Through extensive experimental studies on simulated and real-world data, we demonstrate that the proposed approach consistently improves over the current state-of-the-art. Specifically, our approach empirically attains the information-theoretic limits for community recovery under the benchmark Stochastic Block Models for graph generation and exhibits b…
To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as degree centrality, betweenness centrality, or PageRank neglect the community structure found in real-world networks. To study node importance based on network flows from a mesoscopic perspective, we analytically derive a community-aware information-theoretic centrality score based on network flow and the coding principles behind the map equation: map equation c…
Community detection is an important task in social network analysis, allowing us to identify and understand the communities within the social structures. However, many community detection approaches either fail to assign low degree (or lowly-connected) users to communities, or assign them to trivially small communities that prevent them from being included in analysis. In this work, we investigate how excluding these users can bias analysis results. We then introduce an approach that is more inclusive for lowly-connected users by incorporating them into larger groups. Experiments show that our…
Community analysis is an important way to ascertain whether or not a complex system consists of sub-structures with different properties. In this paper, we give a two level community structure analysis for the SSCI journal system by most similar co-citation pattern. Five different strategies for the selection of most similar node (journal) pairs are introduced. The efficiency is checked by the normalized mutual information technique. Statistical properties and comparisons of the community results show that both of the two level detection could give instructional information for the community s…
The relationship of friends in social networks can be strong or weak. Some research works have shown that a close relationship between friends conducts good community structure. Based on this result, we propose an effective method in detecting community structure in social networks based on the closeness of relations among neighbors. This method calculates the gravity between each neighbor node to core nodes, then makes judgement if the node should be classified in the community or not, and finally form the process of community detection. The experimental results show that the proposed method …
Community Discovery in complex networks is the problem of detecting, for each node of the network, its membership to one of more groups of nodes, the communities, that are densely connected, or highly interactive, or, more in general, similar, according to a similarity function. So far, the problem has been widely studied in monodimensional networks, i.e. networks where only one connection between two entities can exist. However, real networks are often multidimensional, i.e., multiple connections between any two nodes can exist, either reflecting different kinds of relationships, or represent…
In this paper we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describe relationships between two types of nodes. Our method improves performance by recognizing the distinction between two types of missing edges---ones among the nodes in each node type and the others between two node types. Our method can also explicitly assign community membership and distinguish outliers from overlapping nodes, as well as incorporating existing knowledge on the network. We propose a generalized partition density for bip…
Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network. The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence. This …
Community detection is a significant and challenging task in network research. Nowadays, plenty of attention has been focused on local methods of community detection. Among them, community detection with a greedy algorithm typically starts from the identification of local essential nodes called central nodes of the network; communities expand later from these central nodes by optimizing a modularity function. In this paper, we propose a new central node indicator and a new modularity function. Our central node indicator, which we call local centrality indicator (LCI), is as efficient as the we…
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…
Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can id…
We present NECTAR, a community detection algorithm that generalizes Louvain method's local search heuristic for overlapping community structures. NECTAR chooses dynamically which objective function to optimize based on the network on which it is invoked. Our experimental evaluation on both synthetic benchmark graphs and real-world networks, based on ground-truth communities, shows that NECTAR provides excellent results as compared with state of the art community detection algorithms.
Community identification of network components enables us to understand the mesoscale clustering structure of networks. A number of algorithms have been developed to determine the most likely community structures in networks. Such a probabilistic or stochastic nature of this problem can naturally involve the ambiguity in resultant community structures. More specifically, stochastic algorithms can result in different community structures for each realization in principle. In this study, instead of trying to "solve" this community degeneracy problem, we turn the tables by taking the degeneracy a…
Community detection is a well established method for studying the meso scale structure of social networks. Applying a community detection algorithm results in a division of a network into communities that is often used to inspect and reason about community membership of specific nodes. This micro level interpretation step of community structure is a crucial step in typical social science research. However, the methodological caveat in this step is that virtually all modern community detection methods are non-deterministic and based on randomization and approximated results. This needs to be ex…
The goal of community detection algorithms is to identify densely-connected units within large networks. An implicit assumption is that all the constituent nodes belong equally to their associated community. However, some nodes are more important in the community than others. To date, efforts have been primarily driven to identify communities as a whole, rather than understanding to what extent an individual node belongs to its community. Therefore, most metrics for evaluating communities, for example modularity, are global. These metrics produce a score for each community, not for each indivi…
Community detection algorithms are fundamental tools to understand organizational principles in social networks. With the increasing power of social media platforms, when detecting communities there are two possi- ble sources of information one can use: the structure of social network and node attributes. However structure of social networks and node attributes are often interpreted separately in the research of community detection. When these two sources are interpreted simultaneously, one common as- sumption shared by previous studies is that nodes attributes are correlated with communities.…
The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities.
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…
Although community structure is ubiquitous in complex networks, few works exploit this topological property to control epidemics. In this work, devoted to networks with non-overlapping community structure (i.e, a node belongs to a single community), we propose and investigate three deterministic immunization strategies. In order to characterize the influence of a node, various pieces of information are used such as the number of communities that the node can reach in one hop, the nature of the links (intra community links, inter community links), the size of the communities, and the interconne…
Community-aware centrality is an emerging research area in network science concerned with the importance of nodes in relation to community structure. Measures are a function of a network's structure and a given partition. Previous approaches extend classical centrality measures to account for community structure with little connection to community detection theory. In contrast, we propose cluster-quality vitality measures, i.e., modularity vitality, a community-aware measure which is well-grounded in both centrality and community detection theory. Modularity vitality quantifies positive and ne…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these methods treat the relations between nodes as a binary variable and ignore the rich semantics of edges. In this work, we attempt to learn network embeddings which simultaneously preserve network structure and relations between nodes. Experiments on several real-world networks illustrate that by considering different relations between different node pairs, our m…
Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order …
Many methods have been proposed for community detection in networks, but most of them do not take into account additional information on the nodes that is often available in practice. In this paper, we propose a new joint community detection criterion that uses both the network edge information and the node features to detect community structures. One advantage our method has over existing joint detection approaches is the flexibility of learning the impact of different features which may differ across communities. Another advantage is the flexibility of choosing the amount of influence the fe…
Advanced Digital Sciences Center（高级数字科学中心）；Nanyang Technological University（南洋理工大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the success of embedding individual nodes for graph analytics, we notice that an important concept of embedding communities (i.e., groups of nodes) is missing. Embedding communities is useful, not only for supporting various community-level applications, but also to help preserve community structure in graph embedding. In fact, we see community embedding as providing…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure. The K-core of a graph is the largest subgraph within which each node has at least K connections. We propose a framework that accelerates community detection by applying an expensive algorithm (modularity optimization, the Louvain method, spectral clustering, etc.) to the K-core and then using an inexpensive heuristic (such as local modularity maximization) to…
In real-world complex networks, understanding the dynamics of their evolution has been of great interest to the scientific community. Predicting future links is an essential task of social network analysis as the addition or removal of the links over time leads to the network evolution. In a network, links can be categorized as intra-community links if both end nodes of the link belong to the same community, otherwise inter-community links. The existing link-prediction methods have mainly focused on achieving high accuracy for intra-community link prediction. In this work, we propose a network…
Social networks facilitate the social space where actors or the users have ties among them. The ties and their patterns are based on their life styles and communication. Similarly, in online social media networks like Facebook, Twitter, Myspace etc., multiple users belong to multiple specific communities. The social network represents large real-world directed social graphs. Detection of communities or clusters from these graphs is a problem of considerable research interest. The communities are formed using the neighboring nodes that have common edges and common attributes. Most of the existi…
Social networks have enabled user-specific advertisements and recommendations on their platforms, which puts a significant focus on Influence Maximisation (IM) for target advertising and related tasks. The aim is to identify nodes in the network which can maximize the spread of information through a diffusion cascade. We propose a community structures-based approach that employs K-Shell algorithm with community structures to generate a score for the connections between seed nodes and communities. Further, our approach employs entropy within communities to ensure the proper spread of informatio…
Many real world systems or web services can be represented as a network such as social networks and transportation networks. In the past decade, many algorithms have been developed to detect the communities in a network using connections between nodes. However in many real world networks, the locations of nodes have great influence on the community structure. For example, in a social network, more connections are established between geographically proximate users. The impact of locations on community has not been fully investigated by the research literature. In this paper, we propose a commun…
Communities in social networks evolve over time as people enter and leave the network and their activity behaviors shift. The task of predicting structural changes in communities over time is known as community evolution prediction. Existing work in this area has focused on the development of frameworks for defining events while using traditional classification methods to perform the actual prediction. We present a novel graph neural network for predicting community evolution events from structural and temporal information. The model (GNAN) includes a group-node attention component which enabl…
Understanding how the network topology affects the spread of an epidemic is a main concern in order to develop efficient immunization strategies. While there is a great deal of work dealing with the macroscopic topological properties of the networks, few studies have been devoted to the influence of the community structure. Furthermore, while in many real-world networks communities may overlap, in these studies non-overlapping community structures are considered. In order to gain insight about the influence of the overlapping nodes in the epidemic process we conduct an empirical evaluation of …
Finding a small subset of influential nodes to maximise influence spread in a complex network is an active area of research. Different methods have been proposed in the past to identify a set of seed nodes that can help achieve a faster spread of influence in the network. This paper combines driver node selection methods from the field of network control, with the divide-and-conquer approach of using community structure to guide the selection of candidate seed nodes from the driver nodes of the communities. The use of driver nodes in communities as seed nodes is a comparatively new idea. We id…
Over the last couple of decades, Social Networks have connected people on the web from across the globe and have become a crucial part of our daily life. These networks have also rapidly grown as platforms for propagating products, ideas, and opinions to target a wider audience. This calls for the need to find influential nodes in a network for a variety of reasons, including the curb of misinformation being spread across the networks, advertising products efficiently, finding prominent protein structures in biological networks, etc. In this paper, we propose Modified Community Diversity (MCD)…
Community detection in networks is commonly performed using information about interactions between nodes. Recent advances have been made to incorporate multiple types of interactions, thus generalizing standard methods to multilayer networks. Often though, one can access additional information regarding individual nodes, attributes or covariates. A relevant question is thus how to properly incorporate this extra information in such frameworks. Here we develop a method that incorporates both the topology of interactions and node attributes to extract communities in multilayer networks. We propo…
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…
Michigan State University（密歇根州立大学）；NEC Laboratories America（美国 NEC 实验室）
This paper addresses the problem of community detection in networked data that combines link and content analysis. Most existing work combines link and content information by a generative model. There are two major shortcomings with the existing approaches. First, they assume that the probability of creating a link between two nodes is determined only by the community memberships of the nodes; however other factors (e.g. popularity) could also affect the link pattern. Second, they use generative models to model the content of individual nodes, whereas these generative models are vulnerable to …
Most real-world networks exhibit community structure, a phenomenon characterized by existence of node clusters whose intra-edge connectivity is stronger than edge connectivities between nodes belonging to different clusters. In addition to facilitating a better understanding of network behavior, community detection finds many practical applications in diverse settings. Communities in online social networks are indicative of shared functional roles, or affiliation to a common socio-economic status, the knowledge of which is vital for targeted advertisement. In buyer-seller networks, community d…
Community networks differ from regular networks by their organic growth patterns -- there is no central planning body that would decide how the network is built. Instead, the network grows in a bottom-up fashion as more people express interest in participating in the community and connect with their neighbours. People who participate in community networks are usually volunteers with limited free time. Due to these factors, making the management of community networks simpler and easier for all participants is the key component in boosting their growth. Specifics of individual networks often for…
Local community detection has attracted much research attention recently, and many methods have been proposed for the single local community detection that finds a community containing the given set of query nodes. However, nodes may belong to several communities in the network, and detecting all the communities for the query node set, termed as the multiple local community detection (MLCD), is more important as it could uncover more potential information. MLCD is also more challenging because when a query node belongs to multiple communities, it always locates in the complicated overlapping r…
The joint use of node features and network topology to detect communities is called community detection in attributed networks. Most of the existing work along this line has been carried out through objective function optimization and has proposed numerous approaches. However, they tend to focus only on lower-order details, i.e., capture node features and network topology from node and edge views, and purely seek a higher degree of optimization to guarantee the quality of the found communities, which exacerbates unbalanced communities and free-rider effect. To further clarify and reveal the in…
National Taiwan University（台湾大学）；Mila-Quebec Institute for Learning Algorithms（Mila-魁北克学习算法研究所）；Harvard University（哈佛大学）；Element AI；HEC Montreal（蒙特利尔高等商学院）
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both…
Community Search, or finding a connected subgraph (known as a community) containing the given query nodes in a social network, is a fundamental problem. Most of the existing community search models only focus on the internal cohesiveness of a community. However, a high-quality community often has high modularity, which means dense connections inside communities and sparse connections to the nodes outside the community. In this paper, we conduct a pioneer study on searching a community with high modularity. We point out that while modularity has been popularly used in community detection (witho…
Community affiliation of a node plays an important role in determining its contextual position in the network, which may raise privacy concerns when a sensitive node wants to hide its identity in a network. Oftentimes, a target community seeks to protect itself from adversaries so that its constituent members remain hidden inside the network. The current study focuses on hiding such sensitive communities so that the community affiliation of the targeted nodes can be concealed. This leads to the problem of community deception which investigates the avenues of minimally rewiring nodes in a netwo…
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…
