Node Degree Research Articles

Altered individual-based morphological brain network in type 2 diabetes mellitus.

Type 2 diabetes mellitus (T2DM) is recognized as a risk factor for cognitive decline, potentially linked to disrupted network connectivity. However, few previous studies have examined individual-based morphological brain networks in T2DM and their association with clinical characteristics. In our study, we enrolled 123 patients with T2DM and 91 healthy controls (HC). We constructed the networks using symmetric KL divergence-based similarity (KLS) and calculated various global and nodal metrics based on graph theory to describe the topological properties of the networks. Firstly, T2DM exhibited increased nodal degree in the left para-hippocampus, left amygdala, left precuneus, bilateral putamen, and right inferior temporal gyrus, and the concentrations of glycosylated hemoglobin (HbA1c) were positively correlated with the nodal degree of the left precuneus. Secondly, we identified hypo-connected and hyper-connected subnetworks, primarily involved with reward circuits and attention network, respectively. Lastly, altered morphological connectivity (MC) was linked to cognitive performance, and the aforementioned subnetworks may serve as predictors of cognitive performance. In conclusion, this study provided neuroimaging evidence for understanding cognitive changes by analyzing the properties and connections of iSCN in T2DM patients.

Identification of Key Risk Factors in Mechanical Cross Passage Construction Based on the Decision-Making Test and Evaluation Test Method and the Interpretation Structure Model

In order to solve the problem that the key risk factors in the construction of mechanical cross passages are relatively vague, the decision-making test and evaluation test method (DEMATEL) and the interpretation structure model (ISM) are combined to analyze safety risks in the construction of mechanical cross passages scientifically and reasonably. Based on the ‘personnel’, ‘material’, ‘machine’, ‘method’, and ‘environment’ of 4M1E comprehensive management, the construction safety risk index system of mechanical method cross passage, including 18 risk factors, is extracted. DEMATEL was used to divide the risk factors into four factor sets: strong cause, weak cause, strong result, and weak result. Furthermore, ISM is used to construct a hierarchical structure diagram of risk factors, and deep risk factors and risk factors with a high node degree are divided. The results show that the safety awareness of construction personnel, the safety technology level of construction personnel, the establishment and implementation of the safety construction system, the level of construction management, and the degree of geological complexity are strong cause-type risk factors with both high centrality and high causality. Additionally, the effect of reinforcement of the internal support system, the setting of the digging parameter, the effect of grouting, and the effect of assembling the pipe sheet comprise the strong result-type risk factors with high centrality. The risk factors with higher node degree in ISM are consistent with the risk factors with higher centrality in the DEMATEL model, which are key factors that play an important role in risk control.

Correlation of P53 expression and epithelial-mesenchymal transition in non-small cell lung cancer.

Investigation of a potential prognostic marker expressed in non-small cell lung cancer (NSCLC) can help patients benefit from new target therapeuticmodalities. To study the expression and correlation of P53 protein and epithelial-mesenchymal transition (EMT) related makers in NSCLC. 32 cases were selected for immunohistochemistry analysis to evaluate the expression of P53 and EMT-related makers. The positive expression rate of P53 and the incidence of EMT in NSCLC were closely linked to TNM stages, differentiation degree, and lymph node metastasis (P < 0.05). A positive association was found between P53 and EMT (r = 0.380, P < 0.05). There is a positive association between P53, snail, and EMT. P53 may affect EMT in NSCLC by up-regulating the expression of Snail and further promoting cancer invasion and metastasis.

Topology Control of Low-Connection UAV Laser Network with Virtual Nodes

Space laser communication technology has advantages such as high bandwidth and low interference, but the limitation of the load capacity of an unmanned aerial vehicle (UAV) makes it difficult for UAV clusters to have sufficient communication links to build a stable communication network. Aiming to address the problem of the low upper limit of the node degree of the self-organized network after the introduction of space laser communication technology for UAVs, a virtual node topology control (VNTC) algorithm is proposed for constructing an efficient and stable communication network structure. The algorithm is based on the unit disc graph model and achieves a lower-node-degree upper bound while maintaining connectivity through node pairing and virtual graph construction. The theoretical analysis and experimental results of the algorithm show that the algorithm can effectively deal with the topology control problem in UAV laser networks. In contrast to the XTC algorithm (exceptional topology control), the VNTC algorithm maintains the connectivity and most of the planarizability of the network, and, at the same time, it performs better in reducing the node degree and number of edges, thus providing an effective solution for low-connectivity topology control.

Network Analyses to Explore Comorbidities Among Older Adults Living With Dementia.

Older persons living with dementia (PLWD) often have multiple other chronic health conditions (i.e., comorbidities). Network analyses can describe complex profiles of chronic health conditions through graphical displays grounded in empirical data. Our study compared patterns of chronic health conditions among PLWD residing in and outside of long-term care (LTC) settings. Population-based administrative data, including outpatient physician claims, inpatient records, pharmaceutical records, and LTC records, for the study were from the Canadian province of Manitoba. We included PLWD, ages ≥ 67 years, with two or more other chronic health conditions, who resided in Manitoba from 2017 to 2020. A total of 138 chronic health conditions were ascertained using a modification of the open-source Clinical Classification Software. Networks defined by nodes (health conditions) and edges (associations between nodes) were stratified by residence location (in versus outside LTC). Network properties were described, including: density (ratio of number of edges to number of potential edges), and modularity (associations between and within clusters of health conditions), and the median and interquartile range (IQR) for node degree (number of associations per node). The population comprised 19,672 PLWD, of which 17,534 (89.1%) had two or more chronic health conditions. The median number of co-occurring conditions was similar among PLWD in LTC (median: 6, IQR: 3-10) versus outside LTC (median: 7, IQR: 4-10). Network properties were similar for PLWD and multiple comorbidities residing in versus outside LTC, including node degree (median 11 vs. 12), density (0.15 vs. 0.14), and modularity (0.18 vs. 0.26). Multiple chronic diseases characterize PLWD residing in and outside of LTC. Using network analyses, chronic diseases among PLWD do not form easily distinguishable groups or patterns. This suggests the need for comprehensive clinical assessments, individualized approaches for disease management, and highlights the importance of person-specific care.

Abnormal alterations in structure-function coupling at the modular level in patients with postherpetic neuralgia

To investigate the presence of modular loss of coupling and abnormal alterations in functional and structural networks in the brain networks of patients with postherpetic neuralgia (PHN). We collected resting-state functional magnetic resonance imaging data and diffusion tensor imaging data from 82 healthy controls (HCs) and 71 PHN patients, generated structural connectivity (SC) and functional connectivity (FC) networks, and assessed the corresponding clinical information assessment. Based on AAL(90) mapping, the brain network was divided into 9 modules, and the structural–functional connectivity (SC–FC) coupling was compared at the whole-brain level and within the modules, as well as alterations in the topological properties of the brain network in the patient group. Finally, correlation analyses were performed using the following clinical scales: Visual Analogue Scale (VAS), Hamilton Anxiety Scale (HAMA), and Hamilton Depression Scale (HAMD). Compared with HCs, patients with PHN had reduced global efficiency (Eg) and local efficiency (Eloc) of structural and functional networks. The FC in the PHN group presented abnormal node clustering coefficients (NCp), local node efficiencies (NLe), and node efficiencies (Ne), and the SC presented abnormal node degrees (Dc), NCp, NLe, characteristic path lengths (NLp), and Ne. In addition, SC–FC coupling was reduced in the patient default network (DMN), salient network (SN), and visual network (VIS). Moreover, the degree of impairment of graph theory indicators was significantly positively correlated with scales such as VAS scores, and the coupling of modules was significantly negatively correlated with the early course of the patient’s disease. Large-scale impaired topological properties of the FC and SC networks were observed in patients with PHN, and SC–FC decoupling was detected in these modules of the DMN, SN, and VIS. These aberrant alterations may have led to over-transmission of pain information or central sensitization of pain.

Evolution characteristics and invulnerability simulation analysis of global zirconium ore trade network

The burgeoning demand for zirconium, driven by the rapid development of smart devices, low-carbon energy technologies, and other emerging industries, underscores the importance of understanding the dynamics of its global trade network. However, the evolutionary patterns of the international zircon ore trade network and its resilience to disruptions remain unclear. This study constructs the international zircon ore trade network from 2013 to 2022, analyzes its structural evolution at both the network and node levels, and evaluates its robustness in 2022 using five attack strategies: random node removal, random edge removal, edge degradation, targeted removal based on node degree, and targeted removal based on node betweenness centrality. Our findings reveal that: (1) the international zircon ore trade network exhibits a shift in the import market towards Asia, with the export market dominated by Spain, the United States, and Brazil. China plays a crucial role as a bridge connecting various countries, while Japan exerts significant influence within the network; (2) the network is particularly vulnerable to targeted attacks based on node degree and betweenness centrality, highlighting the potential for significant disruption following the removal of key nodes. This study provides valuable insights for ensuring the stable and sustainable supply and consumption of zirconium resources, informing the development of targeted policies for countries and relevant industries.

Altered Intracerebellar Functional Connectivity in Friedreich’s Ataxia: A Graph-Theory Functional MRI Study

Historically, Friedreich’s Ataxia (FRDA) has been linked to a relatively preserved cerebellar cortex. Recent advances in neuroimaging have revealed altered cerebello-cerebral functional connectivity (FC), but the extent of intra-cerebellar FC changes and their impact on cognition remains unclear. This study investigates intra-cerebellar FC alterations and their cognitive implications in FRDA. In this cross-sectional, single-center study, resting-state functional MRI data from 17 patients with FRDA (average age 27.7 ± 13.6 years; F/M = 6/11) and 20 healthy controls (HC) (average age 29.4 ± 9.7 years; F/M = 9/11), all of whom underwent neuropsychological testing, were analyzed. From functional connectivity matrices, graph measures were computed at both the network and node levels using two complementary parcellations. FRDA patients exhibited decreased global efficiency (p = 0.04), nodal degree (p = 0.001) and betweenness centrality (p = 0.04) in the vermal portion of lobule VIII, along with reduced global efficiency in cerebellar regions belonging to the Control-A network (p = 0.02), one of the three subdivisions of the Frontoparietal network. Verbal memory deficits correlated with global efficiency in both the vermal portion of lobule VIII (r = 0.53, p = 0.02) and the cerebellar regions of the Control-A network (r = 0.49, p = 0.05). Graph analysis revealed regional intra-cerebellar FC changes in FRDA, marked by reduced functional centrality in cerebellar regions of the vermis and responsible for executive functions. These changes correlated with cognitive alterations, highlighting the role of the cerebellar cortex in the cognitive impairment observed in FRDA.

Evolutionary Game Analysis of Complex Networks in Enterprise Green Technology Innovation From a Prospect Theory Perspective

ABSTRACTGreen technological innovation in enterprises is a key driving force for achieving sustainable development and industrial transformation. However, how enterprises formulate effective innovation strategies by integrating subjective factors with objective market conditions within complex industrial networks remains an area requiring further exploration. This study aims to construct a complex network evolution model based on prospect theory and examines how subjective factors, such as reference points, risk preferences, and loss aversion, influence the adoption of green technology innovation in different network environments. It further explores how network characteristics, including topology, size, and node degree, affect the diffusion of innovation. Numerical analysis results indicate that in scale‐free networks, lowering reference points for enterprise gains, reducing loss aversion, increasing risk preference, expanding network size, and raising average node degree generally promote higher adoption of green technology innovation. In small‐world networks, the dependence on reference points is relatively lower, risk preference and average node degree demonstrate more complex impacts. Additionally, a moderate rewiring probability can enhance green technology innovation adoption in small‐world networks. These findings provide new insights and practical implications for understanding the driving mechanisms of green technological innovation in enterprises. They further emphasize the importance of government interventions tailored to the specific characteristics of industrial networks to effectively facilitate the diffusion of green technological innovation.

Accurate identification of snoRNA targets using variational graph autoencoder to advance the redevelopment of traditional medicines.

Existing studies indicate that dysregulation or abnormal expression of small nucleolar RNA (snoRNA) is closely associated with various diseases, including lung cancer. Furthermore, these diseases often involve multiple targets, making the redevelopment of traditional medicines highly promising. Accurate prediction of potential snoRNA therapeutic targets is essential for early disease intervention and the redevelopment of traditional medicines. Additionally, researchers have developed artificial intelligence (AI)-based methods to screen and predict potential snoRNA therapeutic targets, thereby advancing traditional drug redevelopment. However, existing methods face challenges such as imbalanced datasets and the dominance of high-degree nodes in graph neural networks (GNNs), which compromise the accuracy of node representations. To address these challenges, we propose an AI model based on variational graph autoencoders (VGAEs) that integrates decoupling and Kolmogorov-Arnold Network (KAN) technologies. The model reconstructs snoRNA-disease graphs by learning snoRNA and disease representations, accurately identifying potential snoRNA therapeutic targets. By decoupling similarity from node degree, the model mitigates the dominance of high-degree nodes, enhances prediction accuracy in scenarios like lung cancer, and leverages KAN technology to improve adaptability and flexibility to new data. Case studies revealed that snoRNA SNORA21 and SNORD33 are abnormally expressed in lung cancer patients and are strong candidates for potential therapeutic targets. These findings validate the proposed model's effectiveness in identifying therapeutic targets for diseases like lung cancer, supporting early screening and treatment, and advancing the redevelopment of traditional medicines. Data and experimental findings are archived in: https://github.com/shmildsj/data.

Vulnerability analysis of power grid structure based on complex network theory

IntroductionThe key nodes of an intelligent distribution network significantly impact the reliability and stability of the distribution network’s operation. The failure of these key nodes can severely affect the safe operation of the distribution network. Therefore, vulnerability analysis of key nodes is particularly important.MethodsThis article proposes a comprehensive weighting method for evaluating indicators,combining the analytic hierarchy process (AHP) and entropy weighting method, while considering the structure and operational status of the power system grid. Key node structural evaluation indicators, such as node degree, node shrinkage centrality, and electric mediator, are established considering “significance” and “destructiveness.” State indicators are established based on the degree of impact of current, voltage, and load changes on the grid, as well as the uniformity of their distribution, including the improved current distribution entropy, voltage terre entropy, and three-phase state indicators of lost load. Subsequently, based on the AHP and entropy weighting method, a comprehensive weighting method is proposed to assign subjective and objective weights to the comprehensive evaluation indicators, obtaining the comprehensive weights of the indicators. Finally, the gray correlation degree is introduced to improve the ideal solution of the multi-objective decision making method, obtaining the criticality of the grid nodes and then identifying the critical nodes.Results and DiscussionThe example analysis presented in this article shows that the identified critical nodes of the power grid have a high degree of overlap with the identification results of different methods, can better identify edge nodes, and validate the effectiveness of the proposed evaluation indicators and key node identification methods.

Adaptive Neural Message Passing for Inductive Learning on Hypergraphs.

Graphs are the most ubiquitous data structures for representing relational datasets and performing inferences in them. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations. This drawback is mitigated by hypergraphs, in which an edge can connect an arbitrary number of nodes. Most hypergraph learning approaches convert the hypergraph structure to that of a graph and then deploy existing geometric deep learning methods. This transformation leads to information loss, and sub-optimal exploitation of the hypergraph's expressive power. We present HyperMSG, a novel hypergraph learning framework that uses a modular two-level neural message passing strategy to accurately and efficiently propagate information within each hyperedge and across the hyperedges. HyperMSG adapts to the data and task by learning an attention weight associated with each node's degree centrality. Such a mechanism quantifies both local and global importance of a node, capturing the structural properties of a hypergraph. HyperMSG is inductive, allowing inference on previously unseen nodes. Further, it is robust and outperforms state-of-the-art hypergraph learning methods on a wide range of tasks and datasets. Finally, we demonstrate the effectiveness of HyperMSG in learning multimodal relations through detailed experimentation on a challenging multimedia dataset.

Effects of electroconvulsive therapy on functional connectome abnormalities in adolescents with depression and suicidal ideation.

Major depressive disorder (MDD) in adolescents is associated with an increased risk of suicide, and electroconvulsive therapy (ECT) is an effective treatment for MDD and suicidal ideation. To investigate underlying central mechanisms, this study examined functional connectome topological organization in adolescents with MDD and suicidal ideation prior to and following ECT. Resting-state fMRI images were collected from 28 adolescents with MDD and suicidal ideation and 31 demographically similar healthy adolescents. Whole-brain functional networks were constructed and topological metrics were analyzed using graph theory approaches. Prior to ECT, depressed adolescents showed disrupted global and nodal properties, indicating altered functional connectivity. Following ECT, significant reductions in depression and suicidality symptoms were observed, with a 75 % response rate. ECT led to an increase in the small-worldness of the brain network, suggesting restoration of functional connectivity. Significant improvements were seen in nodal properties, particularly in the central executive network. Group-by-time interactions revealed differences between responders and non-responders in nodal degree and efficiency. Larger sample sizes and extended followed-up periods following ECT treatment are needed to further investigate the neural basis of clinical changes. The results of this study reveal dynamic changes in brain network topology of adolescents with depression during the course of ECT, and have an advanced understanding of the neurobiological biomarkers associated with the efficacy of ECT treatment.

A novel method for functional brain networks based on static cerebral blood flow.

Cerebral blood flow (CBF) offers a quantitative and reliable measurement for brain activity and is increasingly used to study functional networks. However, current methods evaluate inter-regional relations mainly based on CBF temporal dynamics, which suffers from low signal-to-noise ratio and poor temporal resolution. Here we proposed a method to construct functional brain networks by estimating shape similarity (index by Jensen-Shannon divergence) in probability distributions of regional static CBF measured by arterial spin labeling perfusion imaging over a scanning period. Based on CBF data of 30 healthy participants from 10 visits, we found that the CBF networks exhibited non-trivial topological features (e.g., small-world organization, modular architecture, and hubs) and showed low-to-fair test-retest reliability and high between-subject consistency. We further found that interregional CBF similarities were depended on anatomical distance and differed between high- and lower-order subnetworks. Moreover, interregional CBF similarities within high-order subnetworks showed significantly lower reliability than those within low-order subnetworks. Finally, we showed that nodal degree of the CBF networks were related to regional sizes and CBF levels and spatially aligned with maps of the dopamine transporter and metabolic glutamate receptor 5 intensities, expression levels of genes primarily enriched in cholesterol-related pathways and endothelial cells, and meta-analytic activations related to memory, language, and executive function. Altogether, our proposed method provide a novel, relatively reliable, and neurobiologically meaningful means to study functional network organization of the human brain.

A time-domain finite element formulation of the equivalent fluid model for the acoustic wave equation

Sound-absorptive materials such as foam can be described by the equivalent fluid (EF) model. The homogenized fluid’s acoustic behavior is thereby described by complex-valued, frequency-dependent acoustic material parameters. When transforming the acoustic wave equation for the EF model from the frequency domain to the time domain, convolution integrals arise. The auxiliary differential equation (ADE) method is used to circumvent the direct calculation of these convolution integrals. The wave equation and the coupled set of ordinary ADEs are solved in the time domain using the finite element (FE) method. The approach relies on approximating the complex-valued frequency response functions of the inverse equivalent bulk modulus and density by a sum of rational functions consisting of real and complex poles. The order of the rational function approximation defines the number of additionally introduced auxiliary variables per nodal degree of freedom. The presented FE formulation includes a narrow-band non-reflecting boundary condition (NRBC) for normal incidence. The implementation in openCFS shows optimal temporal and spatial convergence for a semi-infinite duct based on the analytic plane wave solution for harmonic excitation. The simulation of a pressure pulse propagating in an infinite EF domain with a scatterer demonstrates the capability for multidimensional, actual transient problems.

Potential therapeutic intervention of melatonin against COVID-19: A comparative pharmacokinetic study

Melatonin synthesis is primarily regulated by environmental light-dark cycle and is well known for its biological rhythm regulation and its potent antioxidant and anti-inflammatory properties across species. The present investigation focuses on the potential actions of melatonin as a therapeutic agent against COVID-19 and these actions are compared with other commonly used pharmacological agents of this kind including methylprednisolone, doxycycline, oseltamivir, and remdesivir. The comprehensive comparisons of pharmacokinetic profiles include their absorption, distribution, metabolism, and excretion (ADME) properties. The further in-depth analyses on their target identification, functional enrichment are performed by Gene Ontology (GO), Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways, construction of protein-protein interaction (PPI) networks, and molecular docking. These analyses elucidate the potential correlation of melatonin with critical hub targets implicated in COVID-19 pathogenesis. The results from pharmacokinetics indicates that melatonin has the higher bioavailability than the other tested drugs due to its low molecular weight, lipophilicity, lack of P-glycoprotein (P-gp) along with inhibitory action on cytochrome P450 1A2 (CYP1A2). GO and enriched KEGG analyses suggests that melatonin-mediated modulation of COVID-19 pathogenesis likely targets the AGE-RAGE pathway, HIF-1α signaling, and apoptosis. Furthermore, PPI network analysis also shows that melatonin has the highest nodes and edges, as well as the greatest average node degree score and highest common potential targets with the genes associated with the development of COVID-19. Notably, molecular docking study demonstrates the substantial interactions of melatonin with principal hub targets TP53, AKT1, IL6, TNF, IL1B, BCL2, EGFR, STAT3, CASP3, and NFKB1. Hence, melatonin has several significant pharmacokinetic advantages compared to selected therapeutic agents which may appear to modulate multiple facets of COVID-19 pathology. Based on the significant pharmacokinetic advantages of melatonin over the commonly used other drugs, the substantial clinical studies are necessary to establish its methods of application as a potential therapeutic against SARS-CoV-2 in the near future.

Relationship between δ-catenin expression and whole-brain small-world network in breast cancer patients before chemotherapy

Our study aimed to investigate the relationship between δ-catenin expression and whole-brain small-world network in breast cancer patients before chemotherapy using rs-fMRI. The study was based on the hypothesis that different δ-catenin expression levels correspond to distinct brain imaging characteristics. A total of 105 pathologically confirmed breast cancer patients were collected and categorized into high δ-catenin expression (DH, 52 cases) and low expression (DL, 53 cases) groups. Additionally, 36 age-matched healthy women were enrolled as a healthy control group (HC). The results demonstrated differences in several network topology attributes among the three groups. Furthermore, in addition to differences in nodal efficiency, betweenness, and degree centrality metrics observed between the patient groups and HCs across multiple brain regions, significant alterations were also identified between the DL and DH groups, particularly in the supramarginal gyrus and inferior frontal gyrus. Correlation analysis revealed associations between cognitive and memory-related brain regions, such as the caudate nucleus and frontal lobe, and scores on cognitive and verbal memory scales (all P < 0.05). This study concludes that high and low expression levels of δ-catenin in breast cancer patients are associated with distinct whole-brain network topology patterns, and that these differences in network segregation and integration functions are associated with alterations in cognition and verbal memory.

Altered neurovascular coupling and structure-function coupling in Moyamoya disease affect postoperative collateral formation

Chronic ischemia in moyamoya disease (MMD) impaired white matter microstructure and neural functional network. However, the coupling between cerebral blood flow (CBF) and functional connectivity and the association between structural and functional network are largely unknown. 38 MMD patients and 20 sex/age-matched healthy controls (HC) were included for T1-weighted imaging, arterial spin labeling imaging, resting-state functional MRI and diffusion tensor imaging. All patients had preoperative and postoperative digital subtraction angiography. Upon constructing the structural connectivity (SC) and functional connectivity (FC) networks, the SC-FC coupling was calculated. After obtaining the graph theoretical parameters, neurovascular coupling represented the spatial correlation between node degree centrality (DC) of functional networks and CBF. The CBF-DC coupling and SC-FC coupling were compared between MMD and HC groups. We further analyzed the correlation between coupling indexes and cognitive scores, as well as postoperative collateral formation. Compared with HC, CBF-DC coupling was decreased in MMD (p = 0.021), especially in the parietal lobe (p = 0.047). SC-FC coupling in MMD decreased in frontal, occipital, and subcortical regions. Cognitive scores were correlated with the CBF-DC coupling in frontal lobes (r = 0.394, p = 0.029) and SC-FC coupling (r = 0.397, p = 0.027). The CBF-DC coupling of patients with good postoperative collateral formation was higher (p = 0.041). Overall, neurovascular decoupling and structure-functional decoupling at the cortical level may be the underlying neuropathological mechanisms of MMD.

Structure and dynamics analysis of brain functional hypernetworks based on the null models.

Brain functional hypernetworks that can characterize the complex and multivariate interactions among multiple brain regions have been widely used in the diagnosis and prediction of brain diseases. However, there are few studies on the structure and dynamics of brain functional hypernetworks. Such studies can help to explore how the important functional features of brain functional hypernetworks characterize the working and pathological mechanisms of the human brain. Therefore, this article introduces the hypernetwork null model to analyze the dependencies between the features of interest. Specifically, first, based on the original brain functional hypernetwork, this article proposed the optimized hyper dK-series algorithm with hyperedges to construct null models that preserved the different node attributes and hyperedge attributes of the original brain functional hypernetwork, respectively. Next, based on the original hypernetwork model and the null model, multiple node attributes and hyperedge attributes were respectively introduced. Then, the level of similarity and correlation between the topological attributes of the original brain functional hypernetwork and the topological attributes of the brain functional hypernetwork null model were calculated to analyze the dependencies between the features of interest. The results showed that there were differences in the level of dependence between the features of interest. Node degree is the main dependency attribute for multiple metrics. Hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient are partial dependency attributes for some metrics. The dependency attributes and level of dependency are the same for the hypernetwork clustering coefficients-HCC2 and HCC3. This indicates that the node degree is redundant with respect to other attributes, while the hyperedge degree, node degree-dependent redundancy coefficient, and hyperedge degree-dependent redundancy coefficient perhaps contain other topology information. In addition, there is redundancy between HCC2 and HCC3. Therefore, the effects of these redundant attributes need to be considered when performing network analysis.

A novel approach to Fuzzy mixed graph structure with application towards trade relations between countries

Many of the phenomena around us are a combination of directed and undirected relationships between different subjects, which will be more complex despite the existence of multiple relationships between objects. For example, in business relations between countries and social networks, communication is sometimes one-way or two-way. Checking and processing such information is managed in mixed graphs. Previous research has been based on the assumption that there is a general relationship between all vertices in a mixed graph. In this article, a new framework for fuzzy information management is introduced by combining fuzzy mixed graph and graph structure along with mentioning its properties. The concept of connectedness has been considered as one of the topics in this study. In this regard, some of their properties were examined by introducing some basic concepts such as paths, cycles, bridges, and cut vertices. Also, some attributes such as degree, neighborhood, order and size are defined. The results showed that although there existed a close relationship between the fuzzy mixed graph structure and the graph structure, the existence of multiple and distinct relationships between the vertices has created new definitions of concepts. This change can be seen especially in the degree of nodes and neighborhoods. Finally, its application in the field of trade relations between countries is presented.