Community Structure In Complex Networks Research Articles

Community structure of complex networks based on continuous neural network

As a new subject, the research of complex networks has attracted the attention of researchers from different disciplines. Community structure is one of the key structures of complex networks, so it is a very important task to analyze the community structure of complex networks accurately. In this paper, we study the problem of extracting the community structure of complex networks, and propose a continuous neural network (CNN) algorithm. It is proved that for any given initial value, the continuous neural network algorithm converges to the eigenvector of the maximum eigenvalue of the network modularity matrix. Therefore, according to the stability of the evolution of the network symbol will be able to get two community structure.

A spectral method to detect community structure based on distance modularity matrix

There are many community organizations in social and biological networks. How to identify these community structure in complex networks has become a hot issue. In this paper, an algorithm to detect community structure of networks is proposed by using spectra of distance modularity matrix. The proposed algorithm focuses on the distance of vertices within communities, rather than the most weakly connected vertex pairs or number of edges between communities. The experimental results show that our method achieves better effectiveness to identify community structure for a variety of real-world networks and computer generated networks with a little more time-consumption.

Mitigation of attacks and errors on community structure in complex networks

The community structure is one property of complex networks and depicts the potential functionality of networked systems. Attacks and errors exist broadly in daily life, and the tolerance or the robustness of networks against these failures is crucial to systems. The robustness of communities has drawn a lot of attention in recent studies. Intuitively, a robust community should keep much similarity with the original partition under structural fluctuations. Most previous studies focused on evaluating the robustness of communities through the fraction of correct-detected members. However, the ability of this criterion in reflecting the variation of integral network communities is weak, and several specific structures tend to get the same evaluating value in terms of this criterion. In this paper, we propose a metric (RNMI) to evaluate the community robustness based on the normalized mutual information. Then, a simulated annealing algorithm is devised to mitigate the damage on communities under attacks or errors. Experimental results on various networks show that the robustness of communities can be improved while greatly preserving the intrinsic allocation. Furthermore, we study the different optimal structures against attacks and errors to reveal the uncorrelation between them, and design a weighed metric to obtain balanced optimal solutions.

Emergence of communities and diversity in social networks

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite widespread interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties arise in social networks with great individual diversity. Here, we answer this question using the ultimatum game, which has been a paradigm for characterizing altruism and fairness. We experimentally show that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to populations with random interactions. Diverse communities and social norms come from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually become the community leaders. This result indicates that networks are significant in the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about strategies for developing network models and theories of evolutionary games and social dynamics.

Study on similarity based on connection degree in social network

Application of set pair analysis theory, the social network is as an identical---discrepancy---contrary system. Firstly, based on connection degree to descript the identical---discrepancy---contrary relation between vertices, considering the contribution of local features and the topological structure to the similarity between vertices, we define the similarity based on connection degree taking into account weight and clustering coefficient. The similarity can better describe network structure characteristics, overcome the under-estimating for the local similarity indices, and reduce the computational complexity of the global indices. Secondly, in order to apply the similarity to community discovery, combined with agglomerative hierarchical clustering algorithm, we propose a new community discovery algorithm Vertices Similarity First and Communities Mean (VSFCM), so that it is applicable to detect community structures in complex networks with any object that has similarity. Finally, the correctness and effectiveness of the similarity measurement and algorithm VSFCM are terrified through the experiments.

Complexity and dynamics of topological and community structure in complex networks

Complexity is highly susceptible to variations in the network dynamics, reflected on its underlying architecture where topological organization of cohesive subsets into clusters, system’s modular structure and resulting hierarchical patterns, are cross-linked with functional dynamics of the system. Here we study connection between hierarchical topological scales of the simplicial complexes and the organization of functional clusters – communities in complex networks. The analysis reveals the full dynamics of different combinatorial structures of q-th-dimensional simplicial complexes and their Laplacian spectra, presenting spectral properties of resulting symmetric and positive semidefinite matrices. The emergence of system’s collective behavior from inhomogeneous statistical distribution is induced by hierarchically ordered topological structure, which is mapped to simplicial complex where local interactions between the nodes clustered into subcomplexes generate flow of information that characterizes complexity and dynamics of the full system.

Locating Structural Centers: A Density-Based Clustering Method for Community Detection.

Uncovering underlying community structures in complex networks has received considerable attention because of its importance in understanding structural attributes and group characteristics of networks. The algorithmic identification of such structures is a significant challenge. Local expanding methods have proven to be efficient and effective in community detection, but most methods are sensitive to initial seeds and built-in parameters. In this paper, we present a local expansion method by density-based clustering, which aims to uncover the intrinsic network communities by locating the structural centers of communities based on a proposed structural centrality. The structural centrality takes into account local density of nodes and relative distance between nodes. The proposed algorithm expands a community from the structural center to the border with a single local search procedure. The local expanding procedure follows a heuristic strategy as allowing it to find complete community structures. Moreover, it can identify different node roles (cores and outliers) in communities by defining a border region. The experiments involve both on real-world and artificial networks, and give a comparison view to evaluate the proposed method. The result of these experiments shows that the proposed method performs more efficiently with a comparative clustering performance than current state of the art methods.

Estimation of Distribution Algorithm with Local Sampling Strategy for Community Detection in Complex Networks

It is important to discover the potential community structure for analyzing complex networks. In this paper, an estimation of distribution algorithm with local sampling strategy for community detection in complex networks is presented to optimize the modularity density function. In the proposed algorithm, the evolution probability model is built according to eminent individuals selected by simulated annealing mechanism and a local sampling strategy based on a local similarity model is adopted to improve both the speed and the accuracy for detecting community structure in complex networks. At the same time, a more general version of the criterion function with a tunable parameter λ is used to avoid the resolution limit. Experiments on synthetic and real-life networks demonstrate the performance and the comparison of experimental results with those of several state-of-the-art methods, the proposed algorithm is considerably efficient and competitive.

Surveying traffic congestion based on the concept of community structure of complex networks

In this paper, taking the traffic of Beijing city as an instance, we study city traffic states, especially traffic congestion, based on the concept of network community structure. Concretely, using the floating car data (FCD) information of vehicles gained from the intelligent transport system (ITS) of the city, we construct a new traffic network model which is with floating cars as network nodes and time-varying. It shows that this traffic network has Gaussian degree distributions at different time points. Furthermore, compared with free traffic situations, our simulations show that the traffic network generally has more obvious community structures with larger values of network fitness for congested traffic situations, and through the GPSspg web page, we show that all of our results are consistent with the reality. Then, it indicates that network community structure should be an available way for investigating city traffic congestion problems.

A graph clustering method for community detection in complex networks

Abstract Information mining from complex networks by identifying communities is an important problem in a number of research fields, including the social sciences, biology, physics and medicine. First, two concepts are introduced, Attracting Degree and Recommending Degree. Second, a graph clustering method, referred to as AR-Cluster, is presented for detecting community structures in complex networks. Third, a novel collaborative similarity measure is adopted to calculate node similarities. In the AR-Cluster method, vertices are grouped together based on calculated similarity under a K-Medoids framework. Extensive experimental results on two real datasets show the effectiveness of AR-Cluster.

Permanence and Community Structure in Complex Networks

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 made 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 individual node. In this article, we argue that the belongingness of nodes in a community is not uniform. We quantify the degree of belongingness of a vertex within a community by a new vertex-based metric called permanence . The central idea of permanence is based on the observation that the strength of membership of a vertex to a community depends upon two factors (i) the extent of connections of the vertex within its community versus outside its community, and (ii) how tightly the vertex is connected internally. We present the formulation of permanence based on these two quantities. We demonstrate that compared to other existing metrics (such as modularity, conductance, and cut-ratio), the change in permanence is more commensurate to the level of perturbation in ground-truth communities. We discuss how permanence can help us understand and utilize the structure and evolution of communities by demonstrating that it can be used to -- (i) measure the persistence of a vertex in a community, (ii) design strategies to strengthen the community structure, (iii) explore the core-periphery structure within a community, and (iv) select suitable initiators for message spreading. We further show that permanence is an excellent metric for identifying communities. We demonstrate that the process of maximizing permanence (abbreviated as MaxPerm ) produces meaningful communities that concur with the ground-truth community structure of the networks more accurately than eight other popular community detection algorithms. Finally, we provide mathematical proofs to demonstrate the correctness of finding communities by maximizing permanence. In particular, we show that the communities obtained by this method are (i) less affected by the changes in vertex ordering, and (ii) more resilient to resolution limit, degeneracy of solutions, and asymptotic growth of values.

Emergence of Communities and Diversity in Social Networks

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite much interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties could arise in social networks with great individual diversity. Here, we answer this question in virtue of the experiment of the ultimatum game that has been a paradigm to characterize altruism and fairness. We find that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to the scenario of populations with random interactions. The diverse communities and social norms stem from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually becomes the leaders of communities. This indicates that networks are significant for the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about individual strategies for the development of network models and theories of evolutionary games and social dynamics.

Effective Detection of Modular and Granular Overlaps in Online Social Networks Using Fuzzy ART

There has been lot of research endeavours in detecting overlapping community structures in complex networks. This paper concentrates on one of the most popular complex networks of recent times—online social networks. Some of the existing methodologies in community detection for online social networks are discussed. The goal of the proposed algorithm is to solve the stability–plasticity dilemma and to suggest a new technique for detecting modular and granular overlaps in community detection. The stability–plasticity dilemma is solved using a Fuzzy ART-inspired algorithm for overlapping community detection for detecting modular and granular overlaps. The algorithm is designed by making use of network measures such as vertex betweenness, betweenness centrality, and split betweenness. The validation metrics used for testing the algorithm were sensitivity, specificity, accuracy and normalized mutual information. The algorithm has been tested and validated using benchmark datasets and real network datasets and gives a cumulative performance of 3.1/4.0.

Detecting community structure in complex networks using an interaction optimization process

Abstract Most complex networks contain community structures. Detecting these community structures is important for understanding and controlling the networks. Most community detection methods use network topology and edge density to identify optimal communities; however, these methods have a high computational complexity and are sensitive to network forms and types. To address these problems, in this paper, we propose an algorithm that uses an interaction optimization process to detect community structures in complex networks. This algorithm efficiently searches the candidates of optimal communities by optimizing the interactions of the members within each community based on the concept of greedy optimization. During this process, each candidate is evaluated using an interaction-based community model. This model quickly and accurately measures the difference between the quantity and quality of intra- and inter-community interactions. We test our algorithm on several benchmark networks with known community structures that include diverse communities detected by other methods. Additionally, after applying our algorithm to several real-world complex networks, we compare our algorithm with other methods. We find that the structure quality and coverage results achieved by our algorithm surpass those of the other methods.

Adaptive Label Propagation Algorithm to Detect Overlapping Community in Complex Networks

According to the defects that community detection algorithm in unknown complex networks has a pre-parameter. We propose Adaptive Label Propagation Algorithm (ALPA) to detect community structures in complex networks. The ALPA algorithm find out all disjoint Maximal Clique (MC) and let each MC share the identical weight and unique label so as to reduce the redundant labels and uncontrollable factors. The stability of ALPA algorithm is enhanced by synchronous update during iterations. Meanwhile it will converge easily due to the termination condition that all of the vertexes have the label. During iterations we use the adaptive threshold method to overcome the pre-parameter limitation. Compared with other community detection algorithms in synthetic networks and real networks, our experiments show that ALPA algorithm not only improves the tolerance of mixing parameter, but also enhances its robustness.

Empirical analysis of aircraft clusters in air traffic situation networks

The existing research on air traffic complexity ignores the effects of air traffic situation structure and, thus, cannot reflect the heterogeneous traffic density distribution in airspace. In this study, the structure of air traffic situation was characterized using the idea of community structure in complex networks. An aircraft cluster model was built, and an aircraft cluster discovery method based on depth-first traversal was proposed. The aircraft cluster division effect was comprehensively represented by cluster performance indices, including cohesion and stability. The routinely recorded radar data in two air traffic control sectors were collected to assess the cluster division results. Through statistics, the threshold intervals with 95% of best performance are 40–60 km and 20–50 km for the two sectors, respectively. The value 40 km was selected to further statistically characterize the aircraft clusters. Compared with K-means clustering, the proposed method does not require the predefined number of clusters and has high stability, which confirms its feasibility into cluster division in dynamic air traffic situation. The structural characteristics of aircraft clusters, including the average intra-cluster horizontal distance, number of clusters, and size and life cycle of clusters, were statistically analyzed. Comparison of cluster structures with the commonly used dynamic density index shows that in air traffic situation with relatively large number big size of clusters, the aircraft trajectory changes more frequently. Structural characterization of aircraft clusters is able to portray the nonuniformity of traffic density distribution, and contributes to comprehensive description of air traffic situation, thus providing a new prospect for analysis of air traffic complexity. Moreover, aircraft cluster division contributes to auto-identification of hot-spots on radar screen, and efficiently eliminates the workload imposed on controllers during judgment of these congestion hot-spots, thereby improving the air traffic operation efficiency.

A Michigan memetic algorithm for solving the community detection problem in complex network

Community structure is an important feature in complex networks which has great significant for organization of networks. The community detection is the process of partitioning the network into some communities in such a way that there exist many connections in the communities and few connections between them. In this paper a Michigan memetic algorithm; called MLAMA-Net; is proposed for solving the community detection problem. The proposed algorithm is an evolutionary algorithm in which each chromosome represents a part of the solution and the whole population represents the solution. In the proposed algorithm, the population of chromosomes is a network of chromosomes which is isomorphic to the input network. Each node has a chromosome and a learning automaton (LA). The chromosome represents the community of corresponding node and saves the histories of exploration. The learning automaton represents a meme and saves the histories of the exploitation. The proposed algorithm is a distributed algorithm in which each chromosome locally evolves by evolutionary operators and improves by a local search. By interacting with both the evolutionary operators and local search, our algorithm effectively detects the community structure in complex networks and solves the resolution limit problem of modularity optimization. To show the superiority of our proposed algorithm over the some well-known algorithms, several computer experiments have been conducted. The obtained results show MLAMA-Net is effective and efficient at detecting the community structure in complex networks.

Weighted-spectral clustering algorithm for detecting community structures in complex networks

The community structure is a common non-trivial topological feature of many complex real-world networks. Existing methods for identifying the community structure are generally based on statistical-type properties, such as the degree of centrality, the shortest path betweenness centrality, the modularity, and so forth. However, the form of the community structure may vary widely, even if the number of vertices and edges are fixed. Consequently, it is difficult to be certain of the exact number of clusters within the network. Clustering schemes which require the number of clusters to be specified in advance often misjudge the community structure and yield a poor clustering performance as a result. Accordingly, the present study proposes a clustering algorithm, designated as the Weighted-Spectral Clustering Algorithm, capable of detecting the community structure of a network with no prior knowledge of the cluster number. The proposed method is tested on both computer-generated networks and several real-world networks for which the community structures are already known. The results confirm the ability of the proposed algorithm to partition the network into an appropriate number of clusters in every case.

Estimating the optimal number of communities by cluster analysis

How to identify community structure in complex network is of theoretical significance, which relates to help to analyze the network topology and understand the network works. Determining the optimal number of communities is a nontrivial problem in detecting community structure. In this paper, we propose a novel method for detecting the optimal number of communities. Based on the local random walk (LRW) measurement, the distance index between each pair of nodes of a network is calculated firstly. Then the optimal number of communities can be found based on the idea that community centers are characterized by a higher density than their neighbors and by a relatively large distance from nodes with higher densities. The experimental results show that the method is effective and efficient in both artificial and real-world networks.

Comprehensive spectral approach for community structure analysis on complex networks.

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a "multipartite" component. These two matrices reveal the structure of the network from different perspectives and can be analyzed at different levels of detail. Their entries, or the entries of their lower-rank approximations, provide measures of the affinity or antagonism between the nodes that highlight the communities and the "gateway" links that connect them together. An algorithm is then proposed to achieve the automatic assignment of the nodes to communities based on the information provided by either matrix. This algorithm naturally generates overlapping communities but can also be tuned to eliminate the overlaps.