Detecting the optimal number of communities in complex networks

To obtain the optimal number of communities is an important problem in detecting community structures. In this paper, we use the extended measurement of community detecting algorithms to find the optimal community number. Based on the normalized mutual information index, which has been used as a measure for similarity of communities, a statistic Ω(c) is proposed to detect the optimal number of communities. In general, when Ω(c) reaches its local maximum, especially the first one, the corresponding number of communities c is likely to be optimal in community detection. Moreover, the statistic Ω(c) can also measure the significance of community structures in complex networks, which has been paid more attention recently. Numerical and empirical results show that the index Ω(c) is effective in both artificial and real world networks.     

Detecting community structure in complex networks via node similarity

The detection of the community structure in networks is beneficial to understand the network structure and to analyze the network properties. Based on node similarity, a fast and efficient method for detecting community structure is proposed, which discovers the community structure by iteratively incorporating the community containing a node with the communities that contain the nodes with maximum similarity to this node to form a new community. The presented method has low computational complexity because of requiring only the local information of the network, and it does not need any prior knowledge about the communities and its detection results are robust on the selection of the initial node. Some real-world and computer-generated networks are used to evaluate the performance of the presented method. The simulation results demonstrate that this method is efficient to detect community structure in complex networks, and the ZLZ metrics used in the proposed method is the most suitable one among local indices in community detection.     

Detecting local community structures in complex networks based on local degree central nodes

Detecting local communities in real-world graphs such as large social networks, web graphs, and biological networks has received a great deal of attention because obtaining complete information from a large network is still difficult and unrealistic nowadays. In this paper, we define the term local degree central node whose degree is greater than or equal to the degree of its neighbor nodes. A new method based on the local degree central node to detect the local community is proposed. In our method, the local community is not discovered from the given starting node, but from the local degree central node that is associated with the given starting node. Experiments show that the local central nodes are key nodes of communities in complex networks and the local communities detected by our method have high accuracy. Our algorithm can discover local communities accurately for more nodes and is an effective method to explore community structures of large networks.     

Detecting overlapping communities by seed community in weighted complex networks

Detection of community structures in the weighted complex networks is significant to understand the network structures and analysis of the network properties. We present a unique algorithm to detect overlapping communities in the weighted complex networks with considerable accuracy. For a given weighted network, all the seed communities are first extracted. Then to each seed community, more community members are absorbed using the absorbing degree function. In addition, our algorithm successfully finds common nodes between communities. The experiments using some real-world networks show that the performance of our algorithm is satisfactory.     

A fast and efficient heuristic algorithm for detecting community structures in complex networks

Community structure is an important property of complex networks. How to detect the communities is significant for understanding the network structure and to analyze the network properties. Many algorithms, such as K-L and GN, have been proposed to detect community structures in complex networks. According to daily experience, a community should have many nodes and connections. Based on these principles and existing researches, a fast and efficient algorithm for detecting community structures in complex networks is proposed in this paper. The key strategy of the algorithm is to mine a node with the closest relations with the community and assign it to this community. Four real-world networks are used to test the performance of the algorithm. Experimental results demonstrate that the algorithm proposed is rather efficient for detecting community structures in complex networks.     

Detecting the community structure in complex networks based on quantum mechanics

In this paper, we develop a novel method to detect the community structure in complex networks. This approach is based on the combination of kernel-based clustering using quantum mechanics, the spectral clustering technique and the concept of the Bayesian information criterion. We test the proposed algorithm on Zachary’s karate club network and the world of American college football. Experimental results indicate that our algorithm is efficient and effective at finding both the optimal number of clusters, and the best clustering of community structures.     

Self-similar scaling of density in complex real-world networks

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome of the evolution of real-world systems has also attracted much attention within the physics literature. Here we investigate the scaling of density in complex networks under two classical box-covering renormalizations–network coarse-graining–and also different community-based renormalizations. The analysis on over 50 real-world networks reveals a power-law scaling of network density and size under adequate renormalization technique, yet irrespective of network type and origin. The results thus advance a recent discovery of a universal scaling of density among different real-world networks [P.J. Laurienti, K.E. Joyce, Q.K. Telesford, J.H. Burdette, S. Hayasaka, Universal fractal scaling of self-organized networks, Physica A 390 (20) (2011) 3608–3613] and imply an existence of a scale-free density also within–among different self-similar scales of–complex real-world networks. The latter further improves the comprehension of self-similar structure in large real-world networks with several possible applications.     

Detecting the structure of complex networks by quantum bosonic dynamics

In this paper, we introduce a non-interacting boson model to investigate the topological structure of complex networks. By exactly solving this model, we show that it provides a powerful analytical tool in uncovering the important properties of realistic networks. We find that the ground-state degeneracy of this model is equal to the number of connected components in a network and the square of each coefficient in the expansion of the ground state gives the average time that a random walker spends at each node in the infinite time limit. To show the usefulness of this approach in practice, we also carry out numerical simulations on some concrete complex networks. Our results are completely consistent with the previous conclusions derived by graph theory methods. Furthermore, we show that the first excited state appears always on the largest connected component of the network. The relationship between the first excited energy and the average shortest path length in networks is also discussed.     

Communities and dynamical processes in a complex software network

Complex technological networks represent a growing challenge to support and maintain as their number of elements become higher and their interdependencies more involved. On the other hand, for networks that grow in a decentralized manner, it is possible to observe certain patterns in their overall structure that may be taken into account for a more tractable analysis. An example of such a pattern is the spontaneous formation of communities or modules. An important question regarding the detection of communities is if these are really representative of any internal network feature. In this work, we explore the community structure of a real complex software network, and correlate this modularity information with the internal dynamical processes that the network is designed to support. Our results show that the dependence between community structure and internal dynamical processes is remarkable, supporting the fact that a community division of this complex network is helpful in the assessment of the underlying dynamical structure, and thus is a useful tool to achieve a simpler representation of the complexity of the network.     

Semi-supervised clustering algorithm for community structure detection in complex networks

Discovering a community structure is fundamental for uncovering the links between structure and function in complex networks. In this paper, we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization (SNMF) and the maximum optimization of modularity density. Based on this equivalence, we develop a new algorithm, named the so-called SNMF-SS, by combining SNMF and a semi-supervised clustering approach. Previous NMF-based algorithms often suffer from the restriction of measuring network topology from only one perspective, but our algorithm uses a semi-supervised mechanism to get rid of the restriction. The algorithm is illustrated and compared with spectral clustering and NMF by using artificial examples and other classic real world networks. Experimental results show the significance of the proposed approach, particularly, in the cases when community structure is obscure.     

Computing communities in complex networks using the Dirichlet processing Gaussian mixture model with spectral clustering

Community detection becomes a significant tool for the complex network analysis. The study of the community detection algorithms has received an enormous amount of attention. It is still an open question whether a highly accurate and efficient algorithm is found in most data sets. We propose the Dirichlet Processing Gaussian Mixture Model with Spectral Clustering algorithm for detecting the community structures. The combination of traditional spectral algorithm and new non-parametric Bayesian model provides high accuracy and quality. We compare the proposed algorithm with other existing community detecting algorithms using different real-world data sets and computer-generated synthetic data sets. We show that the proposed algorithm results in high modularity, and better accuracy in a wide range of networks. We find that the proposed algorithm works best for the large size of the data sets.     

Quantum inspired evolutionary algorithm for community detection in complex networks

Community structure is indispensable to discover the potential property of complex network systems. In this paper we propose two algorithms (QIEA-net and iQIEA-net) to discover communities in social networks by optimizing modularity. Unlike many existing methods, the proposed algorithms adopt quantum inspired evolutionary algorithm (QIEA) to optimize a population of solutions and do not need to give the number of community beforehand, which is determined by optimizing the value of modularity function and needs no human intervention. In order to accelerate the convergence speed, in iQIEA-net, we apply the result of classical partitioning algorithm as a guiding quantum individual, which can instruct other quantum individuals' evolution. We demonstrate the potential of two algorithms on five real social networks. The results of comparison with other community detection algorithms prove our approaches have very competitive performance.     

Detecting community structure in complex networks based on a measure of information discrepancy

Properties of complex networks, such as small-world property, power-law degree distribution, network transitivity, and network- community structure which seem to be common to many real-world networks have attracted great interest among researchers. In this study, global information of the networks is considered by defining the profile of any node based on the shortest paths between it and all the other nodes in the network; then a useful iterative procedure for community detection based on a measure of information discrepancy and the popular modular function Q is presented. The new iterative method does not need any prior knowledge about the community structure and can detect an appropriate number of communities, which can be hub communities or non-hub communities. The computational results of the method on real networks confirm its capability.     

A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate.     

Efficient algorithm based on neighborhood overlap for community identification in complex networks

Community structure is an important feature in many real-world networks. Many methods and algorithms for identifying communities have been proposed and have attracted great attention in recent years. In this paper, we present a new approach for discovering the community structure in networks. The novelty is that the algorithm uses the strength of the ties for sorting out nodes into communities. More specifically, we use the principle of weak ties hypothesis to determine to what community the node belongs. The advantages of this method are its simplicity, accuracy, and low computational cost. We demonstrate the effectiveness and efficiency of our algorithm both on real-world networks and on benchmark graphs. We also show that the distribution of link strength can give a general view of the basic structure information of graphs.     

Growing community networks with local events

The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes’ degrees.     

Community structure of complex software systems: Analysis and applications

Due to notable discoveries in the fast evolving field of complex networks, recent research in software engineering has also focused on representing software systems with networks. Previous work has observed that these networks follow scale-free degree distributions and reveal small-world phenomena, while we here explore another property commonly found in different complex networks, i.e. community structure. We adopt class dependency networks, where nodes represent software classes and edges represent dependencies among them, and show that these networks reveal a significant community structure, characterized by similar properties as observed in other complex networks. However, although intuitive and anticipated by different phenomena, identified communities do not exactly correspond to software packages. We empirically confirm our observations on several networks constructed from Java and various third party libraries, and propose different applications of community detection to software engineering.     

Analyzing topological characteristics of neuronal functional networks in the rat brain

In this study, we recorded spike trains from brain cortical neurons of several behavioral rats in vivo by using multi-electrode recordings. An NFN was constructed in each trial, obtaining a total of 150 NFNs in this study. The topological characteristics of NFNs were analyzed by using the two most important characteristics of complex networks, namely, small-world structure and community structure. We found that the small-world properties exist in different NFNs constructed in this study. Modular function Q was used to determine the existence of community structure in NFNs, through which we found that community-structure characteristics, which are related to recorded spike train data sets, are more evident in the Y-maze task than in the DM-GM task. Our results can also be used to analyze further the relationship between small-world characteristics and the cognitive behavioral responses of rats.     

Community structure and ethnic preferences in school friendship networks

Recently developed concepts and techniques of analyzing complex systems provide new insight into the structure of social networks. Uncovering recurrent preferences and organizational principles in such networks is a key issue to characterize them. We investigate school friendship networks from the Add Health database. Applying threshold analysis, we find that the friendship networks do not form a single connected component through mutual strong nominations within a school, while under weaker conditions such interconnectedness is present. We extract the networks of overlapping communities at the schools (c-networks) and find that they are scale free and disassortative in contrast to the direct friendship networks, which have an exponential degree distribution and are assortative. Based on the network analysis we study the ethnic preferences in friendship selection. The clique percolation method we use reveals that when in minority, the students tend to build more densely interconnected groups of friends. We also find an asymmetry in the behavior of black minorities in a white majority as compared to that of white minorities in a black majority.