CGNLib: A Python library for Girvan–Newman community detection with customizable node-based centrality metrics

Previous examinations of astrophysical chemical reaction networks found that Earth's atmospheric network was distinct in its hierarchical organization and scale‐free nature. If Earth's unique atmospheric network structure is due to the coevolution between the biosphere and atmosphere, it may hint at a novel planetary‐scale biosignature. Here, we use updated chemical reaction networks of planetary atmospheres and explore their topologies using a plethora of diagnostic techniques from network science and graph theory, including global metrics, centrality metrics, community detection, and cluster analysis methods. We show that the topologies of atmospheric chemical reaction networks of different planetary bodies in the Solar System are distinct from one another. While we find that model networks of Earth's atmosphere do not display scale‐free topology, Earth's chemical reaction network is nonetheless distinguishable from those of other Solar System atmospheres through various other metrics. Earth's network has the most nonrandom topology of all the planetary networks and, in some global metrics, is more similar to biological networks than are the other planetary networks. Finally, we discuss how further investigations of atmospheric chemical networks using more advanced network representations and novel network metrics may lead to the development of a network‐based biosignature applicable to exoplanets.

Measuring the influence of users in social networks is key for numerous applications. A recently proposed influence metric, coined as Ψ-score, allows to go beyond traditional centrality metrics, which only assess structural graph importance, by further incorporating the rich information provided by the posting and re-posting activity of users. The Ψ-score is shown in fact to generalize PageRank for non-homogeneous node activity. Despite its significance, it scales poorly to large datasets; for a network of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> users, it requires to solve <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> linear systems of equations of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> . To address this problem, this work introduces a novel scalable algorithm for the fast approximation of Ψ- score, named Power-Ψ. The proposed algorithm is based on a novel equation indicating that it suffices to solve one system of equations of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> to compute the Ψ-score. Then, our algorithm exploits the fact that such a system can be recursively and distributedly approximated to any desired error. This permits the Ψ-score, summarizing both structural and behavioral information for the nodes, to run as fast as PageRank. We validate the effectiveness of the proposed algorithm, which we release as an open source Python library, on several real-world datasets.

Complex network-based analysis of inter-basin water transfer networks

This study aimed to systematically understand the knowledge structure and time-series changes in domestic meditation intervention research from 2016 to 2025. The main focus was to investigate research trend shifts and paradigm transitions before, during, and after the COVID-19 pandemic. Keyword Network Analysis (KNA) was performed on 1,442 domestic meditation intervention studies published in KCI-listed or candidate journals between 2016 and 2025. A co-occurrence frequency matrix was constructed using 196 core keywords as nodes, and the structural characteristics were identified through centrality analysis and clustering analysis (Louvain Community Detection). The overall network analysis confirmed that ‘Mindfulness’ served as the absolute core hub, dominating all centrality metrics 18. Mental health keywords such as ‘Depression,’ ‘Stress,’ and ‘Anxiety’ showed high centrality, establishing them as key application areas 19. The time-series analysis empirically demonstrated a clear three-stage paradigm shift: ‘Traditional Theory Focus’ (Pre-COVID) → ‘Clinical Application Transition’ (COVID Period) → ‘Integrated Development’ (Post-COVID) 2016-2019. During the transition period (2020-2023), the centrality of ‘Depression’ and ‘Stress’ surged, reflecting a focus on immediate clinical crisis response. The ‘Integrated Development’ period (2024-2025) showed a return to a balanced path, integrating traditional theory and modern psychological mechanisms through the re-emergence of ‘Vipassana’ and the consolidation of ‘Self-Compassion.’ This study suggests that meditation intervention research is maturing into an integrated developmental structure (‘Traditional Theory → Mindfulness → Self-Compassion → Mental Health Effects’) that is highly responsive to external shocks (COVID-19 pandemic). This solidifies the value of meditation as a scientifically validated alternative approach that possesses both academic depth and clinical utility in the context of the modern mental health crisis.

This study integrates network science and intersection graph theory to analyse the structural properties of recipe networks in Catalan cuisine. Using three distinct cookbooks, two traditional and one haute cuisine, we construct the recipe similarity networks by linking recipes based on shared ingredients, with link weights reflecting ingredient similarity. We introduce a new, ad hoc, similarity measure that overcomes some limitations of traditional similarity metrics. We explore how different methodological approaches, such as the substitution of recipes/ingredients with their composing ingredients and link weight normalisation, influence network structure and node centrality. Our analysis reveals that recipe similarity networks are highly interconnected but show structural differences across cuisines, particularly in haute cuisine, which features more specialised recipes. Node centrality metrics identify key recipes that define culinary traditions, such as “Allioli” in traditional Catalan cuisine and “Becada con brioche de su salmis” in haute cuisine. We also develop a community detection algorithm based on link removal and clique identification, which uncovers tightly-knit recipe groups. This study advances the field of computational gastronomy by providing a methodological foundation that can be integrated with artificial intelligence techniques to support recipe personalisation, food recommendations, and gastronomic innovation.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-17189-6.

Literature network analysis is an emerging area in the computational research domain. Literature network is a type of social network with various distinct features. The analysis explores significance of human behavior and complex social relationships. The story consists of some characters and creates an interconnected social system. Each character of the literature represents a node and the edge between any two nodes offered the interaction between them. An annotation and a novel character categorization method are developed to extract interactive social network from the Bengali drama. We analyze Raktakarabi and Muktodhara , two renowned Bengali dramas of Rabindranath Tagore. Weighted degree, closeness, and betweenness centrality analyze the correlation among the characters. We propose an edge contribution-based centrality and diversity metric of a node to determine the influence of one character over others. High diverse nodes show low clustering coefficient and vice versa. We propose a novel idea to analyze the characteristics of protagonist and antagonist from the influential nodes based on the complex graph. We also present a game theory-based community detection method that clusters the actors with a high degree of relationship. Evaluation on real-world networks demonstrates the superiority of the proposed method over the other existing algorithms. Interrelationship of the actors within the drama is also shown from the detected communities, as underlying theme of the narrations is identical. The analytical results show that our method efficiently finds the protagonist and antagonist from the literature network. The method is unique, and the analytical results are more accurate and unbiased than the human perspective. Our approach establishes similar results compared with the benchmark analysis available in Tagore’s Bengali literature.