Finding Communities In Networks Research Articles

Node similarity and modularity for finding communities in networks

Community detection in networks has become a very important axis of research for understanding the structure of networks. Several methods have been proposed to detect the most optimal community structure in networks. In this article, we present a novel method for detecting community structure ComDBNS (Community Detection Based on Node Similarity) for unweighted and undirected networks; it performs in two steps. The first step uses the similarity between endpoints of each link to find the inter-community links to remove in order to create basic groups of nodes properly connected. In the second step we propose a strategy to merge these initial groups to identify the final community structure (with k communities or the structure that maximizes the modularity in Community Detection Based on Node Similarity and Modularity Q (ComDBNSQ)). The proposed method is tested on the real and computer-generated networks, and it demonstrates the effectiveness and correctness of the method. Also, the method saves the time complexity.

Parallel Multi-Label Propagation Based on Influence Model and Its Application to Overlapping Community Discovery

Finding communities in networks is one of the challenging issues in complex network research. We have to deal with very large networks that contain billions of vertices, which makes community discovery a computationally intensive work. Moreover, communities usually overlap each other, which greatly increases the difficulty of identifying the boundaries of communities. In this paper, we propose a parallel multi-label propagation algorithm (PMLPA) that enhances traditional multi-label propagation algorithm (MLPA) in two ways. First, the critical steps of MLPA are parallelized based on the MapReduce model to get higher scalability. Second, new label updating strategy is used to automatically determine the most valuable labels of each vertex. Furthermore, we study the improvement of PMLPA through considering the influence of vertices and labels on label updating. In this way, the importance of each label can be described with higher precision. Experiments on artificial and real networks prove that the proposed algorithms can achieve both high discovering accuracy and high scalability.

A genetic algorithm using K-path initialization for community detection in complex networks

Genetic algorithms have been used in community detection due to their efficiency and accuracy in automatic discovery of communities in complex networks. The traditional method of population initialization for genetic algorithms does not fully consider topology of a network. Therefore, the quality of the initial population may be poor, which may consequently slow down the convergence of the entire process. According to the characteristics of social networks, we propose a K-path initialization method which makes full use of the topological information of a given network. The main focus of our study is to find whether a K-path initialized generic algorithm can bring significant increase in Q value after the FIRST iteration, and to prove whether such algorithm can accelerate the convergence of the entire process for faster community detection over a randomly initialized genetic algorithm. By applying this new algorithm to Karate, Football, and Jazz, we found that the K-path initialized algorithm can increase the Q value by 50---160% on average over that without using K-path initialization after the first round of iteration. This initial advantage is then accumulated during the subsequent iterations by reducing the number of total iterations by at least 28% and at most 41%.

Finding network communities using modularity density

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 random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.

Tiles: an online algorithm for community discovery in dynamic social networks

Community discovery has emerged during the last decade as one of the most challenging problems in social network analysis. Many algorithms have been proposed to find communities on static networks, i.e. networks which do not change in time. However, social networks are dynamic realities (e.g. call graphs, online social networks): in such scenarios static community discovery fails to identify a partition of the graph that is semantically consistent with the temporal information expressed by the data. In this work we propose Tiles, an algorithm that extracts overlapping communities and tracks their evolution in time following an online iterative procedure. Our algorithm operates following a domino effect strategy, dynamically recomputing nodes community memberships whenever a new interaction takes place. We compare Tiles with state-of-the-art community detection algorithms on both synthetic and real world networks having annotated community structure: our experiments show that the proposed approach is able to guarantee lower execution times and better correspondence with the ground truth communities than its competitors. Moreover, we illustrate the specifics of the proposed approach by discussing the properties of identified communities it is able to identify.

Local community detection as pattern restoration by attractor dynamics of recurrent neural networks

Densely connected parts in networks are referred to as “communities”. Community structure is a hallmark of a variety of real-world networks. Individual communities in networks form functional modules of complex systems described by networks. Therefore, finding communities in networks is essential to approaching and understanding complex systems described by networks. In fact, network science has made a great deal of effort to develop effective and efficient methods for detecting communities in networks. Here we put forward a type of community detection, which has been little examined so far but will be practically useful. Suppose that we are given a set of source nodes that includes some (but not all) of “true” members of a particular community; suppose also that the set includes some nodes that are not the members of this community (i.e., “false” members of the community). We propose to detect the community from this “imperfect” and “inaccurate” set of source nodes using attractor dynamics of recurrent neural networks. Community detection by the proposed method can be viewed as restoration of the original pattern from a deteriorated pattern, which is analogous to cue-triggered recall of short-term memory in the brain. We demonstrate the effectiveness of the proposed method using synthetic networks and real social networks for which correct communities are known.

Comparing Alzheimer’s and Parkinson’s diseases networks using graph communities structure

BackgroundRecent advances in large datasets analysis offer new insights to modern biology allowing system-level investigation of pathologies. Here we describe a novel computational method that exploits the ever-growing amount of “omics” data to shed light on Alzheimer’s and Parkinson’s diseases. Neurological disorders exhibit a huge number of molecular alterations due to a complex interplay between genetic and environmental factors. Classical reductionist approaches are focused on a few elements, providing a narrow overview of the etiopathogenic complexity of multifactorial diseases. On the other hand, high-throughput technologies allow the evaluation of many components of biological systems and their behaviors. Analysis of Parkinson’s Disease (PD) and Alzheimer’s Disease (AD) from a network perspective can highlight proteins or pathways common but differently represented that can be discriminating between the two pathological conditions, thus highlight similarities and differences.ResultsIn this work we propose a strategy that exploits network community structure identified with a state-of-the-art network community discovery algorithm called InfoMap, which takes advantage of information theory principles. We used two similarity measurements to quantify functional and topological similarities between the two pathologies. We built a Similarity Matrix to highlight similar communities and we analyzed statistically significant GO terms found in clustered areas of the matrix and in network communities. Our strategy allowed us to identify common known and unknown processes including DNA repair, RNA metabolism and glucose metabolism not detected with simple GO enrichment analysis. In particular, we were able to capture the connection between mitochondrial dysfunction and metabolism (glucose and glutamate/glutamine).ConclusionsThis approach allows the identification of communities present in both pathologies which highlight common biological processes. Conversely, the identification of communities without any counterpart can be used to investigate processes that are characteristic of only one of the two pathologies. In general, the same strategy can be applied to compare any pair of biological networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0270-7) contains supplementary material, which is available to authorized users.

Topical Influence Analysis Algorithm based on Information Propagation in Microblogs

With the development and popularization of the Internet, the different microblog topics are disscussed everyday, so the microblog can product a large number of various topics,which can reflect the influence of different users in a given topic. In the microblog topics,the key users of microblog topics are found by discovering the influential sensitive topics and calculating the influence value of the user,which are the focus of attention in the fields of microblog public opinion supervision and safety management. In order to accurately measure the influencers in the given topic and to calculate the user influence value, the thesis proposes the method of constructing the propagation network which is based on attention and forward relationship between users, and then proposes TDN-If algorithm by using PageRank algorithm. When we calculate the transition probability in propagation network by using the TDN-If algorithm, the information propagation is considered to measure influencers. This method can resolve the defects of discovering the user's influence by only using followers of this single indicator in the current microblog topics. The experimental results show that the TDN-If algorithm has important theoretical and practical value, which is better than TwitterRank algorithm and other influential individuals found algorithm. Thus, the method proposed in this paper can not only effectively solve the problem about discovering and persuading the key users in the sensitive topics who have influences and have the unique insights on the significant events, for example, which can provide the strong guarantee for the governments in the fight against terrorism, but also provide the important theory and method for the complex network community discovery, microblog public opinion supervision , microblog safety management and so on.

Evolutionary Clustering for Mining and Tracking Dynamic Multilayer Networks

This article proposes a framework for community discovery in temporal multiplex networks by extending the evolutionary clustering approach to encompass both time and multiple dimensions. In this extended framework, the problem of finding community structures for time‐evolving networks with multiple types of ties is reformulated by adding the concept of dimensional smoothness, relative to a single timestamp, to that of temporal smoothness, at the base of evolutionary clustering. At each timestamp, the method tries to maximize the quality of the clustering obtained for the current multidimensional network and to minimize the differences with respect to that obtained at the previous timestamp. Moreover, the evolution of a community between two consecutive timestamps is maintained by exploiting the Hungarian approach, which determines the best cluster correspondence between two consecutive timestamps. Experiments on synthetic and real‐world networks show the capability of the approach in discovering and tracking group organization of actors constituting the network.

Community Detection by Consensus Genetic-based Algorithm for Directed Networks

Finding communities in networks is a commonly used form of network analysis. There is a myriad of community detection algorithms in the literature to perform this task. In spite of that, the number of community detection algorithms in directed networks is much lower than in undirected networks. However, evaluation measures to estimate the quality of communities in undirected networks nowadays have its adaptation to directed networks as, for example, the well-known modularity measure. This paper introduces a genetic-based consensus clustering to detect communities in directed networks with the directed modularity as the fitness function. Consensus strategies involve combining computational models to improve the quality of solutions generated by a single model. The reason behind the development of a consensus strategy relies on the fact that recent studies indicate that the modularity may fail in detecting expected clusterings. Computational experiments with artificial LFR networks show that the proposed method was very competitive in comparison to existing strategies in the literature.

Label propagation based evolutionary clustering for detecting overlapping and non-overlapping communities in dynamic networks

Since real-world networks evolve over time, detecting communities in dynamic networks is a challenging research problem with wide applications. In this paper, we first improve our previous method and propose a more stable algorithm which is label-propagation-based for the discovery of communities in complex networks. Then, we present a novel evolutionary clustering approach DLPAE for dynamic networks based on the stable algorithm. According to DLPAE, community labels of nodes are determined by their neighbors, and a confidence (i.e., the importance of its neighbor to the node) is attached to each neighbor. During clustering, the confidences of nodes are calculated in terms of the structures of the current network and the network at last timestamp. We compute confidences’ variance of each node and update nodes’ labels in a descending order according to the values. In our setting, each node can keep one or more labels with belonging coefficients no less than a threshold, which renders DLPAE suitable for detecting overlapping and non-overlapping communities in dynamic networks. Experimental results on both real and synthetic datasets show the ability of DLPAE to detect overlapping and non-overlapping communities in dynamic networks, and demonstrate its higher accuracy compared to other related methods.

Clustering attributed graphs: Models, measures and methods

AbstractClustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on graphs without attributes, with the notable exception of edge weights. However, these models only provide a partial representation of real social systems, that are thus often described using node attributes, representing features of the actors, and edge attributes, representing different kinds of relationships among them. We refer to these models asattributed graphs. Consequently, existing graph clustering methods have been recently extended to deal with node and edge attributes. This article is a literature survey on this topic, organizing, and presenting recent research results in a uniform way, characterizing the main existing clustering methods and highlighting their conceptual differences. We also cover the important topic of clustering evaluation and identify current open problems.

A Stochastic Model for Detecting Heterogeneous Link Communities in Complex Networks

Discovery of communities in networks is a fundamental data analysis problem. Most of the existing approaches have focused on discovering communities of nodes, while recent studies have shown great advantages and utilities of the knowledge of communities of links. Stochastic models provides a promising class of techniques for the identification of modular structures, but most stochastic models mainly focus on the detection of node communities rather than link communities. We propose a stochastic model, which not only describes the structure of link communities, but also considers the heterogeneous distribution of community sizes, a property which is often ignored by other models. We then learn the model parameters using a method of maximum likelihood based on an expectation-maximization algorithm. To deal with large complex real networks, we extend the method by a strategy of iterative bipartition. The extended method is not only efficient, but is also able to determine the number of communities for a given network. We test our approach on both synthetic benchmarks and real-world networks including an application to a large biological network, and also compare it with two existing methods. The results demonstrate the superior performance of our approach over the competing methods for detecting link communities.

Uncovering Hierarchical and Overlapping Communities with a Local-First Approach

Community discovery in complex networks is the task of organizing a network’s structure by grouping together nodes related to each other. Traditional approaches are based on the assumption that there is a global-level organization in the network. However, in many scenarios, each node is the bearer of complex information and cannot be classified in disjoint clusters. The top-down global view of the partition approach is not designed for this. Here, we represent this complex information as multiple latent labels, and we postulate that edges in the networks are created among nodes carrying similar labels. The latent labels are the communities a node belongs to and we discover them with a simple local-first approach to community discovery. This is achieved by democratically letting each node vote for the communities it sees surrounding it in its limited view of the global system, its ego neighborhood, using a label propagation algorithm, assuming that each node is aware of the label it shares with each of its connections. The local communities are merged hierarchically, unveiling the modular organization of the network at the global level and identifying overlapping groups and groups of groups. We tested this intuition against the state-of-the-art overlapping community discovery and found that our new method advances in the chosen scenarios in the quality of the obtained communities. We perform a test on benchmark and on real-world networks, evaluating the quality of the community coverage by using the extracted communities to predict the metadata attached to the nodes, which we consider external information about the latent labels. We also provide an explanation about why real-world networks contain overlapping communities and how our logic is able to capture them. Finally, we show how our method is deterministic, is incremental, and has a limited time complexity, so that it can be used on real-world scale networks.

NEIWalk: Community Discovery in Dynamic Content-Based Networks

Recently, discovering dynamic communities has become an increasingly important task. Many algorithms have been proposed, most of which only use linkage structure. However, rich information is encoded in the content of social networks such as node content and edge content, which is essential to discover topically meaningful communities. Therefore, to detect both structurally and topically meaningful communities, linkage structure, node content and edge content should be integrated. The main challenge lies in how to integrate them dynamically in a seamless way. This paper proposes a novel transformation of content-based network into a Node-Edge Interaction (NEI) network where linkage structure, node content and edge content are embedded seamlessly. A differential activity based approach is proposed to incrementally maintain the NEI network as the content-based network evolves. To capture the semantic effect of different edge types, a transition probability matrix is devised for the NEI network. Based on this, heterogeneous random walk is applied to discover dynamic communities, leading to a new dynamic community detection method termed NEIWalk (NEI network based random Walk). Theoretical analysis shows that the proposed NEIWalk method gets a bounded accuracy loss due to the random walk sampling. Experimental results demonstrate the effectiveness and efficiency of NEIWalk.

Constant community discovery in network based on consensus clustering

Community detection is a fundamental work to analyze the structural and functional properties of complex networks. There are many algorithms proposed to find the optimal communities of network. In this paper, we focus on how vertex order influences the results of community detection. By using consensus clustering, we discover communities and get a consensus matrix under different vertex orders. Based on the consensus matrix, we study the phenomenon that some nodes are always allocated in the same community even with different vertex permutations. We call this group of nodes as constant community and propose a constant community detection algorithm (CCDA) to find constant communities in network. We also further study the internal properties of constant communities and find constant communities play a guiding role in community detection. Finally, a discussion of constant communities is given in the hope of being useful to others working in this field.

Solving sparse non-negative tensor equations: algorithms and applications

We study iterative methods for solving a set of sparse non-negative tensor equations (multivariate polynomial systems) arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.

Community discovery and importance analysis in social network

Social networks are widespread and important in our daily life. Finding communities and reveal node characteristics in community are crucial to understand the network structure and function. Many methods based on Nonnegative matrix factorization NMF are proposed to find communities, while these results appear uncertain with the initial condition especially in weighted directed network. In this paper, firstly we improve the nonnegative matrix factorization NMF method with modeling network as the weighted directed graph and using diagonally dominant matrix as constraint condition to obtain the community membership of each node as well as the interaction among communities. Furthermore, we raise methods to evaluate nodes importance and to discuss node characteristics in community to analyze the network structure. Some experiments on the Zachary club datasets and other real-world datasets have been did to demonstrate the superiority of our methods for community discovery over other related matrix factorization methods. The results demonstrate that our methods are useful and applicable both in weighted directed model and undirected model for community discovery, and the results are more reliable. Experiments also illustrate the meaningful results by discussing the node characteristics in community. All those provide a useful way for analyzing social network.

Link Community Detection Using Generative Model and Nonnegative Matrix Factorization

Discovery of communities in complex networks is a fundamental data analysis problem with applications in various domains. While most of the existing approaches have focused on discovering communities of nodes, recent studies have shown the advantages and uses of link community discovery in networks. Generative models provide a promising class of techniques for the identification of modular structures in networks, but most generative models mainly focus on the detection of node communities rather than link communities. In this work, we propose a generative model, which is based on the importance of each node when forming links in each community, to describe the structure of link communities. We proceed to fit the model parameters by taking it as an optimization problem, and solve it using nonnegative matrix factorization. Thereafter, in order to automatically determine the number of communities, we extend the above method by introducing a strategy of iterative bipartition. This extended method not only finds the number of communities all by itself, but also obtains high efficiency, and thus it is more suitable to deal with large and unexplored real networks. We test this approach on both synthetic benchmarks and real-world networks including an application on a large biological network, and compare it with two highly related methods. Results demonstrate the superior performance of our approach over competing methods for the detection of link communities.

Simultaneous community discovery and user interests extraction in social network based on probabilistic model

This article addresses the problem of discovering latent communities and topics simultaneously in social network. With the advent of online social networking, the automatic discovering communities is vital for understanding the cooperation and interaction patterns of users in these social networks. In this paper, we propose probabilistic generative models to detect latent communities by incorporating both the information of relationships and the textural content. Different from previous work, topics and user community memberships cannot be generated independently, but have a greater degree of correspondence between them. We assume that community membership is dependent on the user and a subset of topics which the user is really interested in. Furthermore, the heterogeneous relationship strengths were used to improve community discovery. These models treat community and topic as different latent variables but interdependent with each other and mutually reinforcing. Experiments on real-world dataset have shown that our models have the capability to detect well-connected and topically meaningful communities.