Extension of Modularity Density for overlapping community structure

Community structure is one of the most important properties in networks, and community detection has received an enormous amount of attention in recent years. Modularity is by far the most used and best known quality function for measuring the quality of a partition of a network, and many community detection algorithms are developed to optimize it. However, there is a resolution limit problem in modularity optimization methods. In this study, a memetic algorithm, named Meme-Net, is proposed to optimize another quality function, modularity density, which includes a tunable parameter that allows one to explore the network at different resolutions. Our proposed algorithm is a synergy of a genetic algorithm with a hill-climbing strategy as the local search procedure. Experiments on computer-generated and real-world networks show the effectiveness and the multiresolution ability of the proposed method.

Many real-world complex networks exhibit a community structure, in which the modules correspond to actual functional units. Identifying these communities is a key challenge for scientists. A common approach is to search for the network partition that maximizes a quality function. Here, we present a detailed analysis of a recently proposed function, namely modularity density. We show that it does not incur in the drawbacks suffered by traditional modularity, and that it can identify networks without ground-truth community structure, deriving its analytical dependence on link density in generic random graphs. In addition, we show that modularity density allows an easy comparison between networks of different sizes, and we also present some limitations that methods based on modularity density may suffer from. Finally, we introduce an efficient, quadratic community detection algorithm based on modularity density maximization, validating its accuracy against theoretical predictions and on a set of benchmark networks.

With the rapid increase in popularity of online social networks, community detection in these networks has become a key aspect of research field. Overlapping community detection is an important NP-hard problem of social network analysis. Modularity-based community detection is one of the most widely used approaches for social network analysis. However, modularity-based community detection technique may fail to resolve small-size communities. Hence, we propose a novel two-step approach for overlapping community detection in social networks. In the first step, modularity density-based hybrid meta-heuristics approach is used to find the disjoint communities and the quality of these disjoint communities can be verified using Silhouette coefficient. In the second step, the quality disjoint communities with low computation cost are used to detect overlapping nodes based on Min-Max Ratio of minimum(indegree, outdegree) to the maximum(indegree, outdegree) values of nodes. We tested the proposed algorithm based on 10 standard community quality metrics along with Silhouette score using seven standard datasets. Experimental results demonstrate that the proposed approach outperforms the current state-of-the-art works in terms of quality and scalability.

Community detection is one of the primary tools to discover useful information that is hidden in complex networks. Some community detection algorithms for bipartite networks have been proposed from various viewpoints. However, the performance of these algorithms deteriorates when the community structure becomes unclear. Enhancing community structure remains a nontrivial task. In this paper, we propose a community detection algorithm, called ECD, that enhances community structure in bipartite networks. In the proposed ECD, the topology of a network is modified by reducing unnecessary edges that are connected to neighboring low-weight communities. Therefore, an ambiguous community structure is converted into a structure that is much clearer than the original structure. The experimental results on both artificial and real-world networks verify the accuracy and reliability of our algorithm. Compared with existing community detection algorithms using state-of-the-art methods, our algorithm has better performance.

Detecting communities in complex networks using triangles and modularity density

With the development of network technology and the continuous advancement of society, the combination of various industries and the Internet has produced many large-scale complex networks. A common feature of complex networks is the community structure, which divides the network into clusters with tight internal connections and loose external connections. The community structure reveals the important structure and topological characteristics of the network. The detection of the community structure plays an important role in social network analysis and information recommendation. Therefore, based on the relevant theory of complex networks, this paper introduces several common community detection algorithms, analyzes the principles of particle swarm optimization (PSO) and genetic algorithm and proposes a particle swarm-genetic algorithm based on the hybrid algorithm strategy. According to the test function, the single and the proposed algorithm are tested, respectively. The results show that the algorithm can maintain the good local search performance of the particle swarm optimization algorithm and also utilizes the good global search ability of the genetic algorithm (GA) and has good algorithm performance. Experiments on each community detection algorithm on real network and artificially generated network data sets show that the particle swarm-genetic algorithm has better efficiency in large-scale complex real networks or artificially generated networks.

The role of influential nodes and their influence domain in community detection: An approximate method for maximizing modularity

There are currently many approaches to identify the community structure of a network, but relatively few specific to detect overlapping community structures. Likewise, there are few networks with ground truth overlapping nodes. For this reason,we introduce a new network, Pilgrim, with known overlapping nodes, and a new genetic algorithm for detecting such nodes. Pilgrim is comprised of a variety of structures including two communities with dense overlap,which is common in real social structures. This study initially explores the potential of the community detection algorithm LabelRank for consistent overlap detection; however, the deterministic nature of this algorithm restricts it to very few candidate solutions. Therefore, we propose a genetic algorithm using a restricted edge-based clustering technique to detect overlapping communities by maximizing an efficient overlapping modularity function. The proposed restriction to the edge-based representation precludes the possibility of disjoint communities, thereby, dramatically reducing the search space and decreasing the number of generations required to produce an optimal solution. A tunable parameterr allows the strictness of the definition of overlap to be adjusted allowing for refinement in the number of identified overlapping nodes. Our method, tested on several real social networks, yields results comparable to the most effective overlapping community detection algorithms to date.

Community detection has become a very important part in complex networks analysis. Authors traditionally test their algorithms on a few real or artificial networks. Testing on real networks is necessary, but also limited: the considered real networks are usually small, the actual underlying communities are generally not defined objectively, and it is not possible to control their properties. Generating artificial networks makes it possible to overcome these limitations. Until recently though, most works used variations of the classic Erdős-Rényi random model and consequently suffered from the same flaws, generating networks not realistic enough. In this work, we use Lancichinetti et al. model, which is able to generate networks with controlled power-law degree and community distributions, to test some community detection algorithms. We analyze the properties of the generated networks and use the normalized mutual information measure to assess the quality of the results and compare the considered algorithms.

To unravel the driving patterns of networks, the most popular models rely on community detection algorithms. However, these approaches are generally unable to reproduce the structural features of the network. Therefore, attempts are always made to develop models that incorporate these network properties beside the community structure. In this article, we present a probabilistic generative model and an efficient algorithm to both perform community detection and capture reciprocity in networks. Our approach jointly models pairs of edges with exact two-edge joint distributions. In addition, it provides closed-form analytical expressions for both marginal and conditional distributions. We validate our model on synthetic data in recovering communities, edge prediction tasks and generating synthetic networks that replicate the reciprocity values observed in real networks. We also highlight these findings on two real datasets that are relevant for social scientists and behavioural ecologists. Our method overcomes the limitations of both standard algorithms and recent models that incorporate reciprocity through a pseudo-likelihood approximation. The inference of the model parameters is implemented by the efficient and scalable expectation–maximization algorithm, as it exploits the sparsity of the dataset. We provide an open-source implementation of the code online.

Overlapping community is a phenomenon often observed in numerous real-world networks. Fire-spread (Pattanayak et al. in Swarm Evol Comput. 44: 1–48 (2019) [11]) community detection algorithm is an efficient algorithm to detect overlapping community structures. In this work, the Fire-spread algorithm is modified to establish a relationship between community structure and clustering coefficient. By using different networks and executing the modified Fire-spread algorithm, it is found that the clustering coefficient is highly correlated with community structure. Finally, a simpler community detection algorithm, derived from the fire-spread algorithm, is proposed, where the clustering coefficient is used as a threshold value. To validate the proposed algorithm, it is compared with some state of art community detection algorithms based on the NMI score.

This thesis focuses on the pressing issue of illicit drug trafficking and its impact on public health and safety at a global level. With the advent of digital technologies and social media platforms, combating drug trafficking has become increasingly challenging for law enforcement and researchers alike. Among these platforms, Instagram, a popular photo and video-sharing social networking platform, has emerged as a prominent hub for drug trafficking activities. In this study, we delve into the effectiveness of community and key player detection algorithms in identifying and disrupting illicit drug supply networks on Instagram. To conduct our research, we collected real Instagram data spanning from June to August 2022. We examined several community detection algorithms, including Louvain, Newman-Girvan, Infomap, Label Propagation, and Hierarchical Clustering. Additionally, we explored key player algorithms, namely CDKPE, TopRank, K-core, and KPEI, the latter being a novel algorithm introduced in this study. Our objective was to assess the performance of these algorithms in accurately identifying and targeting drug trafficking networks. Our findings reveal that the Louvain and Newman-Girvan algorithms outperformed others in terms of community detection, demonstrating their effectiveness in identifying cohesive groups involved in drug trafficking on Instagram. In terms of key player detection, the CDKPE and KPEI algorithms emerged as the most effective, highlighting the individuals who play pivotal roles within these networks. These algorithms offer practical applications for law enforcement agencies seeking to disrupt drug trafficking operations on Instagram. By emphasizing the importance of leveraging advanced analytical tools, our study underscores the significance of combating drug trafficking on social media platforms.

Association rules are widely used to extract patterns from a given database. The association rules are capable of finding correlations among items, making it possible for the user to learn which items are present in the transactions and which of them have a significant correlation. One of the major problems with association rules is that the number of extracted rules usually exceeds the number of transactions present in the database, also surpassing the user’s capability to explore the obtained knowledge. To overcome this problem, the post-processing phase was proposed with the objective of directing the user to the rules that potentially have the most interesting knowledge. One of the used approaches is to divide the association rules into groups (or clusters), so that rules behave similarly are on the same group, facilitating the rule set understanding. In the literature, there are some works that uses clustering algorithms to split the rules while some other works use community detection algorithms. As both approaches obtain groups of association rules, but using different premises, different results can be obtained. No study has been done on the differences among clustering and community detection algorithms, which makes the selection of the algorithm hard, once their behavior is not well known in the association rule post-processing phase. This paper presents an analysis on both approaches, aiming to find the differences and the similarities among them, making it easier to select an approach by knowing its behavior.

The complexity of many community detection algorithms is usually an exponential function with the scale which hard to uncover community structure with high speed. Inspired by the ideas of the famous modularity optimization, in this paper, we proposed a proper weighting scheme utilizing a novel k-strength relationship which naturally represents the coupling distance between two nodes. Community structure detection using a generalized weighted modularity measure is refined based on the weighted k-strength matrix. We apply our algorithm on both the famous benchmark network and the real networks. Theoretical analysis and experiments show that the weighted algorithm can uncover communities fast and accurately and can be easily extended to large-scale real networks.

Complex networks are composed of nodes and complex relationships between nodes, which are the abstraction of various complex systems in the real world. Community structure is a remarkable characteristic of complex networks.Community detection algorithms can reveal the topological structure of the networks and mine the potential information in complex networks, which can be widely used in personalized recommendation, public security, social science and other fields, and has important research significance. The community detection algorithm based on seeds extension is a classic community detection algorithm, which has high execution efficiency, but there are some problems. Aiming at the problems of poor seed nodes selection and improper community expansion method of seeds expansion algorithm, this paper proposes a seed expansion algorithm based on CRITIC method and node gravity which is called SECNG. The contributions of the algorithm are as follows: At first, we introduced CRITIC method to measure the importance of nodes, which can objectively measure the importance of nodes in the networks. Secondly, we propose node gravity and community gravity to guide the expansion of communities. In addition, modularity maximization strategy is used to merge communities. We verify the effectiveness of the SECNG algorithm through the real networks and artificial generated networks. The results show that the Q value and NMI values of the algorithm are higher than other algorithms.