Identifying and evaluating community structure in complex networks

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.

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.

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.

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.

In recent years, community structure has emerged as a key component of complex network analysis. As more data have been collected, researchers have begun investigating changing community structure across multiple networks. Several methods exist to analyze changing communities, but most of these are limited to evolution of a single network over time. In addition, most of the existing methods are more concerned with change at the community level than at the level of the individual node. In this paper, we introduce scaled inclusivity, which is a method to quantify the change in community structure across networks. Scaled inclusivity evaluates the consistency of the classification of every node in a network independently. In addition, the method can be applied cross sectionally as well as longitudinally. In this paper, we calculate the scaled inclusivity for a set of simulated networks of United States cities and a set of real networks consisting of teams that play in the top division of American college football. We found that scaled inclusivity yields reasonable results for the consistency of individual nodes in both sets of networks. We propose that scaled inclusivity may provide a useful way to quantify the change in a network's community structure.

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.

Detecting quality community structures in complex networks is an important and highly active research area. Plenty of methods have been proposed for community detection in recent years. Among them, Genetic Algorithms (GAs) have been widely explored for community detection due to their strong competence at exploring the global discrete search space. However, existing GA algorithms for community detection still face major challenges when handling large and complex networks due to their use of random mutation operators. Whenever any candidate community structure in a GA population is mutated, a mutated node of the network under processing is often associated to a community with loose connections, seriously hurting GA’s effectiveness and scalability. To address this issue, a newly designed Leiden-based GA (LGA) with a novel mutation operator based on the Leiden algorithm is proposed in this paper to improve the effectiveness of the mutation operator and the performance of the GA approach. Experiment results clearly show that LGA can achieve highly competitive performance in comparison to several state-of-the-art GA and non-GA community detection algorithms on multiple synthetic and real-world networks.KeywordsCommunity detectionLeiden algorithmGenetic algorithm

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.

A wireless sensor network (WSN) is a large collection of sensor nodes with limited power supply and constrained computational capability. Clustering routing method in wireless sensor networks has been considered as an important field of research recently to prolong the network lifetime of WSNs. We present a novel clustering method that can balance the energy consumption and extend the lifetime of WSN. Network nodes can be divided into densely connected subgroups through the algorithm of detecting community structure in complex networks. Moreover, the role of cluster-head is scheduled among the cluster members according to the residual energy of nodes, and then the cluster heads send the data to the sink directly. Based on the community clustering strategy, a novel routing protocol, called community structure clustering routing protocol (CSCR), has been raised for WSN. Performance evaluation has shown that the proposed method can achieve improvement compared with LEACH and SEP.

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.

When studying dynamic networks, it is often of interest to understand how the community structure of the network changes. However, before studying the community structure of dynamic social networks, one must first collect appropriate network data. In this paper we present a network sampling technique to crawl the community structure of dynamic networks when there is a limitation on the number of nodes that can be queried. The process begins by obtaining a sample for the first time step. In subsequent time steps, the crawling process is guided by community structure discoveries made in the past. Experiments conducted on the proposed approach and certain baseline techniques reveal the proposed approach has at least 35% performance increase in cases when the total query budget is fixed over the entire period and at least 8% increase in cases when the query budget is fixed per time step.

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

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.

The main problem on community detection using traditional genetic algorithms (GA) lies in the slow speed of convergence. This paper attempts to apply parallel genetic algorithms (PGA) to explore community structure in complex networks in order to improve the efficiency of traditional genetic algorithms. Several different designing ways of PGA are discussed and compared. Experimental results based on the GN benchmark networks, LFR benchmark networks, and eight real-world networks, confirm the PGA with coarse-grained-master-slave hybrid model spends less time yet achieves higher accuracy than traditional genetic algorithms.

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.