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Community detection recognizes groups of densely connected nodes across networks, one of the fundamental procedures in network analysis. This research boosts the standard but locally optimized Greedy Modularity algorithm for community detection. We introduce innovative exploration techniques that include a variety of node and community disassembly strategies. These strategies include methods like non-triad creating, feeble, random as well as inadequate embeddedness for nodes, as well as low internal edge density, low triad participation ratio, weak, low conductance as well as random tactics for communities. We present a methodology that showcases the improvement in modularity across the wide variety of real-world and synthetic networks over the standard approaches. A detailed comparison against other well-known community detection algorithms further illustrates the better performance of our improved method. This study not only optimizes the process of community detection but also broadens the scope for a more nuanced and effective network analysis that may pave the way for more insights as to the dynamism and structures of its functioning by effectively addressing and overcoming the limitations that are inherently attached with the existing community detection algorithms.

NOABSTRACTThis study focuses on understanding the collaboration relationships among mathematicians, particularly those esteemed as elites, to reveal the structures of their communities and evaluate their impact on the field of mathematics.Two community detection algorithms, namely Greedy Modularity Maximization and Infomap, are utilized to examine collaboration patterns among mathematicians. We conduct a comparative analysis of mathematicians’ centrality, emphasizing the influence of award-winning individuals in connecting network roles such as Betweenness, Closeness, and Harmonic centrality. Additionally, we investigate the distribution of elite mathematicians across communities and their relationships within different mathematical sub-fields.The study identifies the substantial influence exerted by award-winning mathematicians in connecting network roles. The elite distribution across the network is uneven, with a concentration within specific communities rather than being evenly dispersed. Secondly, the research identifies a positive correlation between distinct mathematical sub-fields and the communities, indicating collaborative tendencies among scientists engaged in related domains. Lastly, the study suggests that reduced research diversity within a community might lead to a higher concentration of elite scientists within that specific community.The study’s limitations include its narrow focus on mathematicians, which may limit the applicability of the findings to broader scientific fields. Issues with manually collected data affect the reliability of conclusions about collaborative networks.This study offers valuable insights into how elite mathematicians collaborate and how knowledge is disseminated within mathematical circles. Understanding these collaborative behaviors could aid in fostering better collaboration strategies among mathematicians and institutions, potentially enhancing scientific progress in mathematics.The study adds value to understanding collaborative dynamics within the realm of mathematics, offering a unique angle for further exploration and research.

Community detection is crucial for understanding the structure and function of biological, social, and technological systems. This paper presents a novel algorithm, fast local move iterated greedy (FLMIG), which enhances the Louvain Prune heuristic using an iterated greedy (IG) framework to maximize modularity in non-overlapping communities. FLMIG combines efficient local optimization from the fast local move heuristic with iterative refinement through destruction and reconstruction phases. A key refinement step ensures that detected communities remain internally connected, addressing limitations of previous methods. The algorithm is scalable, parameter-light, and performs efficiently on large networks. Comparative evaluations against state-of-the-art methods, such as Leiden, iterated carousel greedy, and Louvain Prune algorithms, show that FLMIG delivers statistically comparable results with lower computational complexity. Extensive experiments on synthetic and real-world networks confirm FLMIG’s ability to detect high-quality communities while maintaining robust performance across various network sizes, particularly improving modularity and execution time in large-scale networks.

Large scale software systems must be decomposed into modular units to reduce maintenance efforts. Software Architecture Recovery (SAR) approaches have been introduced to analyze dependencies among software modules and automatically cluster them to achieve high modularity. These approaches employ various types of algorithms for clustering software modules. In this paper, we discuss design decisions and variations in existing genetic algorithms devised for SAR. We present a novel hybrid genetic algorithm that introduces three major differences with respect to these algorithms. First, it employs a greedy heuristic algorithm to automatically determine the number of clusters and enrich the initial population that is generated randomly. Second, it uses a different solution representation that facilitates an arithmetic crossover operator. Third, it is hybridized with a heuristic that improves solutions in each iteration. We present an empirical evaluation with seven real systems as experimental objects. We compare the effectiveness of our algorithm with respect to a baseline and state-of-the-art hybrid genetic algorithms. Our algorithm outperforms others in maximizing the modularity of the obtained clusters.

Community structure is one of the most important properties in complex networks. Detecting such communities plays an important role in a wide range of applications such as information sharing and diffusion, recommendation, and classification. In this paper, we propose a novel iterated greedy algorithm for detecting communities in complex networks. The algorithm is based on an iterative process that combines a destruction phase and a reconstruction phase. During the destruction phase, the algorithm destructs community indexes of a certain percent nodes having lower modularity contribution. In the reconstruction phase, their community indexes are reconstructed using the well-known Louvain construction heuristic. A local search procedure can be applied after the reconstruction phase to improve the performance of the algorithm. Experiments on the computer-generated networks and real-world networks show that our algorithm is very efficient and competitive compared with several state-of-the-art methods.

In order to improve the precision of modularity optimization and community detection, this paper presented a complex network community detection algorithm based on cross learning among individuals of population combining greedy search. Individuals' codes indicated community partition. Individuals comparatively studied with each other to spread good genes and optimize modularity fast. Besides, aiming at improving the algorithm, the best communities, where some randomly selected nodes will move in, would be found by using greedy search maximizing the local modularity increment. The algorithm was tested on artificial networks and some typical real networks, compared with some typical algorithms. The results show that algorithm can get convergence quickly, achieve better modularity value, and finely detect and identify community structures.

Deep learning of artificial neural networks (ANNs) is creating highly functional processes that are, unfortunately, nearly as hard to interpret as their biological counterparts. Identification of functional modules in natural brains plays an important role in cognitive and neuroscience alike, and can be carried out using a wide range of technologies such as fMRI, EEG/ERP, MEG, or calcium imaging. However, we do not have such robust methods at our disposal when it comes to understanding functional modules in artificial neural networks. Ideally, understanding which parts of an artificial neural network perform what function might help us to address a number of vexing problems in ANN research, such as catastrophic forgetting and overfitting. Furthermore, revealing a network’s modularity could improve our trust in them by making these black boxes more transparent. Here, we introduce a new information-theoretic concept that proves useful in understanding and analyzing a network’s functional modularity: the relay information IR. The relay information measures how much information groups of neurons that participate in a particular function (modules) relay from inputs to outputs. Combined with a greedy search algorithm, relay information can be used to identify computational modules in neural networks. We also show that the functionality of modules correlates with the amount of relay information they carry.

The neighborhood overlap (NOVER) of an edge u-v is defined as the ratio of the number of nodes who are neighbors for both u and v to that of the number of nodes who are neighbors of at least u or v. In this paper, we hypothesize that an edge u-v with a lower NOVER score bridges two or more sets of vertices, with very few edges (other than u-v) connecting vertices from one set to another set. Accordingly, we propose a greedy algorithm of iteratively removing the edges of a network in the increasing order of their neighborhood overlap and calculating the modularity score of the resulting network component(s) after the removal of each edge. The network component(s) that have the largest cumulative modularity score are identified as the different communities of the network. We evaluate the performance of the proposed NOVER-based community detection algorithm on nine real-world network graphs and compare the performance against the multi-level aggregation-based Louvain algorithm, as well as the original and time-efficient versions of the edge betweenness-based Girvan-Newman (GN) community detection algorithm.

Community detection has been a subject of extensive research due to its broad applications across social media, computer science, biology, and complex systems. Modularity stands out as a predominant metric guiding community detection, with numerous algorithms aimed at maximizing modularity. However, modularity encounters a resolution limit problem when identifying small community structures. To tackle this challenge, this paper presents a novel approach by defining community structure information from the perspective of encoding edge information. This pioneering definition lays the foundation for the proposed fast community detection algorithm CSIM, boasting an average time complexity of only O(nlogn). Experimental results showcase that communities identified via the CSIM algorithm across various graph data types closely resemble ground truth community structures compared to those revealed via modularity-based algorithms. Furthermore, CSIM not only boasts lower time complexity than greedy algorithms optimizing community structure information but also achieves superior optimization results. Notably, in cyclic network graphs, CSIM surpasses modularity-based algorithms in effectively addressing the resolution limit problem.

Complex industrial processes usually exhibit multimode characteristics, meaning that statistical features of process data, such as mean, variance, and correlation, vary across different modes. Extracting critical information from these distinct modes can significantly enhance the accuracy and robustness of data‐driven models in process monitoring, condition evaluation, and quality improvement. Consequently, the multimode identification of industrial data becomes a paramount concern in data‐driven modelling. However, existing methods for multimode identification require prior knowledge to predetermine the number of modes and struggle to describe the similarity between high‐dimensional samples effectively. To address this issue, this study introduces an automatic multimode identification method based on complex network community detection. In this approach, each data sample is considered as a node, and manifold similarity is calculated to construct the complex network model. The method leverages weighted geodesic distances to capture the data's manifold structure and potential density, enabling better distinction between high‐dimensional samples in different modes. The greedy search algorithm with modularity maximisation is employed to partition nodes into modes without manual selection of the number of modes. Furthermore, a node degree‐based indicator is developed for online mode monitoring. Experimental studies on two examples demonstrate the effectiveness of the proposed method in uncovering multimode characteristics of complex industrial processes, highlighting its promising application potential. Extracting critical information from different modes can significantly improve the accuracy and robustness of data‐driven models in process monitoring, condition evaluation, and quality improvement. However, the existing multimode identification methods rely on prior knowledge to determine the number of modes in advance and cannot describe the similarity between high‐dimensional samples well. Therefore, a novel mode identification method is proposed based on a complex network to overcome mode number selection's difficulty.