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Deep learning struggles with unsupervised tasks like community detection in networks. This work proposes the Enhanced Community Detection with Structural Information VGAE (VGAE-ECF) method, a method that enhances variational graph autoencoders (VGAEs) for community detection in large networks. It incorporates community structure information and edge weights alongside traditional network data. This combined input leads to improved latent representations for community identification via K-means clustering. We perform experiments and show that our method works better than previous approaches of community-aware VGAEs. [ABSTRACT FROM AUTHOR]

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric ( M C ) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities. [ABSTRACT FROM AUTHOR]

With the rapid advancement in Building Information Modelling (BIM) technology to strengthen the Building and Construction (B&C) industry, effective methods are required for the analysis and improvement of as-built BIM, which reflects the completed building project and captures all deviations and updates from the initial design. However, most existing studies are focused on as-designed BIM, while the analysis and inspection of as-built BIM rely on labour-intensive visual and manual approaches that overlook interdependent relationships among components. To address these issues, we propose a network analysis-based approach for managing and improving as-built BIM. Networks are generated from geometric attributes extracted from Industry Foundation Classes (IFC) documents, and network analytical techniques are applied to facilitate BIM analysis. In addition, a practical dataset is utilised to verify the feasibility of the proposed approach. The results demonstrate that our method significantly enhances the analysis and comparison of as-built BIM from model analysis and matching. Specifically, the innovative contribution leverages global information and interdependent relations, providing a more comprehensive understanding of the as-built BIM for effective management and optimisation. Our findings suggest that network analysis can serve as a powerful tool for structure and asset management in the B&C industry, offering new perspectives and methodologies for as-built BIM analysis and comparison. Finally, detailed discussion and future suggestions are presented. [ABSTRACT FROM AUTHOR]

Community detection can help analyze the structural features and functions of complex networks, and plays important roles in many aspects such as project recommendation and network evolution analysis. Therefore, community detection has always been a hot topic in the field of complex networks. Although various community-detection methods have been proposed, how to improve their accuracy and efficiency is still an ambition pursued by researchers. In view of this, this paper proposes a community-detection method for complex networks based on node influence analysis. First, the influence of nodes is represented as a vector composed by neighborhood degree centrality, betweennes centrality and clustering coefficient. Then, Pareto dominance is used to rank the influence of nodes. After that, the community centers are selected by comprehensively considering the node influence and crowding degree. Finally, the remaining nodes are allocated to different communities using a labeling algorithm. The proposed method in this paper is applied to several actual networks. The comparison results with other methods demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity. By leveraging the connectivity-based metric and employing a heuristic algorithm, we develop a novel complementary graph for the Max-Min Modularity that enhances its effectiveness. We formulate community detection as an integer programming problem of an equivalent yet more compact counterpart model of the revised Max-Min Modularity maximization problem. Using a row generation technique alongside the heuristic approach, we then provide a hybrid procedure for near-optimally solving the model and discovering high-quality communities. Through a series of experiments, we demonstrate the success of our algorithm, showcasing its efficiency in detecting communities, particularly in extensive networks. [ABSTRACT FROM AUTHOR]

People who inject drugs (PWID) have an increased risk of HIV infection partly due to injection behaviors often related to opioid use. Medications for opioid use disorder (MOUD) have been shown to reduce HIV infection risk, possibly by reducing injection risk behaviors. MOUD may benefit individuals who do not receive it themselves but are connected through social, sexual, or drug use networks with individuals who are treated. This is known as spillover. Valid estimation of spillover in network studies requires considering the network's community structure. Communities are groups of densely connected individuals with sparse connections to other groups. We analyzed a network of 277 PWID and their contacts from the Transmission Reduction Intervention Project. We assessed the effect of MOUD on reductions in injection risk behaviors and the possible benefit for network contacts of participants treated with MOUD. We identified communities using modularity-based methods and employed inverse probability weighting with community-level propensity scores to adjust for measured confounding. We found that MOUD may have beneficial spillover effects on reducing injection risk behaviors. The magnitudes of estimated effects were sensitive to the community detection method. Careful consideration should be paid to the significance of community structure in network studies evaluating spillover. [ABSTRACT FROM AUTHOR]

Recently, community detection has emerged as a prominent research area in the analysis of complex network structures. Community detection models based on non-negative matrix factorization (NMF) are shallow and fail to fully discover the internal structure of complex networks. Thus, this article introduces a novel constrained symmetric non-negative matrix factorization with deep autoencoders (CSDNMF) as a solution to this issue. The model possesses the following advantages: (1) By integrating a deep autoencoder to discern the latent attributes bridging the original network and community assignments, it adeptly captures hierarchical information. (2) Introducing a graph regularizer facilitates a thorough comprehension of the community structure inherent within the target network. (3) By integrating a symmetry regularizer, the model's capacity to learn undirected networks is augmented, thereby facilitating the precise detection of symmetry within the target network. The proposed CSDNMF model exhibits superior performance in community detection when compared to state-of-the-art models, as demonstrated by eight experimental results conducted on real-world networks. [ABSTRACT FROM AUTHOR]

Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars' attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In real-world scenarios, obtaining the relationships between nodes is often challenging, resulting in incomplete network topology. This limitation significantly reduces the applicability of community detection methods, particularly neighborhood aggregation-based approaches, on structurally incomplete networks. Therefore, in this situation, it is crucial to obtain meaningful community information from the limited network structure. To address this challenge, the LPGSE algorithm was designed and implemented, which includes four parts: link prediction, structure observation, network estimation, and community partitioning. LPGSE demonstrated its performance in community detection in structurally incomplete networks with 10% missing edges on multiple datasets. Compared with traditional community detection algorithms, LPGSE achieved improvements in NMI and ARI metrics of 1.5781% to 29.0780% and 0.4332% to 31.9820%, respectively. Compared with similar community detection algorithms for structurally incomplete networks, LPGSE also outperformed other algorithms on all datasets. In addition, different edge-missing ratio settings were also attempted, and the performance of different algorithms in these situations was compared and analyzed. The results showed that the algorithm can still maintain high accuracy and stability in community detection across different edge-missing ratios. [ABSTRACT FROM AUTHOR]

During economic crises, diversifying industrial production emerges as a critical strategy to address societal challenges. The Product Space, a graph representing industrial knowledge proximity, acts as a valuable tool for recommending diversified product offerings. These recommendations rely on the edges of the graph to identify suitable products. They can be improved by grouping similar products together, which results in more precise suggestions. Unlike the topology, the textual data in nodes of the Product Space graph are typically unutilized in graph clustering methods. In this context, we propose a novel approach for economic graph learning that incorporates learning node data alongside network topology. By applying this method to the Product Space dataset, we demonstrate how recommendations have been improved by presenting real-life applications. Our research employing a graph neural network demonstrates superior performance compared to methods like Louvain and I-Louvain. Our contribution introduces a node data-based deep graph clustering graph neural network that significantly advances the macroeconomic literature and addresses the imperative of diversifying industrial production. We discuss both the advantages and limitations of deep graph learning models in economics, laying the groundwork for future research. [ABSTRACT FROM AUTHOR]

Community detection is a widely studied topic in network structure analysis. We propose a community detection method based on the search for the local maxima of an objective function. This objective function reflects the quality of candidate communities in the network structure. The objective function can be constructed from a probability matrix that describes interactions in a network. Different models, such as network structure models and network flow models, can be used to build the probability matrix, and it acts as a link between network models and community detection models. In our influence-spreading model, the probability matrix is called an influence-spreading matrix, which describes the directed influence between all pairs of nodes in the network. By using the local maxima of an objective function, our method can standardise and help in comparing different definitions and approaches of community detection. Our proposed approach can detect overlapping and hierarchical communities and their building blocks within a network. To compare different structures in the network, we define a cohesion measure. The objective function can be expressed as a sum of these cohesion measures. We also discuss the probability of community formation to analyse a different aspect of group behaviour in a network. It is essential to recognise that this concept is separate from the notion of community cohesion, which emphasises the need for varying objective functions in different applications. Furthermore, we demonstrate that normalising objective functions by the size of detected communities can alter their rankings. [ABSTRACT FROM AUTHOR]

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 (n log n) . 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. [ABSTRACT FROM AUTHOR]

Community detection in social networks is of great importance and is used in a variety of applications such as recommendation systems and targeted advertising. While detecting dense groups with high levels of connectivity and similar interests between their members is the main target of traditional network analysis, finding network members with quite different behavior than the majority of nodes is important as well. These nodes are known as outliers, and their accurate detection can be very useful; when outliers are marked as noisy nodes, their early exclusion from analysis can lead to high computational profits. On the other hand, they can represent interesting components that call for further investigation to find the reasons for their outlying behavior and possible ways to include them in a neighboring community. Both community and outlier detection are challenging in temporal environments where changes occur in real time; thus, dynamic methods need to be deployed rather than to static methods. In our work, we take into account the content of the network, in contrast to most of related studies, where only the network's structure contributes to community formation. We define an adaptive outlier score to be assigned to each node in order to quantify its outlierness, and introduce a complete online community detection algorithm that analyzes both the network's structure and content while at the same time detecting community outliers. To evaluate our method, we retrieved and processed two real datasets regarding social networks with temporal and content information. Experimental results show that our method is capable of detecting outliers in real-time evolving communities and provides an outlier score which is a better metric of each node's outlierness compared to widely used metrics. Finally, experimental results indicate that our method is suitable for predicting the status of future nodes based on their current outlier score. [ABSTRACT FROM AUTHOR]

We address the challenge of identifying meaningful communities by proposing a model based on convex game theory and a measure of community strength. Many existing community detection methods fail to provide unique solutions, and it remains unclear how the solutions depend on initial conditions. Our approach identifies strong communities with a hierarchical structure, visualizable as a dendrogram, and computable in polynomial time using submodular function minimization. This framework extends beyond graphs to hypergraphs or even polymatroids. In the case when the model is graphical, a more efficient algorithm based on the max-flow min-cut algorithm can be devised. Though not achieving near-linear time complexity, the pursuit of practical algorithms is an intriguing avenue for future research. Our work serves as the foundation, offering an analytical framework that yields unique solutions with clear operational meaning for the communities identified. [ABSTRACT FROM AUTHOR]

Having emerged as strategic focal points in industrial transformation and technological innovation, intelligent machine tools are pivotal in the field of intelligent manufacturing. Accurately forecasting emerging technologies within this domain is crucial for guiding intelligent manufacturing's evolution and fostering rapid innovation. However, prevailing research methodologies exhibit limitations, often concentrating on popular topics at the expense of lesser-known yet significant areas, thereby impacting the accurate identification of research priorities. The complex, systemic, and interdisciplinary nature of intelligent machine tool technology challenges traditional research approaches, particularly in assessing technological maturity and intricate interactions. To overcome these challenges, we propose a novel framework that leverages technological communities for a comprehensive analysis. This approach clusters data into specific topics which are reflective of the technology system, facilitating detailed investigations within each area. By refining community analysis methods and integrating structural and interactive community features, our framework significantly improves the precision of emerging technology predictions. Our research not only validates the framework but also projects key emerging technologies in intelligent machine tools, offering valuable insights for business leaders and scholars alike. [ABSTRACT FROM AUTHOR]

The hydrogen energy industry, as one of the most important directions for future energy transformation, can promote the sustainable development of the global economy and of society. China has raised the development of hydrogen energy to a strategic position. Based on the patent data in the past two decades, this study investigates the collaborative innovation relationships in China's hydrogen energy field using complex network theory. Firstly, patent data filed between 2003 and 2023 are analyzed and compared in terms of time, geography, and institutional and technological dimensions. Subsequently, a patent collaborative innovation network is constructed to explore the fundamental characteristics and evolutionary patterns over five stages. Furthermore, centrality measures and community detection algorithms are utilized to identify core entities and innovation alliances within the network, which reveal that China's hydrogen energy industry is drifting toward alliance innovation. The study results show the following: (1) the network has grown rapidly in size and scope over the last two decades and evolved from the initial stage to the multi-center stage, before forming innovation alliances; (2) core innovative entities are important supports and bridges for China's hydrogen energy industry, and control most resources and maintain the robustness of the whole network; (3) innovation alliances reveal the closeness of the collaborative relationships between innovative entities and the potential landscape of China's hydrogen energy industry; and (4) most of the innovation alliances cooperate only on a narrow range of technologies, which may hinder the overall sustainable growth of the hydrogen energy industry. Thereafter, some suggestions are put forward from the perspective of an industrial chain and innovation chain, which may provide a theoretical reference for collaborative innovation and the future development and planning in the field of hydrogen energy in China. [ABSTRACT FROM AUTHOR]

Systemic risk refers to the potential for a disruption in one part of a financial system to trigger a cascade of adverse effects, impacting the functioning of the system. Despite the progress on novel systemic risk measures, research on dynamics of systemic risk network structure and its community effect is still in its initial state. In this study, we utilize price data from 107 representative Chinese stocks spanning the period from 2017 to 2022. A systemic risk network is derived from the Risk Transmission Index based on TENET and the QR–Lasso model. By utilizing DBSCAN, HITS and community detection algorithms on the network, we aim to propose a more suitable definition of systemically important companies, explore the interrelationships between companies, and discuss its plausible reasons for dynamics structural changes. The empirical findings demonstrate a substantial involvement of insurance companies in both contributing to and receiving systemic risk within the analyzed context. We identify prominent risk output and input centers, and emphasize the profound impact of the COVID-19 pandemic on the dynamics of systemic risk. [ABSTRACT FROM AUTHOR]

Community structure is a significant characteristic of complex networks, and community detection has valuable applications in network structure analysis. Non-negative matrix factorization (NMF) is a key set of algorithms used to solve the community detection issue. Nevertheless, the localization of feature vectors in the adjacency matrix, which represents the characteristics of complex network structures, frequently leads to the failure of NMF-based approaches when the data matrix has a low density. This paper presents a novel algorithm for detecting sparse network communities using non-negative matrix factorization (NMF). The algorithm utilizes local feature vectors to represent the original network topological features and learns regularization matrices. The resulting feature matrices effectively reveal the global structure of the data matrix, demonstrating enhanced feature expression capabilities. The regularized data matrix resolves the issue of localized feature vectors caused by sparsity or noise, in contrast to the adjacency matrix. The approach has superior accuracy in detecting community structures compared to standard NMF-based community detection algorithms, as evidenced by experimental findings on both simulated and real-world networks. [ABSTRACT FROM AUTHOR]

This study presents a novel approach that synergizes community detection algorithms with various Graph Neural Network (GNN) models to bolster link prediction in scientific literature networks. By integrating the Louvain community detection algorithm into our GNN frameworks, we consistently enhanced the performance across all models tested. For example, integrating the Louvain model with the GAT model resulted in an AUC score increase from 0.777 to 0.823, exemplifying the typical improvements observed. Similar gains were noted when the Louvain model was paired with other GNN architectures, confirming the robustness and effectiveness of incorporating community-level insights. This consistent increase in performance—reflected in our extensive experimentation on bipartite graphs of scientific collaborations and citations—highlights the synergistic potential of combining community detection with GNNs to overcome common link prediction challenges such as scalability and resolution limits. Our findings advocate for the integration of community structures as a significant step forward in the predictive accuracy of network science models, offering a comprehensive understanding of scientific collaboration patterns through the lens of advanced machine learning techniques. [ABSTRACT FROM AUTHOR]

The link prediction problem is a time-evolving model in network science that has simultaneously abetted myriad applications and experienced extensive methodological improvement. Inferring the possibility of emerging links in dynamic social networks, also known as the dynamic link prediction task, is complex and challenging. In contrast to the link prediction in cross-sectional networks, dynamic link prediction methods need to cater to the actor-level temporal changes and associated evolutionary information regarding their micro- (i.e., link formation/deletion) and mesoscale (i.e., community formation) network structure. With the advent of abundant community detection algorithms, the research community has examined community-aware link prediction strategies in static networks. However, the same task in dynamic networks where, apart from the actors and links among them, their community pattern is also dynamic, is yet to be explored. Evolutionary community-aware information, including the associated link structure and temporal neighborhood changes, can effectively be mined to build dynamic similarity metrics for dynamic link prediction. This study aims to develop and integrate such dynamic features with machine learning algorithms for link prediction tasks in dynamic social networks. It also compares the performances of these features against well-known similarity metrics (i.e., ResourceAllocation) for static networks and a time series-based link prediction strategy in dynamic networks. These proposed features achieved high-performance scores, representing them as prospective candidates for both dynamic link prediction tasks and modeling the network growth. [ABSTRACT FROM AUTHOR]

(1) The enhanced capability of graph neural networks (GNNs) in unsupervised community detection of clustered nodes is attributed to their capacity to encode both the connectivity and feature information spaces of graphs. The identification of latent communities holds practical significance in various domains, from social networks to genomics. Current real-world performance benchmarks are perplexing due to the multitude of decisions influencing GNN evaluations for this task. (2) Three metrics are compared to assess the consistency of algorithm rankings in the presence of randomness. The consistency and quality of performance between the results under a hyperparameter optimisation with the default hyperparameters is evaluated. (3) The results compare hyperparameter optimisation with default hyperparameters, revealing a significant performance loss when neglecting hyperparameter investigation. A comparison of metrics indicates that ties in ranks can substantially alter the quantification of randomness. (4) Ensuring adherence to the same evaluation criteria may result in notable differences in the reported performance of methods for this task. The W randomness coefficient, based on the Wasserstein distance, is identified as providing the most robust assessment of randomness. [ABSTRACT FROM AUTHOR]

To address the problem that traditional spectral clustering algorithms cannot obtain the complete structural information of networks, this paper proposes a spectral clustering community detection algorithm, PMIK-SC, based on the point-wise mutual information (PMI) graph kernel. The kernel is constructed according to the point-wise mutual information between nodes, which is then used as a proximity matrix to reconstruct the network and obtain the symmetric normalized Laplacian matrix. Finally, the network is partitioned by the eigendecomposition and eigenvector clustering of the Laplacian matrix. In addition, to determine the number of clusters during spectral clustering, this paper proposes a fast algorithm, BI-CNE, for estimating the number of communities. For a specific network, the algorithm first reconstructs the original network and then runs Monte Carlo sampling to estimate the number of communities by Bayesian inference. Experimental results show that the detection speed and accuracy of the algorithm are superior to other existing algorithms for estimating the number of communities. On this basis, the spectral clustering community detection algorithm PMIK-SC also has high accuracy and stability compared with other community detection algorithms and spectral clustering algorithms. [ABSTRACT FROM AUTHOR]

The evaluation of similarities between natural languages often relies on prior knowledge of the languages being studied. We describe three methods for building phylogenetic trees and clustering languages without the use of language-specific information. The input to our methods is a set of document vectors trained on a corpus of parallel translations of the Bible into 22 Indo-European languages, representing 4 language families: Indo-Iranian, Slavic, Germanic, and Romance. This text corpus consists of a set of 532,092 Bible verses, with 24,186 identical verses translated into each language. The methods are (A) hierarchical clustering using distance between language vector centroids, (B) hierarchical clustering using a network-derived distance measure, and (C) Deep Embedded Clustering (DEC) of language vectors. We evaluate our methods using a ground-truth tree and language families derived from said tree. All three achieve clustering F-scores above 0.9 on the Indo-Iranian and Slavic families; most confusion is between the Germanic and Romance families. The mean F-scores across all families are 0.864 (centroid clustering), 0.953 (network partitioning), and 0.763 (DEC). This shows that document vectors can be used to capture and compare linguistic features of multilingual texts, and thus could help extend language similarity and other translation studies research. [ABSTRACT FROM AUTHOR]

Community detection has been (and remains) a very important topic in several fields. From marketing and social networking to biological studies, community detection plays a key role in advancing research in many different fields. Research on this topic originally looked at classifying nodes into discrete communities (non-overlapping communities) but eventually moved forward to placing nodes in multiple communities (overlapping communities). Unfortunately, community detection has always been a time-inefficient process, and datasets are too large to realistically process them using traditional methods. Because of this, recent methods have turned to parallelism and graph stream models, where the edge list is accessed one edge at a time. However, all these methods, while offering a significant decrease in processing time, still have several shortcomings. We propose a new parallel algorithm called community detection with seed sets (CoDiS), which solves the overlapping community detection problem in graph streams. Initially, some nodes (seed sets) have known community structures, and the aim is to expand these communities by processing one edge at a time. The innovation of our approach is that it splits communities among the parallel computation workers so that each worker is only updating a subset of all the communities. By doing so, we decrease the edge processing throughput and decrease the amount of time each worker spends on each edge. Crucially, we remove the need for every worker to have access to every community. Experimental results show that we are able to gain a significant improvement in running time with no loss of accuracy. [ABSTRACT FROM AUTHOR]

The rapid dissemination of misinformation on social networks, particularly during public health crises like the COVID-19 pandemic, has become a significant concern. This study investigates the spread of misinformation on social network data using social network analysis (SNA) metrics, and more generally by using well known network science metrics. Moreover, we propose a process design that utilizes social network data from Twitter, to analyze the involvement of non-trusted accounts in spreading misinformation supported by a proof-of-concept prototype. The proposed prototype includes modules for data collection, data preprocessing, network creation, centrality calculation, community detection, and misinformation spreading analysis. We conducted an experimental study on a COVID-19-related Twitter dataset using the modules. The results demonstrate the effectiveness of our approach and process steps, and provides valuable insight into the application of network science metrics on social network data for analysing various influence-parameters in misinformation spreading. [ABSTRACT FROM AUTHOR]

Over the years, network analysis has become a promising strategy for analysing complex system, i.e., systems composed of a large number of interacting elements. In particular, multilayer networks have emerged as a powerful framework for modelling and analysing complex systems with multiple types of interactions. Network analysis can be applied to pharmacogenomics to gain insights into the interactions between genes, drugs, and diseases. By integrating network analysis techniques with pharmacogenomic data, the goal consists of uncovering complex relationships and identifying key genes to use in pathway enrichment analysis to figure out biological pathways involved in drug response and adverse reactions. In this study, we modelled omics, disease, and drug data together through multilayer network representation. Then, we mined the multilayer network with a community detection algorithm to obtain the top communities. After that, we used the identified list of genes from the communities to perform pathway enrichment analysis (PEA) to figure out the biological function affected by the selected genes. The results show that the genes forming the top community have multiple roles through different pathways. [ABSTRACT FROM AUTHOR]

Examining the clustering characteristics and fluctuations within urban areas during peak hours through the lens of bike-sharing is of utmost importance in the optimization of bike-sharing systems and urban transportation planning. This investigation adopts the principles of urban spatial interaction network construction and employs streets as the fundamental units of analysis to model bike-sharing activities during morning and evening peak hours within Beijing's six central districts. Subsequent to this, a comprehensive analysis of the network's structural attributes was carried out. A Walktrap method, rooted in modularity analysis, was introduced to discern and scrutinize the clustering patterns and characteristics of communities within the network across different temporal intervals. Empirical findings reveal a predominant usage pattern of shared bicycles for short-distance travel during both morning and evening peak hours. Notably, distinctive community structures manifest during these periods, characterized by two large communities and multiple smaller ones during the morning peak, while the evening peak showcases a single large community alongside several medium-sized and smaller ones. Moreover, the extended interaction radius points to an expanded geographic range of interactions among streets. These findings bear significant implications for the management of urban transportation, bike-sharing enterprises, and urban residents, proffering valuable insights for the optimization of bike-sharing schemes and transportation strategies. These research findings not only contribute to enhancing urban transportation planning and bike-sharing systems but also provide robust guidance for advancing more efficient and sustainable urban transportation solutions, thereby fostering the sustainable development of cities. [ABSTRACT FROM AUTHOR]

Community detection is an important task in the analysis of complex networks, which is significant for mining and analyzing the organization and function of networks. As an unsupervised learning algorithm based on the particle competition mechanism, stochastic competitive learning has been applied in the field of community detection in complex networks, but still has several limitations. In order to improve the stability and accuracy of stochastic competitive learning and solve the problem of community detection, we propose an unsupervised community detection algorithm LNSSCL (Local Node Similarity-Integrated Stochastic Competitive Learning). The algorithm calculates node degree as well as Salton similarity metrics to determine the starting position of particle walk; local node similarity is incorporated into the particle preferential walk rule; the particle is dynamically adjusted to control capability increments according to the control range; particles select the node with the strongest control capability within the node to be resurrected; and the LNSSCL algorithm introduces a node affiliation selection step to adjust the node community labels. Experimental comparisons with 12 representative community detection algorithms on real network datasets and synthetic networks show that the LNSSCL algorithm is overall better than other compared algorithms in terms of standardized mutual information (NMI) and modularity (Q). The improvement effect for the stochastic competition learning algorithm is evident, and it can effectively accomplish the community detection task in complex networks. [ABSTRACT FROM AUTHOR]

Matrix factorization is a long-established method employed for analyzing and extracting valuable insight recommendations from complex networks containing user ratings. The execution time and computational resources demanded by these algorithms pose limitations when confronted with large datasets. Community detection algorithms play a crucial role in identifying groups and communities within intricate networks. To overcome the challenge of extensive computing resources with matrix factorization techniques, we present a novel framework that utilizes the inherent community information of the rating network. Our proposed approach, named Community-Based Matrix Factorization (CBMF), has the following steps: (1) Model the rating network as a complex bipartite network. (2) Divide the network into communities. (3) Extract the rating matrices pertaining only to those communities and apply MF on these matrices in parallel. (4) Merge the predicted rating matrices belonging to communities and evaluate the root mean square error (RMSE). In our experimentation, we use basic MF, SVD++, and FANMF for matrix factorization, and the Louvain algorithm is used for community division. The experimental evaluation on six datasets shows that the proposed CBMF enhances the quality of recommendations in each case. In the MovieLens 100K dataset, RMSE has been reduced to 0.21 from 1.26 using SVD++ by dividing the network into 25 communities. A similar reduction in RMSE is observed for the datasets of FilmTrust, Jester, Wikilens, Good Books, and Cell Phone. [ABSTRACT FROM AUTHOR]

Combining omics data from different layers using integrative methods provides a better understanding of the biology of a complex disease such as cancer. The discovery of biomarkers related to cancer development or prognosis helps to find more effective treatment options. This study integrates multi-omics data of different cancer types with a network-based approach to explore common gene modules among different tumors by running community detection methods on the integrated network. The common modules were evaluated by several biological metrics adapted to cancer. Then, a new prognostic scoring method was developed by weighting mRNA expression, methylation, and mutation status of genes. The survival analysis pointed out statistically significant results for GNG11, CBX2, CDKN3, ARHGEF10, CLN8, SEC61G and PTDSS1 genes. The literature search reveals that the identified biomarkers are associated with the same or different types of cancers. Our method does not only identify known cancer-specific biomarker genes, but also proposes new potential biomarkers. Thus, this study provides a rationale for identifying new gene targets and expanding treatment options across cancer types. [ABSTRACT FROM AUTHOR]

The urban road network is a large and complex system characterized by significant heterogeneity arising from different spatial structures and traffic demands. To facilitate effective management and control, it is necessary to partition the road network into homogeneous sub-areas. In this regard, we aim to propose a hybrid method for partitioning sub-areas with intra-area homogeneity, inter-area heterogeneity, and similar sizes, called CSDRA. It is specifically designed for bidirectional road networks with segment weights that encompass traffic flow, speed, or roadside facility evaluation. Based on community detection and spectral clustering, this proposed method comprises four main modules: initial partition, partitioning of large sub-areas, reassignment of small sub-areas, and boundary adjustment. In the preliminary partitioning work, we also design a road network reconstruction method which further helps to enhance the intra-area homogeneity and inter-area heterogeneity of partitioning results. Furthermore, to align with the requirement for comparable work units in practical traffic management and control, we control the similarity in the size of sub-areas by enforcing upper and lower bound constraints on the size of the sub-areas. We verify the outperformance of the proposed method by an experiment on the partitioning of an urban road network in Guangzhou, China, where we employ sidewalk barrier-free score data as segment weights. The results demonstrate the effectiveness of both the road network reconstruction method and the CSDRA proposed in this paper, as they significantly improve the partitioning outcomes compared with other methods using different evaluation indicators corresponding to the partitioning objectives. Finally, we investigate the influence of constraint parameters on the evaluation indicator. Our findings indicate that appropriately configuring these constraint parameters can effectively minimize sub-region size variations while having minimal impact on other aspects. [ABSTRACT FROM AUTHOR]

The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO-based approach that only needs number-of-nodes qubits and is represented by a QUBO matrix as sparse as the input graph's adjacency matrix. The substantial improvement in the sparsity of the QUBO matrix, which is typically very dense in related work, is achieved through the novel concept of separation nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which, upon its removal from the graph, yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept by achieving an up to 95% optimal solution quality on three established real-world benchmark datasets. This work hence displays a promising approach to NISQ-ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large-scale, real-world problem instances. [ABSTRACT FROM AUTHOR]

Local overlapping community detection is a hot problem in the field of studying complex networks. It is the process of finding dense clusters based on local network information. This paper proposes a method called local greedy extended dynamic overlapping community detection (GLOD) to address the challenges of detecting high-quality overlapping communities in complex networks. The goal is to improve the accuracy of community detection by considering the dynamic nature of community boundaries and leveraging local network information. The GLOD method consists of several steps. First, a coupling seed is constructed by selecting nodes from blank communities (i.e., nodes not assigned to any community) and their similar neighboring nodes. This seed serves as the starting point for community detection. Next, the seed boundaries are extended by applying multiple community fitness functions. These fitness functions determine the likelihood of nodes belonging to a specific community based on various local network properties. By iteratively expanding the seed boundaries, communities with higher density and better internal structure are formed. Finally, the overlapping communities are merged using an improved version of the Jaccard coefficient, which is a measure of similarity between sets. This step ensures that overlapping nodes between communities are properly identified and accounted for in the final community structure. The proposed method is evaluated using real networks and three sets of LFR (Lancichinetti–Fortunato–Radicchi) networks, which are synthetic benchmark networks widely used in community detection research. The experimental results demonstrate that GLOD outperforms existing algorithms and achieves a 2.1% improvement in the F-score, a community quality evaluation metric, compared to the LOCD framework. It outperforms the best existing LOCD algorithm on the real provenance network. In summary, the GLOD method aims to overcome the limitations of existing community detection algorithms by incorporating local network information, considering overlapping communities, and dynamically adjusting community boundaries. The experimental results suggest that GLOD is effective in improving the quality of community detection in complex networks. [ABSTRACT FROM AUTHOR]

The high dropout rates in programming courses emphasise the need for monitoring and understanding student engagement, enabling early interventions. This activity can be supported by insights into students' learning behaviours and their relationship with academic performance, derived from student learning log data in learning management systems. However, the high dimensionality of such data, along with their numerous features, pose challenges to their analysis and interpretability. In this study, we introduce entropy-based metrics as a novel manner to represent students' learning behaviours. Employing these metrics, in conjunction with a proven community detection method, we undertake an analysis of learning behaviours across higher- and lower-performing student communities. Furthermore, we examine the impact of the COVID-19 pandemic on these behaviours. The study is grounded in the analysis of empirical data from 391 Software Engineering students over three academic years. Our findings reveal that students in higher-performing communities typically tend to have lower volatility in entropy values and reach stable learning states earlier than their lower-performing counterparts. Importantly, this study provides evidence of the use of entropy as a simple yet insightful metric for educators to monitor study progress, enhance understanding of student engagement, and enable timely interventions. [ABSTRACT FROM AUTHOR]

One of the most important problems in complex networks is the location of nodes that are essential or play a main role in the network. Nodes with main local roles are the centers of real communities. Communities are sets of nodes of complex networks and are densely connected internally. Choosing the right nodes as seeds of the communities is crucial in determining real communities. We propose a new centrality measure named density-based entropy centrality for the local identification of the most important nodes. It measures the entropy of the sum of the sizes of the maximal cliques to which each node and its neighbor nodes belong. The proposed centrality is a local measure for explaining the local influence of each node, which provides an efficient way to locally identify the most important nodes and for community detection because communities are local structures. It can be computed independently for individual vertices, for large networks, and for not well-specified networks. The use of the proposed density-based entropy centrality for community seed selection and community detection outperforms other centrality measures. [ABSTRACT FROM AUTHOR]

In the era of the popularization of the Internet of Things (IOT), analyzing people's daily life behavior through the data collected by devices is an important method to mine potential daily requirements. The network method is an important means to analyze the relationship between people's daily behaviors, while the mainstream first-order network (FON) method ignores the high-order dependencies between daily behaviors. A higher-order dependency network (HON) can more accurately mine the requirements by considering higher-order dependencies. Firstly, our work adopts indoor daily behavior sequences obtained by video behavior detection, extracts higher-order dependency rules from behavior sequences, and rewires an HON. Secondly, an HON is used for the RandomWalk algorithm. On this basis, research on vital node identification and community detection is carried out. Finally, results on behavioral datasets show that, compared with FONs, HONs can significantly improve the accuracy of random walk, improve the identification of vital nodes, and we find that a node can belong to multiple communities. Our work improves the performance of user behavior analysis and thus benefits the mining of user requirements, which can be used to personalized recommendations and product improvements, and eventually achieve higher commercial profits. [ABSTRACT FROM AUTHOR]

This study addresses the importance of focal nodes in understanding the structural composition of networks. To identify these crucial nodes, a novel technique based on parallel Fuzzy Cognitive Maps (FCMs) is proposed. By utilising the focal nodes produced by the parallel FCMs, the algorithm efficiently creates initial clusters within the population. The community discovery process is accelerated through a distributed genetic algorithm that leverages the focal nodes obtained from the parallel FCM. This approach mitigates the randomness of the algorithm, addressing the limitations of the random population selection commonly found in genetic algorithms. The proposed algorithm improves the performance of the genetic algorithm by enabling informed decision making and forming a better initial population. This enhancement leads to improved convergence and overall algorithm performance. Furthermore, as graph sizes grow, traditional algorithms struggle to handle the increased complexity. To address this challenge, distributed algorithms are necessary for effectively managing larger data sizes and complexity. The proposed method is evaluated on diverse benchmark networks, encompassing both weighted and unweighted networks. The results demonstrate the superior scalability and performance of the proposed approach compared to the existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Community detection is widely used in social networks to uncover groups of related vertices (nodes). In cryptocurrency transaction networks, community detection can help identify users that are most related to known illegal users. However, there are challenges in applying community detection in cryptocurrency transaction networks: (1) the use of pseudonymous addresses that are not directly linked to personal information make it difficult to interpret the detected communities; (2) on Bitcoin, a user usually owns multiple Bitcoin addresses, and nodes in transaction networks do not always represent users. Existing works on cluster analysis on Bitcoin transaction networks focus on addressing the later using different heuristics to cluster addresses that are controlled by the same user. This research focuses on illegal community detection containing one or more illegal Bitcoin addresses. We first investigate the structure of Bitcoin transaction networks and suitable community detection methods, then collect a set of illegal addresses and use them to label the detected communities. The results show that 0.06% of communities from daily transaction networks contain one or more illegal addresses when 2,313,344 illegal addresses are used to label the communities. The results also show that distance-based clustering methods and other methods depending on them, such as network representation learning, are not suitable for Bitcoin transaction networks while community quality optimization and label-propagation-based methods are the most suitable. [ABSTRACT FROM AUTHOR]

Community detection is a crucial research direction in the analysis of complex networks and has been shown to be an NP-hard problem (a problem that is at least as hard as the hardest problems in nondeterministic polynomial time). Multi-objective evolutionary algorithms (MOEAs) have demonstrated promising performance in community detection. Given that distinct crossover operators are suitable for various stages of algorithm evolution, we propose a two-stage algorithm that uses an individual similarity parameter to divide the algorithm into two stages. We employ appropriate crossover operators for each stage to achieve optimal performance. Additionally, a repair operation is applied to boundary-independent nodes during the second phase of the algorithm, resulting in improved community partitioning results. We assessed the effectiveness of the algorithm by measuring its performance on a synthetic network and four real-world network datasets. Compared to four existing competing methods, our algorithm achieves better accuracy and stability. [ABSTRACT FROM AUTHOR]

Graph contrastive learning (GCL) has gained considerable attention as a self-supervised learning technique that has been successfully employed in various applications, such as node classification, node clustering, and link prediction. Despite its achievements, GCL has limited exploration of the community structure of graphs. This paper presents a novel online framework called Community Contrastive Learning (Community-CL) for simultaneously learning node representations and detecting communities in a network. The proposed method employs contrastive learning to minimize the difference in the latent representations of nodes and communities in different graph views. To achieve this, learnable graph augmentation views using a graph auto-encoder (GAE) are proposed, followed by a shared encoder that learns the feature matrix of the original graph and augmentation views. This joint contrastive framework enables more accurate representation learning of the network and results in more expressive embeddings than traditional community detection algorithms that solely optimize for community structure. Experimental results demonstrate that Community-CL achieves superior performance compared to state-of-the-art baselines in community detection. Specifically, the NMI of Community-CL is reported to be 0.714 (0.551) on the Amazon-Photo (Amazon-Computers) dataset, which represents a performance improvement of up to 16% compared with the best baseline. [ABSTRACT FROM AUTHOR]

Our objective is to survey recent results concerning the evolution of random networks and related extreme value statistics, which are a subject of interest due to numerous applications. Our survey concerns the statistical methodology but not the structure of random networks. We focus on the problems arising in evolving networks mainly due to the heavy-tailed nature of node indices. Tail and extremal indices of the node influence characteristics like in-degrees, out-degrees, PageRanks, and Max-linear models arising in the evolving random networks are discussed. Related topics like preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, finding the most influential leading nodes and communities, and related methods are surveyed. This survey tries to propose possible solutions to unsolved problems, like testing the stationarity and dependence of random graphs using known results obtained for random sequences. We provide a discussion of unsolved or insufficiently developed problems like the distribution of triangle and circle counts in evolving networks, or the clustering attachment and the local dependence of the modularity, the impact of node or edge deletion at each step of evolution on extreme value statistics, among many others. Considering existing techniques of community detection, we pay attention to such related topics as coloring graphs and anomaly detection by machine learning algorithms based on extreme value theory. In order to understand how one can compute tail and extremal indices on random graphs, we provide a structured and comprehensive review of their estimators obtained for random sequences. Methods to calculate the PageRank and PageRank vector are shortly presented. This survey aims to provide a better understanding of the directions in which the study of random networks has been done and how extreme value analysis developed for random sequences can be applied to random networks. [ABSTRACT FROM AUTHOR]

Of the various characteristics of network structure, the community structure has received the most research attention. In social networks, communities are divided into overlapping communities and disjoint communities. The former are closer to the actual situation of real society than the latter, making it necessary to explore a more effective overlapping community detection algorithm. The label propagation algorithm (LPA) has been widely used in large-scale data owing to its low time cost. In the traditional LPA, all of the nodes are regarded as equivalent relationships. In this case, unreliable nodes reduce the accuracy of label propagation. To solve this problem, we propose the influence-based community overlap propagation algorithm (INF-COPRA) for ranking the influence of nodes and labels. To control the propagation process and prevent error propagation, the algorithm only provides influential nodes with labels in the initialization phase, and those labels with high influence are preferred in the propagation process. Lastly, the accuracy of INF-COPRA and existing algorithms is compared on benchmark networks and real networks. The experimental results show that the INF-COPRA algorithm significantly improves the extentded modularity (EQ) and normal mutual information (NMI) of the community, indicating that it can outperform state-of-art methods in overlapping community detection tasks. [ABSTRACT FROM AUTHOR]

Effective inter-hospital coordination is crucial in improving the stroke treatment process and outcomes. The introduction of endovascular thrombectomy (EVT) further emphasized the importance of coordination. Although previous studies considered various clinical data besides stroke in terms of the network structure between hospitals, a majority of these studies performed only quantitative analyses instead of topological analyses. This study proposes a new framework (PatientFlow) for constructing a network based on stroke patient transfer data and performing exploratory analysis. The proposed framework can visualize the network structure among hospitals at the national level and analyze the detailed structure through dynamic queries. The hub-and-spoke structure for each cluster derived through community detection can be compared visually and analyzed quantitatively using network measures. Further, the relationship between regions can be analyzed by aggregating the transfer of patients by province. PatientFlow allows medical researchers to perform an exploratory analysis to understand the network at the national, provincial, and community levels with multiple coordinated views. [ABSTRACT FROM AUTHOR]

Community detection remains a challenging research hotspot in network analysis. With the complexity of the network data structures increasing, multilayer networks, in which entities interact through multiple types of connections, prove to be effective in describing complex networks. The layers in a multilayer network may not share a common community structure. In this paper, we propose a joint method based on matrix factorization and spectral embedding to recover the groups not only for the layers but also for nodes. Specifically, the layers are grouped via the matrix factorization method with layer similarity-based regularization in the perspective of a mixture multilayer stochastic block model, and then the node communities within a layer group are revealed by clustering a combination of the spectral embedding derived from the adjacency matrices and the shared approximation matrix. Numerical studies show that the proposed method achieves competitive clustering results as the number of nodes and/or number of layers vary, together with different topologies of network layers. Additionally, we apply the proposed method on two real-world multilayer networks and obtain interesting findings which again highlight the effectiveness of our method. [ABSTRACT FROM AUTHOR]

Community detection in weighted networks has been a popular topic in recent years. However, while there exist several flexible methods for estimating communities in weighted networks, these methods usually assume that the number of communities is known. It is usually unclear how to determine the exact number of communities one should use. Here, to estimate the number of communities for weighted networks generated from arbitrary distribution under the degree-corrected distribution-free model, we propose one approach that combines weighted modularity with spectral clustering. This approach allows a weighted network to have negative edge weights and it also works for signed networks. We compare the proposed method to several existing methods and show that our method is more accurate for estimating the number of communities both numerically and empirically. [ABSTRACT FROM AUTHOR]

Community detection is a significant and challenging task in network research. Nowadays, many community detection methods have been developed. Among them, the classical Louvain algorithm is an excellent method aiming at optimizing an objective function. In this paper, we propose a modularity function F 2 as a new objective function. Our modularity function F 2 overcomes certain disadvantages of the modularity functions raised in previous literature, such as the resolution limit problem. It is desired as a competitive objective function. Then, the constrained Louvain algorithm is proposed by adding some constraints to the classical Louvain algorithm. Finally, through the comparison, we have found that the constrained Louvain algorithm with F 2 is better than the constrained Louvain algorithm with other objective functions on most considered networks. Moreover, the constrained Louvain algorithm with F 2 is superior to the classical Louvain algorithm and the Newman's fast method. [ABSTRACT FROM AUTHOR]

Featured Application: Helping telecom companies retain those with a tendency toward number portability. In 2019, China introduced a policy on Number Portability Management, which has resulted in a rapid increase in the number of lost users among telecom companies. Telecom companies must urgently distinguish those with a tendency toward number portability. However, existing prediction research lacks the input of temporal variations in user data and the graph-based analysis of user relationship characteristics, resulting in a poor prediction effect. In this paper, a neural-network-based approach has been applied to address the limitation, whereby user data do not feature temporal variation. Furthermore, innovative approaches have been proposed to construct multilayer community networks through users' geographic attributes and to analyze community networks with a network embedding method based on the matrix factorization framework. This fills a gap in existing research areas, whereby the geographic attributes of users have not received much attention. Considering the extensive inputs and multiple features of the predicted attributes, in this paper, the strengths and weaknesses of three feature selection methods are compared, as well as the prediction accuracy of each of the five prediction models. Finally, the embedded feature selection method, deep neural network model, and the Light GBM model are shown to provide better results. After introducing the user community network, it was found that the prediction evaluation indicators of both the deep neural network model and the Light GBM model are improved. [ABSTRACT FROM AUTHOR]

Over the years, detecting stable communities in a complex network has been a major challenge in network science. The global and local structures help to detect communities from different perspectives. However, previous methods based on them suffer from high complexity and fall into local optimum, respectively. The Four-Stage Algorithm (FSA) is proposed to reduce these issues and to allocate nodes to stable communities. Balancing global and local information, as well as accuracy and time complexity, while ensuring the allocation of nodes to stable communities, are the fundamental goals of this research. The Four-Stage Algorithm (FSA) is described and demonstrated using four real-world data with ground truth and three real networks without ground truth. In addition, it is evaluated with the results of seven community detection methods: Three-stage algorithm (TS), Louvain, Infomap, Fastgreedy, Walktrap, Eigenvector, and Label propagation (LPA). Experimental results on seven real network data sets show the effectiveness of our proposed approach and confirm that it is sufficiently capable of identifying those communities that are more desirable. The experimental results confirm that the proposed method can detect more stable and assured communities. For future work, deep learning methods can also be used to extract semantic content features that are more beneficial to investigating networks. [ABSTRACT FROM AUTHOR]

The swift development of autonomous vehicles raises the necessity of semantically mapping the environment by producing distinguishable representations to recognise similar areas. To this end, in this article, we present an efficient technique to cut up a robot's trajectory into semantically consistent communities based on graph-inspired descriptors. This allows an agent to localise itself in future tasks under different environmental circumstances in an urban area. The proposed semantic grouping technique utilizes the Leiden Community Detection Algorithm (LeCDA), which is a novel and efficient method of low computational complexity and exploits semantic and topometric information from the observed scenes. The presented experimentation was carried out on a novel dataset from the city of Xanthi, Greece (dubbed as  G r y p h o n u r b a n  urban dataset), which was recorded by RGB-D, IMU and GNSS sensors mounted on a moving vehicle. Our results exhibit the formulation of a semantic map with visually coherent communities and the realisation of an effective localisation mechanism for autonomous vehicles in urban environments. [ABSTRACT FROM AUTHOR]

Disease phenotypes are generally caused by the failure of gene modules which often have similar biological roles. Through the study of biological networks, it is possible to identify the intrinsic structure of molecular interactions in order to identify the so-called "disease modules". Community detection is an interesting and valuable approach to discovering the structure of the community in a complex network, revealing the internal organization of the nodes, and has become a leading research topic in the analysis of complex networks. This work investigates the link between biological modules and network communities in test-case biological networks that are commonly used as a reference point and which include Protein–Protein Interaction Networks, Metabolic Networks and Transcriptional Regulation Networks. In order to identify small and structurally well-defined communities in the biological context, a hybrid immune metaheuristic algorithm Hybrid-IA is proposed and compared with several metaheuristics, hyper-heuristics, and the well-known greedy algorithm Louvain, with respect to modularity maximization. Considering the limitation of modularity optimization, which can fail to identify smaller communities, the reliability of Hybrid-IA was also analyzed with respect to three well-known sensitivity analysis measures (NMI, ARI and NVI) that assess how similar the detected communities are to real ones. By inspecting all outcomes and the performed comparisons, we will see that on one hand Hybrid-IA finds slightly lower modularity values than Louvain, but outperforms all other metaheuristics, while on the other hand, it can detect communities more similar to the real ones when compared to those detected by Louvain. [ABSTRACT FROM AUTHOR]