Discovering community structure in Complex Network through Community Detection Approach

In reality many complex networks present modules or community structures obviously. Modularity is a benefit function used in quantifying the quality of a division of a network into communities. And it usually can be used as a basis for optimization methods of detecting community structure in networks. But the most popular modularity which is proposed by M. E. J. Newman and M. Girvan has the resolution limit in community detection. Multi-resolution modularity cannot overcome the misclassifications caused by merging and splitting the communities either. In this paper, we propose a multi-resolution density modularity based on the network density. The proposed function is tested on the artificial networks. Computational results show that it can reduce the rate of misclassification considerably. And the systematicness of the community structures can be demonstrated by the multi-resolution density modularity.

Identifying and tracking community structures in complex networks are one of the cornerstones of network studies, spanning multiple disciplines, from statistics to machine learning to social sciences, and involving even a broader range of application areas, from biology to politics to blockchain. This survey paper aims to provide an overview of some most popular approaches in statistical network community detection as well as the newly emerging research directions such as community extraction with higher‐order features and community discovery in multilayer and multiscale networks. Our goal is to offer a unified view at methodological interconnections and the wide spectrum of interdisciplinary data science applications of network community analysis.This article is categorized under: Data: Types and Structure > Graph and Network Data Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

Quantum adiabatic optimization has long been expected to outperform classical methods in solving NP -type problems. While this has been proven in certain experiments, its main applications still reside in academic problems where the size of the system to be solved would not represent an obstacle to any modern desktop computer. Here, we develop a systematic procedure to find the global optima of the modularity function to discover community structure in complex networks solely relying on pure annealers rather than hybrid solutions. We bypass the one-hot encoding constraints by hierarchically and recursively encoding binary instances of the problem that can be solved without the need to guess the exact penalties for the Lagrange multipliers. We study the variability and robustness of the annealing process as a function of network size, directness of connections, topology, and the resolution of the communities. We show how our approach produces meaningful and at least equally optimal solutions to state-of-the-art community detection algorithms while maintaining tractable and potentially scalable computing times. Lastly, due to its recursive nature, the annealing process returns intermediate subdivisions, thus offering interpretable rather than black-box solutions. These <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dendrograms</i> can be used to unveil normal and pathological hidden hierarchies in brain networks, hence opening the door to clinical workflows. Overall, this represents a first step towards an applicable practice-oriented usage of pure quantum annealing, potentially bridging two segregated communities in modern science and engineering: that of network science and quantum computing.

Complex networks have in generally communities. These communities are very important. Network’s communities represent sets of nodes, which are very connected. In this research, we developed a new method to find the community structure in networks. Our method is based on flower pollination algorithm (FPA) witch is used in the splitting process. The splitting of networks in our method maximizes a function of quality called modularity. We provide a general framework for implementing our new method to find community structure in networks. We present the effectiveness of our method by comparison with some known methods on computer-generated and real-world networks.

Detecting community structure in complex networks is an active area of research that locates dense regions of connections in networks. We suggest a novel algorithm for community detection using a new node-node association metric (based on Markov chains) and a team formation model.

Networks have become a widely used tool for modeling complex systems in many different fields. This approach is extremely useful for representing interactions among genes, social relationships, Internet communications or correlations of prices within a stock market, to name just a few examples. By analyzing the structure of these networks and understanding how their different elements interact, we could improve our knowledge of the whole system. Usually, nodes that compose these networks tend to create tightly knit groups. This property, of high interest in many scientific fields, is called community structure and improving its detection and characterization is what this thesis is all about. The first objective of this work is the generation of efficient methods able to characterize the communities of a network and to understand its structure. Second, we will try to create a set of tests where such methods can be studied. Finally, we will suggest a statistical measure in order to be able to properly assess the quality of the community structure of a network. To accomplish these objectives, first, we generate a set of algorithms that can transform a network into a hierarchical tree and, from there, to determine their most relevant communities. Furthermore, we have developed a new type of benchmarks for effectively testing these and other community detection algorithms. Finally, and as the most important contribution of this work, it is shown that the community structure of a network can be accurately evaluated using a hypergeometric distribution-based index. Thus, the maximization of this measure, called Surprise, appears as the best proposed strategy for detecting the optimal partition into communities of a network. Surprise exhibits an excellent behavior in all networks analyzed, qualitatively outperforming any previous method. Thus, it appears as the best measure proposed to this end and the data suggests that it could be an optimal strategy to determine the quality of the community structure of complex networks.

Community detection is a fundamental task in network analysis in that it can express the characteristics of individual behaviors and the relationships between individuals in complex networks, thus revealing the functional and structural properties of various networks. However, as networks become larger and larger, how to quickly and accurately detect the community structure of large-scale networks has become a huge challenge nowadays. In this paper, an efficient algorithm, called Local Search for Community Detection (LSCD), is proposed to solve the multi-objective community detection problem. In the algorithm, an iterated local search is performed to search for non-dominated solutions in the solution space. To search for higher quality non-dominated solutions, this paper employs a learning-based strategy to select nodes in each round of the search. The strategy learns from the historical movement of the nodes and changes their selection probability according to their importance. Moreover, to search the entire solution space, this paper proposes a local search strategy that restricts one objective with a bound for a certain round, as well as an adaptive bound update mechanism. Experimental results on synthetic and real-world networks show that the proposed algorithm outperforms several state-of-the-art algorithms in terms of multi-objective optimization performance and accuracy in detecting the community structure of complex networks, since it performs best on 44 instances out of 46 in terms of Modularity (Q) and 29 out of 39 in terms of Normalized Mutual Information (NMI). In addition, the results show that the proposed algorithm has a good ability to handle large-scale networks.

Identifying and evaluating community structure in complex networks

The significance of community structure in complex networks, such as social, biological, and online networks, has been widely recognized. Detecting communities in social media networks typically relies on two sources of information: the network’s topological structure and node attributes. Incorporating rich node content attribute information poses both flexibility and challenges for community detection. Traditional approaches either focus on mining one information source or linearly combining results from both sources, which fails to effectively fuse the information. This paper introduces a practical collaborative learning approach that explores the multi-dimensional attribute characteristics of nodes to facilitate community division. By leveraging graphical matrix decomposition, the proposed algorithm, CDGMF, improves the effectiveness and robustness of community detection. Experimental results demonstrate the method’s ability to effectively utilize node attribute information for guiding community detection, resulting in higher-quality community divisions.

Community structure in networks indicates some meaningful groups or organizations in the real world. Various algorithms to detect community in complex networks were proposed. However, problems about how to judge the goodness and performance of algorithms are still open. This paper reviewed and analyzed the related work and algorithms for community detection, hoping to benefit researchers in related field.

Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of a large interdisciplinary community of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed in order to better understand the impact of community structure and its dynamics on networked systems. Here, we first focus on generative models of communities in complex networks and their role in developing strong foundation for community detection algorithms. We discuss modularity and the use of modularity maximization as the basis for community detection. Then, we follow with an overview of the Stochastic Block Model and its different variants as well as inference of community structures from such models. Next, we focus on time evolving networks, where existing nodes and links can disappear, and in parallel new nodes and links may be introduced. The extraction of communities under such circumstances poses an interesting and non-trivial problem that has gained considerable interest over the last decade. We briefly discuss considerable advances made in this field recently. Finally, we focus on immunization strategies essential for targeting the influential spreaders of epidemics in modular networks. Their main goal is to select and immunize a small proportion of individuals from the whole network to control the diffusion process. Various strategies have emerged over the years suggesting different ways to immunize nodes in networks with overlapping and non-overlapping community structure. We first discuss stochastic strategies that require little or no information about the network topology at the expense of their performance. Then, we introduce deterministic strategies that have proven to be very efficient in controlling the epidemic outbreaks, but require complete knowledge of the network.

This paper presents an iterated tabu search (denoted by ITS) algorithm for optimizing the modularity of community structure in complex networks. The proposed algorithm follows a general framework composed of two phases: basic optimization and postrefinement. When the basic optimization cannot improve the modularity any more, a postrefinement procedure is employed to further optimize the objective function with a global view. For both these two phases, iterated tabu search algorithm is employed to optimize the objective function. Computational results show the high effectiveness of the proposed ITS algorithm compared with six state-of-the-art algorithms in the literature. In particular, our ITS algorithm improves the previous best known modularity for several small and medium size networks.

Nonnegative matrix factorization (NMF) has become a powerful model for community discovery in complex networks. Existing NMF-based methods for community discovery often factorize the corresponding adjacent matrix of complex networks to obtain its community indicator matrix. However, the adjacent matrix cannot represent the global structure feature of complex networks very well, and this leads to the performance degradation of community discovery. Besides, most of existing methods are not robust and scalable enough, so they are not effective to deal with complex networks with noises and large scales. Aiming at these problems above, in this paper we propose a method for community discovery using distributed robust NMF with SimRank similarity measure. This method selects SimRank measure to construct the feature matrix, which can more accurately represent the global structure feature of complex networks. To improve the robustness, we select $$\ell _{2,1}$$ norm instead of the widely used Frobenius norm to construct its NMF-based community discovery model. In addition, to improve the scalability, we implement its key components by using MapReduce distributed computing framework, including computing SimRank feature matrix and iteratively solving the NMF-based model for community discovery. We conduct extensive experiments on several typical complex networks. The results show that our method has better performance and robustness than other representative NMF-based methods for community discovery. Moreover, our method presents good scalability and hence can be used to discover communities in the large-scale complex networks.

Many complex systems can be represented as networks, and separating a network into communities could simplify functional analysis considerably. Many approaches have recently been proposed to detect communities, but a method to determine whether the detected communities are significant is still lacking. In this paper, an index to evaluate the significance of communities in networks is proposed based on perturbation of the network. In contrast to previous approaches, the network is disturbed gradually, and the index is defined by integrating all of the similarities between the community structures before and after perturbation. Moreover, by taking the null model into account, the index eliminates scale effects. Thus, it can evaluate and compare the significance of communities in different networks. The method has been tested in many artificial and real-world networks. The results show that the index is in fact independent of the size of the network and the number of communities. With this approach, clear communities are found to always exist in social networks, but significant communities cannot be found in protein interactions and metabolic networks.

The community structure of complex networks reveals hidden relationships in the organization of their constituent nodes. Indeed, many practical problems stemming from different fields of knowledge such as Biology, Sociology, Chemistry and Computer Science can be modeled as a graph. Therefore, graph analysis and community detection have become a key component for understanding the inherent relational characteristics underlying different systems and processes. In this regard, distinct unsupervised quality metrics such as conductance, coverage and modularity, have upsurged in order to evaluate the clustering arrangements based on structural and topological characteristics of the cluster space. In this regard graph clustering can be formulated as an optimization problem based on the maximization of one of such metrics, for which a number of nature-inspired heuristic solvers has been proposed in the literature. This paper elaborates on a novel local search method that allows boosting the convergence of such heuristics by estimating and sampling the cluster arrangement distribution from the set of intermediate produced solutions of the algorithm at hand. Simulation results reveal a generalized better performance compared towards other community detection algorithms in synthetic and real datasets.