A character network study of two Sci-Fi TV series

Taking Chongqing, Hunan, Shandong, Shaanxi and Sichuan as examples, this paper conducts a comparative study on the robustness of their highway networks, which is helpful for the subsequent construction of China's highway networks. The topology structure of highway networks is studied by complex network theory. The degree distribution, average degree, average clustering coefficient, average path length, network diameter and other parameters of the network were calculated, and the robustness of the highway network in five provinces and cities was compared from four aspects: connectivity, network efficiency, turn rate and robustness r. The results show that Chongqing and Shaanxi have a good performance of highway network robustness, Shandong and Sichuan have a more balanced performance, and Hunan has a weak performance. Enhance network robustness by placing route planning directions in place with fewer route options to provide drivers with more route options.

Leaves are the primary interface through which plants interact with the environment, their functional traits (morphology, anatomy, physiology) directly reflecting ecological strategies that mediate species-environment interactions. These traits link plant performance to ecosystem processes, shaping species distributions and coexistence via their complex relationships with climatic and edaphic factors. Based on previous work, we selected 20 P. euphratica trees along the desert riparian forest of the main stream of the Tarim River for leaf sample collection and habitat survey. We used 27 leaf traits of P. euphratica to visualize the leaf trait network (LTN). Through network structure parameters, such as edge density, diameter, average path length, and average clustering coefficient, the spatial pattern of the LTN and its relationships with 19 climatic factors and 11 soil factors were discussed using principal component analysis and correlation analysis. The results showed that: (1) there were significant differences in the parameters of the leaf trait network of P. euphratica along the main stream of the Tarim River. The variation coefficients of the diameter and average path length were the largest, respectively, whereas that of the average clustering coefficient was the smallest. (2) Among the parameters, only Modularity was significantly correlated with STK and SOM. But Average clustering coefficient was significantly positively correlated with Isothermality, Average path length and Diameter were significantly positively correlated with Min temperature of coldest month and the Average clustering coefficient was significantly negatively correlated with Min temperature of coldest month, the Diameter was significantly positively correlated with Precipitation of wettest month. In general, the correlation between climate factors and LTNs was stronger than soil factors. (3) The explanatory power of climatic factors alone on the leaf traits of P. euphratica was generally higher than that of soil factors, indicating that climatic conditions play a more decisive role in shaping the network structure of leaf traits of P. euphratica. However, the influence of soil conditions on some LTNs parameters cannot be ignored.The spatial variability of leaf trait networks is driven by climate and soil factors, with climate dominating along the Tarim River's main course.

Trust is recognized as a vital component in ensuring secure and stable interactions within Social Internet of Things (SIoT) networks. This study introduces an advanced model for simulating multidimensional trust relationships in SIoT, which is designed based on Watts–Strogatz (WS) random graphs and successfully reproduces the real topological features of SIoT networks with high fidelity. The proposed model incorporates a variety of relationship types such as Co-Location-Based Relationships (CLOR), Ownership-Based Relationships (OOR), Social Relationships (SOR), and Popularity-Based Relationships (POR), and integrates key attributes including spatial density, interaction frequency, owner reliability, and co-presence time to deliver a flexible and scalable structure. Analysis of the results indicates that the model performs significantly well in replicating topological metrics such as average path length, clustering coefficient, and average degree. For instance, in OOR and SOR graphs, the clustering coefficients reached values of 0.9 and 0.7 respectively, and in the CLOR graph, the average path length was limited to 2.4. Furthermore, in the POR graph, the average degree was consistently maintained at a stable value of 120. A comparison between the proposed model and traditional models such as Erdős–Rényi (ER) and Barabási–Albert (BA) graphs reveals that the use of advanced random graphs alongside the integration of additional trust-related features significantly enhances the accuracy, flexibility, and analytical capability of SIoT network behavior. In addition, the application of gradient descent-based optimization algorithms for fine-tuning model parameters ensures the efficiency and structural balance of the model, thereby positioning it as an effective and scalable solution for the analysis and development of Social Internet of Things networks.

The primary aim of this research is to examine the impacts of the interplay between formal and informal institutions on procurement innovation, and in turn, on project performance. In construction, firms, professionals, or individuals, all under the same project-based organization (PBO) umbrella, interact with each other according to different formal institutions associated with a particular procurement system. In recent years, researchers have begun to emphasize the parallel importance of informal institutions. The two types of institutions are characterized by the designed formal networks and the actual informal networks. The informal networks are the organization’s “central nervous system”, and must be appropriately fitted with the formal networks as the organization’s “skeleton”, so that the organizational productive engine could be fully steamed. In this research, the central research hypothesis is: The greater the extent of “fit” between the formal and informal institutions associated with an innovative procurement system, the better the project performance will be. 
\nThe essential part of the methodology is the mixture of quantitative and qualitative methods, and the mixture of plural research methods, including case studies, interviews, questionnaire/survey, archival study, field study, correlational analysis, and Social Network Analysis. Three case studies were conducted; Case Alpha is a public infrastructure project procured by the procurement systems Construction Management, Cases Beta 1 and Beta 2 are two public housing projects procured by Design-Bid-Build, and Case Gamma is a building project procured by Turnkey. The data collected through mixed research methods was fed into the SNA software package Ucinet and R. It was found that the better the fit between the SNA metrics (e.g. density, average path length, diameter, degree centrality, closeness centrality, betweenness centrality, local and global clustering coefficient) of formal and informal social networks of a PBO, the better the project performance. The hypothesis to the central research question is confirmed.
\nTo the best of my knowledge, this is the first study to articulate the interplay of formal and informal institutions in construction procurement innovation and its impacts on project performance, particularly by using the social network approach. In this study, the extent of “fit” is visualized and measurable, and thus its impact on project performance can be empirically examined. Another theoretical contribution of this research lies in its translation of the interplay between formal and informal institutions under different procurement systems into social networks. Practitioners can use this approach to periodically diagnose their procurement systems with a view to continuously improving their project performance, and, whenever possible, intervene to solve these problems.

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As air quality is closely related to human life and physical and mental health, the data of air quality has become a concern of the entire society. This study analyzes the characteristics of air quality data from a visibility graph networks point of view. The authors select eight monitoring stations in Beijing as samples. The time series of air quality data is mapped to a complex network based on the visibility graph algorithm. First, the authors study the topological structure of the networks for all the monitoring stations. Comparison results show that all constructed networks have similar structures in terms of the average path length, the network diameter, average clustering coefficient, density and the average degrees. Then the authors study the evolution of the visibility graph network for Huairou Town station for a long period of time. On the one hand, the value of the node degree indicates that the most important dates for air quality are the end of April, the beginning of May and the first three weeks of winter. On the other hand, the small-world properties of the networks reveals that the air quality data for the year 2014 is more stable without extreme fluctuations. This finding is consistent with the conclusion that air quality is largely affected by the weather while human activities play a more and more important role.

Psychrophilic proteases have attracted enormous attention in past decades, due to their high catalytic activity at low temperatures in a wide range of industrial processes, especially in the detergent and leather industries. Among them, H5 is an alkaline protease mutant, which featuring psychrophilic-like behavior, but the reasons that H5 with higher activity at low temperatures are still poorly understood. Herein, the molecular dynamics (MD) simulations combined with residue interaction network (RIN) were utilized to investigate the mechanisms of the cold-adaption of mutant H5. The results demonstrated that two loops involved in the substrate binding G100-S104 and S125-S129 in H5 had higher mobility, and the distance enlargement between the two loops modulated the substrate's accessibility compared with wild type counterpart. Besides, H5 enhanced conformational flexibility by weakening salt bridges and increasing interaction with the solvent. In particular, the absence of Lys251-Asp197-Arg247 salt bridge network may contribute to the structural mobility. Based on the free energy landscape and molecular mechanics Poisson-Boltzmann surface area of the wild type and H5, it was elucidated that H5 possessed a large population of interconvertible conformations, resulting in the weaker substrate binding free energy. The calculated RIN topology parameters such as the average degree, average cluster coefficient, and average path length further verified that the mutant H5 attenuated residue-to-residue interactions. The investigation of the mechanisms by which how the residue mutation affects the stability and activity of enzymes provides a theoretical basis for the development of cold-adapted protease.

Background Syntrichia caninervis, a representative stress-tolerant moss, thrives under extreme conditions such as extreme temperatures, drought, and intense radiation, making it a top candidate for extraterrestrial colonization. However, whether the ecological adaptation traits of S. caninervis are consistent across different distribution areas and microhabitats and the interactive relationships among functional traits remain unclear. This study employed a plant trait network (PTN) approach to examine the relationships among 25 functional traits of S. caninervis within and outside shrub habitats to assess its ecological adaptability in temperate desert.ResultShrub microhabitats increased the biomass, leaf morphology, and photosynthetic efficiency of S. caninervis by improving the local hydrothermal environment while reducing the physiological stress response. The trait network of S. caninervis under shrub presented a relatively high edge density and average clustering coefficient and relatively low network diameter, average path length, and degree of modularity. These findings suggest that shrubs enhance trait network connectivity and functional collaboration of S. caninervis, effectively mitigating drought stress and optimizing resource utilization efficiency. Central trait analysis revealed that, under shrub conditions, Fv/Fm and soluble sugars were central traits, whereas exposed area, Fv/Fm and POD were central traits. As precipitation decreased and temperature increased, the leaf area and photosynthetic activity of S. caninervis initially tended to increase but then decreased. Simultaneously, its trait network connectivity strengthened, with both modularity and local tightness gradually increasing, reflecting its adaptation to drought and high-temperature stress through trait synergy and functional modular specialization. Structural equation modeling (SEM) analysis revealed that climate dominated the ecological adaptability of S. caninervis through both direct and indirect pathways, whereas shrubs significantly alleviated the negative impacts of drought stress by improving hydrothermal conditions. This study not only reveals the physiological adaptation strategies of moss species in extreme environments but also provides new insights into the adaptive mechanisms of moss species in desert ecosystems.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12870-025-07384-y.

In recent years, increasing attention has been paid to the study of brain connectivity in order to detect brain abnormalities and to raise awareness of brain disorders like Autism spectrum disorder (ASD). In these studies, the brain connectivity network is estimated and its graph parameters are extracted to aid researchers in analyzing brain function and its disorders during various tasks. Selecting the suitable effective connectivity estimator which is able to estimate linear and nonlinear causal relationships is an important issue in accurate estimation of effective connectivity network and exploring its disorders. In this paper, we address this issue and also investigate the effect of choosing the effective connectivity estimator on detected abnormalities of effective connectivity graph of ASD subjects. Two well-known effective connectivity estimators are used: transfer entropy (TE) and granger causality index (GCI). We first simulate three different networks whose their causal connections have different linearity conditions and compare the sensitivity and specificity of TE and GCI in each case. It is shown that except in completely linear networks, TE generally outperforms GCI in terms of both sensitivity and specificity. In the next step, each of TE and GCI is applied to an EEG dataset recorded during a face processing task from two groups of healthy control (He) individuals and people with ASD. The networks estimated from the subjects of two groups are compared in terms of average degree, average path length and total clustering coefficient. It can be seen that just the average degree is significantly different (higher) in healthy subjects than in ASD patients by using both TE and GCI. So the results of both TE and GCI are in accordance with the underconnectivity theory of ASD.

To enhance the accuracy of computer-aided diagnosis of adolescent depression based on electroencephalogram signals, this study collected signals of 32 female adolescents (16 depressed and 16 healthy, age: 16.3 ± 1.3) with eyes colsed for 4 min in a resting state. First, based on the phase synchronization between the signals, the phase-locked value (PLV) method was used to calculate brain functional connectivity in the θ and α frequency bands, respectively. Then based on the graph theory method, the network parameters, such as strength of the weighted network, average characteristic path length, and average clustering coefficient, were calculated separately ( P < 0.05). Next, using the relationship between multiple thresholds and network parameters, the area under the curve (AUC) of each network parameter was extracted as new features ( P < 0.05). Finally, support vector machine (SVM) was used to classify the two groups with the network parameters and their AUC as features. The study results show that with strength, average characteristic path length, and average clustering coefficient as features, the classification accuracy in the θ band is increased from 69% to 71%, 66% to 77%, and 50% to 68%, respectively. In the α band, the accuracy is increased from 72% to 79%, 69% to 82%, and 65% to 75%, respectively. And from overall view, when AUC of network parameters was used as a feature in the α band, the classification accuracy is improved compared to the network parameter feature. In the θ band, only the AUC of average clustering coefficient was applied to classification, and the accuracy is improved by 17.6%. The study proved that based on graph theory, the method of feature optimization of brain function network could provide some theoretical support for the computer-aided diagnosis of adolescent depression.

Many complex networks exist to facilitate the transport of material or information. In this capacity, the authors are often concerned with the continued flow of material or information when a fraction of the links in the complex network is disrupted. In other words, the authors are interested in the robustness of the complex network. In this paper, the authors survey measures of robustness like the average path length, the average clustering coefficient, the global efficiency, the size of largest cluster and use these to analyze the robustness of the bus network in Hanoi, Vietnam. The authors find that the bus network is robust against random failure but sensitive to targeted attack, in agreement with its scale-free character. By examining sharp drops in the average path length within the largest cluster of the Hanoi bus network under successive targeted attack, the authors identify five nodes whose loss lead to the fragmentation of the network into five or six disconnected clusters. These isolated clusters represent geographically the Central, Western, Southern, and Northwestern districts of Hanoi. Special considerations must therefore be given to these five nodes when planners wish to expand the bus network, or make it more robust.

In this paper we hypothesize that education, especially at the scale of curriculum, should be treated as a complex system composed of different ideas and concepts which are inherently connected. Therefore, the task of a good teacher lies in elucidating these connections and helping students make their own connections. Such a pedagogy allows students to personalize learning and strive to be ‘creative’ and make meaning out of old ideas. The novel contribution of this work lies in the mathematical approach we undertake to verify our hypothesis. We take the example of a precalculus course curriculum to make our case. We treat textbooks as exemplars of a specific pedagogy and map several texts into networks of isolated (nodes) and interconnected concepts (edges) thereby permitting computations of metrics which have much relevance to the education theorists, teachers and all others involved in the field of education. We contend that network metrics such as average path length, clustering coefficient and degree distribution provide valuable insights to teachers and students about the kind of pedagogy which encourages good teaching and learning.

In real world, many networks have self-similar structures at different length scales. In this paper, we propose a family of growing symmetrical networks based on toy-model from a deterministic initial graph. We aim to analyze its topological properties, such as the average path length, clustering coefficient and degree distribution, which uses iterative calculations and recursive methods.

Graph theory has been widely used to study structural and functional brain connectivity changes in healthy aging, and occasionally with clinical samples; in both cases, during task-related and resting-state experiments. Recent studies have focused their interest on dynamic changes during a resting-state fMRI register in order to identify differences in non-stationary patterns associated with the aging process. The objective of this study was to characterize resting-state fMRI network dynamics in order to study the healthy aging process. 114 healthy older adults were measured in a resting-state paradigm using fMRI. A sliding-window approach to graph theory was used to measure the mean degree, average path length, clustering coefficient, and small-worldness of each subnetwork, and the impact of age and time in each graph measure was assessed. A combined effect of age and time was detected in mean degree, average path length, and small-worldness, where participants aged 75 to 79 showed a curvilinear trend with reduced network density and increased small-world coefficient in the middle of the register. An effect of age was observed on average path length, with younger participants showing slightly lower scores.

The effective representation of complex systems relies heavily on optimizing network models that capture their intricate and dynamic interdependencies. This study introduces a novel category of polygonal, fractal networks characterized by distinct alteration patterns and structural properties. Through a comprehensive examination of the statistical and topological characteristics of these networks, including clustering coefficient, average path length, degree distribution, and network density, we investigate their properties. A rigorous analysis combining mathematical modeling and empirical evaluation reveals that these fractal networks possess emergent scale-free and small-world properties, which are essential for conferring robustness and efficient information flow. Our findings provide valuable insights into the dynamics of complex systems and lay the groundwork for understanding and designing more efficient network-based systems in socioeconomic and biological contexts. This analysis not only theoretically confirms predictions related to fractal and complex networks but also enhances understanding of the adaptability and scalability of these structures.