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China has extensively implemented the Joint Prevention and Control of Atmospheric Pollution (JPCAP) strategy to address regional air pollution challenges; however, the lack of accurate scope and regional priority control sequence has resulted in reduced pollution control efficiency and high air quality improvement costs. We proposed the following new solutions to these problems: (i) constructing inter-regional network correlation models based on three key network topology parameters and (ii) subdividing large regions into sub-regions using the Girvan Newman (GN) algorithm. To test these methods, we applied them to a case study of China's provincial-level JPCAP areas using hourly air resource endowment (ARE) data obtained from 2013 to 2017. We found that the modularity (Q) values of ARE network partitioning in different seasons were approximately 0.5, indicating the well-structured association of the network constructed in this study. Seven areas were identified based on annual values, while eight, five, four, and six areas were classified for spring, summer, autumn, and winter, respectively. The strength of the interconnectedness of the provinces in the region, as measured by the clustering coefficient ( C ˜ ) value, is ordered as follows: Autumn > winter > spring > summer. For a specific JPCAP region, the priority control level can be dynamically adjusted based on the Pearson correlation coefficient (r-value) between the target city or province and the surrounding region. The regional division results, priority control sequences, and key control seasons identified in this study can provide technical and methodological reference for delineating and optimizing China's JPCAP policy.

A Self-Contained Girvan-Newman Algorithm and Mean Variance Model combined approach is proposed to allocate the defense resource in road dangerous goods transportation network. Firstly, the weighted physical network without direction and its weighted service network with direction are established. The Self-Contained Girvan-Newman Algorithm is applied to separate the whole weighted physical network into several communities. Next, based on the service network, the covariance matrix of each separated community is established, the Mean Variance Model is used to allocate the defense resource for each community, which focuses on selecting the option with the lowest probability of loss caused by the dangerous goods transportation accident/risk. The case study is conducted by using the road network and the dangerous goods transportation volume of Dalian, China as the background. When the whole network is separated into 6 communities, the defense resource capability in the whole network is the best. The Power Function Allocation Model (PFAM) is applied as the comparison approach, the overall rescue capability of the network is defined and applied to evaluate the defense resource allocation schemes. The results show that, the approach proposed in this paper has better effectiveness than PFAM, especially when the whole network is separated into 6 communities.

The discovery and analysis of community structure in complex networks is a hot issue in recent years. In this paper, based on the fast greedy clustering algorithm CNM with the thought of local search, the introduction of the idea of node centrality and the optimal division of the central nodes and their neighbor nodes into correct communities, a new algorithm CNM-Centrality of detecting communities in complex networks is proposed. In order to verify the accuracy and efficiency of this algorithm, the performance of this algorithm is tested on several representative real-world networks and a set of computer-generated networks by LFR-benchmark. The experimental results indicate that this algorithm can identify the communities accurately and efficiently. Furthermore, this algorithm can also acquire higher values of modularity and NMI than the CNM, Infomap, Walktrap algorithms do.

Most of the real-world networks exhibit community structure, a property that reveals the existence of natural vertex clusters whose inter-edge density is lower than intra-edge density between various groups. Despite providing a better understanding of network structure and characteristics, community detection has many practical applications in diverse domains. Communities obtained from the telephone network provides many useful information that can be used for churn prediction, budget control in organizations etc. Detecting communities is a fundamental need in the area of networks, yet challenging. In this paper, we propose an extension to the Girvan-Newman algorithm for finding the betweenness using the transitive closure property and the greedy technique in Dijkstra's single source shortest path method.

Devise an algorithm for updating betweenness centrality in fully dynamic graphs.Recalculate centrality without computing all pairs shortest paths in the entire graph.Adapt a highest centrality edge finding algorithm based on the proposed algorithm.Adapt a community detection algorithm using the proposed algorithms.Experimental results show the proposed algorithm outperforms existing algorithms. Betweenness centrality of a vertex (edge) in a graph is a measure for the relative participation of the vertex (edge) in the shortest paths in the graph. Betweenness centrality is widely used in various areas such as biology, transportation, and social networks. In this paper, we study the update problem of betweenness centrality in fully dynamic graphs. The proposed update algorithm substantially reduces the number of shortest paths which should be re-computed when a graph is changed. In addition, we adapt a community detection algorithm using the proposed algorithm to show how much benefit can be obtained from the proposed algorithm in a practical application. Experimental results on real graphs show that the proposed algorithm efficiently update betweenness centrality and detect communities in a graph.

Understanding and detecting natural communities in networks have been a fundamental challenge in networks, and in science generally. Recently, we proposed a hypothesis that homophyly/kinship is the principle of natural communities based on real network experiments, proposed a model of networks to explore the principle of natural selection in nature evolving, and proposed the measure of structure entropy of networks. Here we proposed a community finding algorithm by our measure of structure entropy of networks. We found that our community finding algorithm exactly identifies almost all natural communities of networks generated by natural selection, if any, and that the algorithm exactly identifies or precisely approximates almost all the communities planted in the networks of the existing models. We verified that our algorithm identifies or very well approximates the ground-truth communities of some real world networks, if the ground-truth communities are semantically well-defined, that our algorithm naturally finds the balanced communities, and that the communities found by our algorithm may have larger modularity than that by the algorithms based on modularity, for some networks. Our algorithm provides for the first time an approach to detecting and analyzing natural or true communities in real world networks. Our results demonstrate that structure entropy minimization is the principle of detecting the natural or true communities in large-scale networks.

Community detection in the social networks is one of the most important tasks of social computing. Highly relevant researches indicate that the social network generally contains both an overlapping and hierarchical structure. This paper introduces an efficient and functional community detection algorithm MOHCC, which can concurrently discover overlapping and hierarchical organization in complex networks. This algorithm first extracts all maximal cliques from the original complex network. Merges all extracted maximal cliques into a dendrogram by using the aggregative framework presented in MOHCC. Finally, it cuts through the dendrogram and obtains a network partition with maximum extended partition density. Experimental results utilizing computer-generated artificial networks and real-world social benchmark networks give satisfactory correspondence.

The determination of community structures within social networks is a significant problem in the area of data mining. A proper community is usually defined as a subgraph with a higher internal density and a lower crossing density with others subgraphs. Hierarchical clustering algorithms produce a set of nested clusters, sometimes called dense subgraphs, organized as a hierarchical system and the output is always referred as a dendrogram. However, determining which of clusters in the dendrogram will be selected to form communities in the final output is a difficult problem. Most implementations of data mining algorithms require expert guidance in the implementation of the algorithm in order to establish the appropriate selection of such communities, and ultimately the output may not be optimized as with fixed height tree-cutting algorithms. In this paper, a novel algorithm for community selection is proposed. The intuition of our approach is based on drops of densities between each pair of parent and child nodes on the dendrogram - the higher the drop in density, the higher probability the child should form an independent community. Based on the Max-Flow Min-Cut theorem, we propose a novel algorithm which can output an optimal set of local communities automatically. In addition, a faster algorithm running in linear time is also presented for the case that the dendrogram is a tree. Finally, we validate this approach through a variety of data sets ranging from synthetic graphs to real world benchmark data sets.

There is a surge of community detection study on complex network analysis in recent years, since communities often play important roles in network systems. However, many real networks have more complex overlapping community structures. This paper proposes a novel algorithm to discover overlapping communities. Different from conventional algorithms based on node clustering, the proposed algorithm is based on link clustering. Since links usually represent unique relations among nodes, the link clustering will discover groups of links that have the same characteristics. Thus nodes naturally belong to multiple communities. The algorithm applies genetic operation to cluster on links. An effective 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 proposed algorithm.

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.

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.

Identification of communities is significant in understanding the structures and functions of networks. Since some nodes naturally belong to several communities, the study of overlapping communities has attracted increasing attention recently, and many algorithms have been designed to detect overlapping communities. In this paper, an overlapping communities detecting algorithm is proposed whose main strategies are finding an initial partial community from a node with maximal node strength and adding tight nodes to expand the partial community. Seven real-world complex networks and one synthetic network are used to evaluate the algorithm. Experimental results demonstrate that the algorithm proposed is efficient for detecting overlapping communities in weighted 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 communities in complex networks is of considerable importance for understanding both the structure and function of the networks. Here, we propose a class of improved algorithms for community detection, by combining the betweenness algorithm of Girvan and Newman with the edge weight defined by the edge-clustering coefficient. The improved algorithms are tested on some artificial and real-world networks, and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases. In addition, the technique for improving the betweenness algorithm in this paper, thanks to its compatibility, can directly be applied to various detection algorithms.