Quantifying the resilience of community structures in 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.

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 evaluating community structure in complex networks

Identifying meaningful cancer driver genes in a cohort of tumors is a challenging task in cancer genomics. Although existing studies have identified known cancer drivers, most of them focus on detecting coding drivers with mutations. It is acknowledged that non-coding drivers can regulate driver mutations to promote cancer growth. In this work, we propose a novel node importance-based network analysis (NIBNA) framework to detect coding and non-coding cancer drivers. We hypothesize that cancer drivers are crucial to the formation of community structures in cancer network, and removing them from the network greatly perturbs the network structure thereby critically affecting the functioning of the network. NIBNA detects cancer drivers using a three-step process: first, a condition-specific network is built by incorporating gene expression data and gene networks; second, the community structures in the network are estimated; and third, a centrality-based metric is applied to compute node importance. We apply NIBNA to the BRCA dataset, and it outperforms existing state-of-art methods in detecting coding cancer drivers. NIBNA also predicts 265 miRNA drivers, and majority of these drivers have been validated in literature. Further we apply NIBNA to detect cancer subtype-specific drivers, and several predicted drivers have been validated to be associated with cancer subtypes. Lastly, we evaluate NIBNA's performance in detecting epithelial-mesenchymal transition drivers, and we confirmed 8 coding and 13 miRNA drivers in the list of known genes. The source code can be accessed at https://github.com/mandarsc/NIBNA. Supplementary data are available at Bioinformatics online.

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.

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.

Community structures are inherent in social networks and finding them is an interesting and well-studied problem. Finding community structures in social networks is similar to locating densely connected clusters of nodes in a graph. One of the popular methods for finding communities is to first find the inter-community edges and then removing them to reveal the communities. It is well-known that a network centrality measure named edge betweenness can be used to detect the inter-community edges. The edges with high edge betweenness are those that fall in a large number of shortest paths out of all possible pairs of shortest paths. Finding all-pair shortest paths is a computationally expensive task, especially for large-sized graphs. So we construct a t-spanner, a known graph sparsification technique, for finding edges with high betweenness and eventually find communities by removing such edges. Using the t-spanner, we then detect the inter-community edges in O(km) running time by building a distance oracle of size O(kn1+1/k), where t = 2k-1. Compared to the traditional community detection methods dependent on calculation of betweenness values, our algorithm runs much faster. Experiments show that our algorithm finds communities of quality comparable to the other state-of-the-art community detection algorithms.

As an open issue, the measure of community influential is no uniform standard, how to measure the influence of community has attracted extensive attention. This paper proposed a quantitative measure to identify the influence of community. Based on the state of critical functionality (SCF), a new function, which names as the weighted state of critical functionality (WSCF), is defined. For the WSCF, not only the connections among communities but also the topology within community is considered. When the community structure of the complex network is divided, each community is renormalized as a node by the renormalization method. Then, the influence of community is measured by the values of WSCF, the greater the value of WSCF, the less the influence of the corresponding community. The influence of community of three classic constructed networks (i.e., a Erodös-Rényi (ER) random network, a BA scale free network and a small-word (SW) network) is measured by the proposed method. To further verify the feasibility of the method, two community detection algorithms are used to divide community structure in the real networks. The influence of the community of the 9/11 terrorist network, a US Air network and a PolBooks network is measured by the proposed method. The influence of each community could be measured and the most influential community in each network is identified by the proposed method. The results reveal that the proposed method is a feasible measure to identify the influence of community, its recognition effect is better than SCF, and accuracy is higher. The SCF is a special case of WSCF, when the weights and cluster coefficients are equal to 1. For the proposed method, once the community structure of the network is divided, the corresponding community influence is identified by the proposed method, which is not affected by the community division algorithms.

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

Community detection via closure extension

In this work a brief overview of several existing approaches to find community structure and their comparison has been done. The best suited algorithm is selected on various grounds such as space and time complexities but sometimes they are not the only factors to decide whether the algorithm is perfect or not. So many factors are responsible for choosing the algorithm which are uncertain. So which algorithm is the best is still an open question? However various changes are suggested to the approaches to optimize them from time to time. Among various community structure, social network, ecological network and neural network are the most popular and currently it is being implemented on several social networking websites like twitter, LinkedIn, Face book, Amazon etc.

The popularity of social networks has grown manifolds in recent years because of various activities like fast propagation of ideas, publicity, and news. Influence maximization (IM) is one of the most highly studied problems in the field of social network analysis due to its business values. Influence maximization aims to identify influential nodes that can spread the information to the maximum number of nodes in the network through diffusion cascade. Traditional methods for IM include centrality based and greedy based measures. However, each method has some limitations. Recently, some methods of IM are introduced, which consider the presence of community structure in networks. Community structure has a significant impact on information diffusion, because of dense connections between the nodes in the community. In this paper, we propose a novel influence maximization algorithm using node seeding, label propagation, and community detection. We first use extended h-index centrality to detect the seed nodes and then use the label propagation technique to detect communities. Further, we merge smaller and related communities to a larger community with the help of a relationship matrix. Finally, top-k influential nodes from these communities are identified. These ideas lead to our proposed algorithm: Influence Maximization using Extended h-index, and Label Propagation with Relationship matrix (IM-ELPR). We adopt Independent Cascade (IC) information diffusion model to spread the information originating from chosen influential nodes. The proposed algorithm intends to identify influential nodes from different communities globally and does not depend on the specific community’s antecedent structural information. Experimental results performed on several real-life data sets reveal that the proposed algorithm performs better than many other existing popular algorithms.

Recently, several social network analysis algorithms have been optimized by leveraging the community structure commonly found in graphs. Since community structure is fun-damental to these algorithms, storing graphs based on their community structure can significantly enhance the performance of graph algorithms that rely on it for optimization. However, existing graph storage systems do not natively store graphs according to the community structure, which limits their per-formance in retrieving communities. To fill this gap, we pro-pose LSM-Community, a graph storage system inspired by the LSM - Tree design that stores graphs on disk based on their community structure. To dynamically maintain the community structure during graph updates, we present the community-centric dynamic community detection algorithm <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(C^{3}D)$</tex>. Experimental results demonstrate that LSM-Community outperforms other storage systems in classical community discovery tasks (e.g., performing CD on UK-2007 dataset with LSM-Community is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$86.12\times$</tex> faster than Neo4j) while maintaining high performance on classical graph analytic algorithms. This indicates that LSM-Community efficiently supports community discovery and query processing while preserving the performance of classical analytic algorithms,

This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where nodes in the network core are seen to be essential in terms of network flow and global structure. Additionally, the connected components in the periphery give information about the community structure of the network, aiding in community detection. A number of explicit results are derived, relating the core and periphery to network flow, community structure, and global network structure, which are corroborated by observational results. The method is illustrated using a real world network (DBLP co-authorship network), with ground-truth communities.

Network analysis involves using graph theory to understand networks. This knowledge is valuable across various disciplines like marketing, management, epidemiology, homeland security, and psychology. An essential task within network analysis is deciphering the structure of complex networks including technological, informational, biological, and social networks. Understanding this structure is crucial for comprehending network performance and organization, shedding light on their underlying structure and potential functions. Community structure detection aims to identify clusters of nodes with high internal link density and low external link density. While there has been extensive research on community structure detection in single‐layer networks, the development of methods for detecting community structure in multilayer networks is still in its nascent stages. In this paper, a new method, namely, IGA‐MCD, has been proposed to tackle the problem of community structure detection in multiplex networks. IGA‐MCD consists of two general phases: flattening and community structure detection. In the flattening phase, the input multiplex network is converted to a weighted monoplex network. In the community structure detection phase, the community structure of the resulting weighted monoplex network is determined using the Improved Genetic Algorithm (IGA). The main aspects that differentiate IGA from other algorithms presented in the literature are as follows: (a) instead of randomly generating the initial population, it is smartly generated using the concept of diffusion. This makes the algorithm converge faster. (b) A dedicated local search is employed at the end of each cycle of the algorithm. This causes the algorithm to come up with better new solutions around the currently found solutions. (c) In the algorithm process, chaotic numbers are used instead of random numbers. This ensures that the diversity of the population is preserved, and the algorithm does not get stuck in the local optimum. Experiments on the various benchmark networks indicate that IGA‐MCD outperforms state‐of‐the‐art algorithms.