Showing papers on "Clique percolation method published in 2011"

Generalized Louvain method for community detection in large networks

Abstract: In this paper we present a novel strategy to discover the community structure of (possibly, large) networks This approach is based on the well-know concept of network modularity optimization To do so, our algorithm exploits a novel measure of edge centrality, based on the κ-paths This technique allows to efficiently compute a edge ranking in large networks in near linear time Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network Finally, it discovers the community structure adopting a strategy inspired by the well-known state-of-the-art Louvain method (henceforth, LM), efficiently maximizing the network modularity The experiments we carried out show that our algorithm outperforms other techniques and slightly improves results of the original LM, providing reliable results Another advantage is that its adoption is naturally extended even to unweighted networks, differently with respect to the LM

Map equation for link communities.

Abstract: 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 identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.

Entropy based community detection in augmented social networks

Abstract: Social network analysis has become a major subject in recent times, bringing also several challenges in the computer science field. One aspect of the social network analysis is the community detection problem, which can be seen as a graph clustering problem. However, social networks are more than a graph, they have an interesting amount of information derived from its social aspect, such as profile information, content sharing and annotations, among others. Most of the community detection algorithms use only the structure of the network, i.e., the graph. In this paper we propose a new method which uses the semantic information along with the network structure in the community detection process. Thus, our method combines an algorithm for optimizing modularity and an entropy-based data clustering algorithm, which tries to find a partition with low entropy and keeping in mind the modularity.

Density-based shrinkage for revealing hierarchical and overlapping community structure in networks

Abstract: The investigation of community structure in networks is an important issue in many disciplines, which still remains a challenging task. First, complex networks often show a hierarchical structure with communities embedded within other communities. Moreover, communities in the network may overlap and have noise, e.g., some nodes belonging to multiple communities and some nodes marginally connected with the communities, which are called hub and outlier, respectively. Therefore, a good algorithm is desirable to be able to not only detect hierarchical communities, but also to identify hubs and outliers. In this paper, we propose a parameter-free hierarchical network clustering algorithm DenShrink. By combining the advantages of density-based clustering and modularity optimization methods, our algorithm can reveal the embedded hierarchical community structure efficiently in large-scale weighted undirected networks, and identify hubs and outliers as well. Moreover, it overcomes the resolution limit possessed by other modularity-based methods. Our experiments on the real-world and synthetic datasets show that DenShrink generates more accurate results than the baseline methods.

Percolation in self-similar networks.

Abstract: We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that self-similar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.

A novel genetic algorithm for overlapping community detection

Abstract: There is a surge of community detection on complex network analysis in recent years, since communities often play special roles in the network systems. However, many community structures are overlapping in real word. For example, a professor collaborates with researchers in different fields. In this paper, we propose a novel algorithm to discover overlapping communities. Different from conventional algorithms based on node clustering, our algorithm is based on edge clustering. Since edges usually represent unique relations among nodes, edge clustering will discover groups of edges that have the same characteristics. Thus nodes naturally belong to multiple communities. The proposed algorithm apply a novel genetic algorithm to cluster on edges. A scalable encoding schema is designed and the number of communities can be automatically determined. Experiments on both artificial networks and real networks validate the effectiveness and efficiency of the algorithm.

Partitioning networks into communities by message passing.

Abstract: Community structures are found to exist ubiquitously in a number of systems conveniently represented as complex networks. Partitioning networks into communities is thus important and crucial to both capture and simplify these systems' complexity. The prevalent and standard approach to meet this goal is related to the maximization of a quality function, modularity, which measures the goodness of a partition of a network into communities. However, it has recently been found that modularity maximization suffers from a resolution limit, which prevents its effectiveness and range of applications. Even when neglecting the resolution limit, methods designed for detecting communities in undirected networks cannot always be easily extended, and even less directly applied, to directed networks (for which specifically designed community detection methods are very limited). Furthermore, real-world networks are frequently found to possess hierarchical structure and the problem of revealing such type of structure is far from being addressed. In this paper, we propose a scheme that partitions networks into communities by electing community leaders via message passing between nodes. Using random walk on networks, this scheme derives an effective similarity measure between nodes, which is closely related to community memberships of nodes. Importantly, this approach can be applied to a very broad range of networks types. In fact, the successful validation of the proposed scheme on real and synthetic networks shows that this approach can effectively (i) address the problem of resolution limit and (ii) find communities in both directed and undirected networks within a unified framework, including revealing multiple levels of robust community partitions.

Community detection by using the extended modularity

Abstract: This article is about community detection algorithms in graphs. First a new method will be introduced, which is based on an extension [16] of the commonly used modularity [17, 18, 19, 20] and gives overlapping communities. We list and compare the results given by our new method and some other algorithms yileding either overlapping or non-overlapping communities. While the main use of the proposed algorithm is benchmarking, we also consider the possibility of hot starts, and some further extensions that considers the degree distribution of the graphs.

Dynamic communities and their detection

Abstract: Overlapping community detection has already become an interesting problem in data mining and also a useful technique in applications. This underlines the importance of following the lifetime of communities in real graphs. Palla et al. developed a promising method, and analyzed community evolution on two large databases [23]. We have followed their footsteps in analyzing large real-world databases and found, that the framework they use to describe the dynamics of communities is insufficient for our data. The method used by Palla et al. is also dependent on a very special community detection algorithm, the clique percolation method, and on its monotonic nature. In this paper we propose an extension of the basic community events described in [23] and a method capable of handling communities found a nonmonotonic community detection algorithm. We also report on findings that came from the tests on real social graphs.

Modularity-based model selection for kernel spectral clustering

Abstract: A proper way of choosing the tuning parameters in a kernel model has a fundamental importance in determining the success of the model for a particular task. This paper is related to model selection in the framework of community detection on weighted and unweighted networks by means of a kernel spectral clustering model. Here we propose a new method based on Modularity (a popular measure of community structure in a network) which can deal with quite general situations (i.e. overlapping communities with different sizes). Thus we use Modularity criterion for model selection and not at the training level, which is the case of all the clustering algorithms proposed so far in the literature.

Finding Community Structure in Complex Networks Using Parallel Approach

Abstract: Network analysis is an important term in different scientific areas and finding the structure of communities is a significant challenge in network analysis. A group of vertices with high intra-connection and sparse inter-connection is called community. In this paper, we propose a novel method for community detection in networks, which works better in time and precision compared to similar methods. The proposed method is able to detect communities of a wide variety of networks with different properties. This method is an agglomerative parallel algorithm. Also it can find multiple communities and exchange the nodes between detected communities simultaneously. It has utilized local modularity for constructing the communities. After all, genetic algorithm is used to optimize the parameters of the proposed method. The algorithm is evaluated by modularity metric and shows a noticeable good precision. Also it has used simulated annealing to maximize the modularity.

The map equation for link community

Abstract: 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 identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.

Discovering Communities in Social Networks Using Topology and Attributes

Abstract: Many online social networks such as Face book, Linked In and My Space have become increasingly important These social networks are rich in information about entities like hobbies, demographic information, friendship, and other attributes This information can be used extensively for network analysis One of the most important problems in social network analysis is community detection The community detection problem is closely related to graph clustering Most of the existing graph clustering algorithms employ only the structure of a graph to find highly connected components These algorithms ignore nodes' attributes that can help in improving the quality of the clustering In this paper, we propose a clustering algorithm which clusters a graph by incorporating both the topological structure of the graph as well as attribute information The aim is to find clusters such that the nodes in each cluster are similar in the attribute space In terms of social networks, we are looking to find communities where the members of the same community have similar profiles The method was evaluated using real and synthetic graph datasets The experimental results demonstrate the effectiveness of the proposed method

The effect of hub nodes on the community structure in scale-free networks

Abstract: Many networks have two important features in common (1) the scale-free degree distribution P ( k ) ∝ k − α and (2) the community structure In this paper, we focus on the relationship between these two features in complex networks We first investigate the effect of the power law exponent α on the community structure in artificial networks and some real-world networks Generally speaking, we find out that the networks with significant community structure, often have a large α Second, hub nodes removal from scale-free networks affects the community structure more considerably than random removal Our observation indicates that hubs may be the explanation for that scale-free networks often have fuzzy community structure

Modeling Evolution of Weighted Clique Networks

Abstract: We propose a weighted clique network evolution model, which expands continuously by the addition of a new clique (maximal complete sub-graph) at each time step. And the cliques in the network overlap with each other. The structural expansion of the weighted clique network is combined with the edges' weight and vertices' strengths dynamical evolution. The model is based on a weight-driven dynamics and a weights' enhancement mechanism combining with the network growth. We study the network properties, which include the distribution of vertices' strength and the distribution of edges' weight, and find that both the distributions follow the scale-free distribution. At the same time, we also find that the relationship between strength and degree of a vertex are linear correlation during the growth of the network. On the basis of mean-field theory, we study the weighted network model and prove that both vertices' strength and edges' weight of this model follow the scale-free distribution. And we exploit an algorithm to forecast the network dynamics, which can be used to reckon the distributions and the corresponding scaling exponents. Furthermore, we observe that mean-field based theoretic results are consistent with the statistical data of the model, which denotes the theoretical result in this paper is effective.

Finding Community Structure with Performance Guarantees in Complex Networks

Abstract: Many networks including social networks, computer networks, and biological networks are found to divide naturally into communities of densely connected individuals Finding community structure is one of fundamental problems in network science Since Newman's suggestion of using \emph{modularity} as a measure to qualify the goodness of community structures, many efficient methods to maximize modularity have been proposed but without a guarantee of optimality In this paper, we propose two polynomial-time algorithms to the modularity maximization problem with theoretical performance guarantees The first algorithm comes with a \emph{priori guarantee} that the modularity of found community structure is within a constant factor of the optimal modularity when the network has the power-law degree distribution Despite being mainly of theoretical interest, to our best knowledge, this is the first approximation algorithm for finding community structure in networks In our second algorithm, we propose a \emph{sparse metric}, a substantially faster linear programming method for maximizing modularity and apply a rounding technique based on this sparse metric with a \emph{posteriori approximation guarantee} Our experiments show that the rounding algorithm returns the optimal solutions in most cases and are very scalable, that is, it can run on a network of a few thousand nodes whereas the LP solution in the literature only ran on a network of at most 235 nodes

Finding Community Structure with Performance Guarantees in Scale-Free Networks

Abstract: A common property of many networks, including the Internet, biological networks, and social networks, is that the degree distribution approximately follows a power law Such networks are found to be naturally divided into communities of densely connected nodes, known as the community structure Despite that the existence of the community structure has been clearly indicated through experiments, there is lack of a theoretical justification for the linkage between the power-law topology and the community structure properties Moreover, most existing community structure detection algorithms, apart from being fast and providing sub-optimal solutions, do not come with any provable solution quality In this paper, we show, using analytical arguments, that the power-law topology indicates the presence of community structure That is we can find in a power-law network a division of the network into communities with significant Newman's modularity values, a well-known measure to qualify the community structure Moreover, we provide an approximation algorithm for finding community structure via maximizing the modularity that guarantees optimal solutions up to a constant factor To the best of our knowledge, this is the first approximation algorithm for the modularity maximization problem

Community Detection in Dynamic Social Networks: A Random Walk Approach

Abstract: This study aims to tackling community detection problems in dynamic social networks. The main approach focuses on exploring the idea of random walk in formulating modularity functions for community detection. Under this approach, a modularity function is defined as the difference between the probability of a Markov chain induced by a community and the probability of a null model that assumes no detectable community structure exists in the network. In this paper, we demonstrate the modularity-based approach by applying it to identify group boundaries in an adolescence friendship networks spanning a period of five months. Results and future directions will be discussed.

Community Detection with Fuzzy Community Structure

Abstract: In order to find a cover which allows nodes to be shared among several communities, we propose a simple fuzzy community detection algorithm, which is based on an existing partition detection technique. For the performance of overlapping nodes that makes the partition ambiguous, a new extended modularity is introduced to qualify covers. With modularity optimization, the cover can be found with a high quality. We applied our method to real networks. The results demonstrate that our method can discover meaningful fuzzy community structure, overlapping community structure and hierarchical structure.

Distributed Community Detection in Complex Networks

Abstract: Network analysis is an important and interesting area of research with many applications in different domains. One of the challenges in network analysis is community detection. Community detection is the process of partitioning the network into some groups in such a way that there exist many interactions in the groups and few interactions among them. Toward improving time complexity and precision of community detection, a novel method is proposed in this paper. This method is able to detect multiple communities simultaneously. No prior knowledge is required about the number of communities or the structure of network in proposed algorithm. This algorithm is evaluated by modularity measure on different networks and the result shows improvements over existing methods. We use local modularity as the similarity measurement to collect similar nodes in one community. Our method is a kind of agglomerative approach.

Detecting communities in clustered networks based on group action on set

Abstract: In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure r -cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks.

Personal recommendation algorithm in multidimensional and weighted social network

Abstract: Personal recommendation is a crucial implementation to solve the problem of information overloading on the Internet.On the basis of researching personal recommendation skills and corresponding technologies,an application-driven personal recommendation algorithm in multidimensional and weighted social network was proposed.First,this algorithm built multidimensional and weighted social network between users,then applied the complex network clustering method—CPM(Clique Percolation Method) to find neighbor users,finally made recommendation on the grounds of the similarity between users.The experimental results show that the recommendation system of multidimensional network applying this algorithm can achieve higher recall and precision compared to content-based and collaborative filtering recommendation systems,and the quality of personal recommendation has been improved to some extent.

Clique communities in social networks

Abstract: There is a pressing need for new pattern recognition tools and statistical methods to quantify large graphs and predict the behaviour of network systems, due to the large amount of data which can be extracted from the web. In this work a graph mining metric, based on k-clique communities, is used, allowing a better understanding of the network structure. The proposed metric shows that for different graph families correspond different k-clique sequences.

Mathematical foundations and algorithms for clique relaxations in networks

Abstract: This dissertation establishes mathematical foundations for the properties exhibited by generalizations of cliques, as well as algorithms to find such objects in a network. Cliques are a model of an ideal group with roots in social network analysis. They have since found applications as a part of grouping mechanisms in computer vision, coding theory, experimental design, genomics, economics, and telecommunications among other fields. Because only groups with ideal properties form a clique, they are often too restrictive for identifying groups in many real-world networks. This motivated the introduction of clique relaxations that preserve some of the various defining properties of cliques in relaxed form. There are six clique relaxations that are the focus of this dissertation: s-clique, s-club, s-plex, k-core, quasi-clique , and k-connected subgraphs. Since cliques have found applications in so many fields, research into these clique relaxations has the potential to steer the course of much future research. The focus of this dissertation is on bringing organization and rigorous methodology to the formation and application of clique relaxations. We provide the first taxonomy focused on how the various clique relaxations relate on key structural properties demonstrated by groups. We also give a framework for how clique relaxations can be formed. This equips researchers with the ability to choose the appropriate clique relaxation for an application based on its structural properties, or, if an appropriate clique relaxation does not exist, form a new one. In addition to identifying the structural properties of the various clique relaxations, we identify properties and prove propositions that are important computationally. These assist in creating algorithms to find a clique relaxation quickly as it is immersed in a network. We give the first ever analysis of the computational complexity of finding the maximum quasi-clique in a graph. Such analysis identifies for researchers the appropriate set of computational tools to solve the maximum quasiclique problem. We further create a polynomial time algorithm for identifying large 2-cliques within unit disk graphs, a special class of graphs often arising in communication networks. We prove the algorithm to have a guaranteed 1/2-approximation ratio and finish with computational results.

Community Detection Through Optimal Density Contrast of Adjacency Matrix

Abstract: Detecting communities in real world networks is an important problem for data analysis in science and engineering. By clustering nodes intelligently, a recursive algorithm is designed to detect community. Since the relabeling of nodes does not alter the topology of the network, the problem of community detection corresponds to the finding of a good labeling of nodes so that the adjacency matrix form blocks. By putting a fictitious interaction between nodes, the relabeling problem becomes one of energy minimization, where the total energy of the network is defined by putting interaction between the labels of nodes so that clustering nodes that are in the same community will decrease the total energy. A greedy method is used for the computation of minimum energy. The method shows efficient detection of community in artificial as well as real world network. The result is illustrated in a tree showing hierarchical structure of communities on the basis of sub-matrix density. Applications of the method to weighted and directed networks are discussed.

An Algorithm for Detecting Community Structure of Complex Networks based on Clustering

Abstract: There are considerable interest in algorithms for detecting community structure, which is fundamental for analyzing the relationship between structure and function in complex networks. In this paper, after the introduction of some traditional approaches for detecting community structure and data mining clustering algorithms, we propose Mapping Vertex into Vector(MVV) algorithm, which can convert network nodes to vector, based on the algorithm, we propose K-means algorithm for detecting community structure based on MVV, and use fuzzy c-means to deal with overlapping community. Finally, experiments show that the algorithm presented in this paper is of high accuracy with good performance.

FLIP-CPM: A Parallel Community Detection Method

Abstract: Uncovering the underlying community structure of networks modelling real-world complex systems is essential way to gain insight both into their structure and their functional organization. Of all the definitions of community proposed by researchers, we focused on the k-clique community definition as we believe it best catches the characteristics of many real networks. Currently, extracting k-clique communities using the methods available in the literature requires a formidable amount of computational load and memory resources. In this paper we propose a new parallel method that has proved its capability in extracting k-clique communities efficiently and effectively from some real-world complex networks for which these communities had never been detected before. This innovative method is much less resource intensive than Clique Percolation Method and experimental results show it is always at least an order of magnitude faster. In addition, tests run on parallel architectures show a noticeable speedup factor, in some cases linear with the number of cores.

Network Community Detection Based on Co-Neighbor Modularity Matrix with Spectral Clustering

Abstract: The problem of community detection is one of the outstanding issues in the study of network systems. This paper presents co-neighbor modularity matrix to measure the quality of community detection. The problem of community detection is projected into clustering of eigenvectors in Euclidean space. Network community structure is detected with spectral clustering algorithm which is free from the noise of initial mean point in K-mean algorithm. The experimental results suggest that the method is efficient in finding the structure of community.

Community identification based on clustering coefficient

Abstract: Researches show that numerous complex networks have clustering effect. It is an indispensable step to identify node clusters in network, namely community, in which nodes are closely related, in many applications such as identification of ringleaders in anti-criminal and anti-terrorist network, efficient storage of data in Wireless Sensor Network (WSN). At present, most of community identification methods still require the specifications of the number or the scale of community by user and still can't handle boundary nodes. In an attempt to solve these problems, a network community identification method based on clustering coefficient is proposed. This method makes use of individual-centered theory for reference and can automatically determine the number of communities. It is shown through contrastive experiments that communities identified by this method have more reasonable size and closer structure than those obtained by other methods which are also based on the individual-centered theory. Finally, a research direction is proposed of network community identification method based on the individual-centered theory.