Node Degree Research Articles

An effective logarithm-degree resource allocation strategy for three-layer networks

Conventional resource allocation strategies, such as the Simplest Average (SA) resource allocation strategy, often assume identical transmission capacity for all nodes, failing to account for the actual importance of nodes within the network, especially in three-layer networks where inadequate resource allocation to hub nodes can significantly impact performance. Existing methods are primarily designed for single-layer networks and struggle to address the complexity and interdependencies of real-world multi-layer structures, thus limiting the optimization of network traffic capacity. This paper proposes an Effective Logarithm-Degree (EL) resource allocation strategy that allocates node delivery capacity based on the ratio of the logarithmic degrees of nodes across the logical and physical layers. Compared to the Simplest Average resource allocation strategy, the Effective Logarithm-Degree strategy significantly enhances network traffic capacity, increasing it by over 1.4 times and reducing traffic load by 60%, while also optimizing the load balance. Simulation results validate the superiority of the Effective Logarithm-Degree strategy in improving performance and resource utilization efficiency in three-layer network environments.

A simulated annealing algorithm for randomizing weighted networks.

Scientific discovery in connectomics relies on network null models. The prominence of network features is conventionally evaluated against null distributions estimated using randomized networks. Modern imaging technologies provide an increasingly rich array of biologically meaningful edge weights. Despite the prevalence of weighted graph analysis in connectomics, randomization models that only preserve binary node degree remain most widely used. Here we propose a simulated annealing procedure for generating randomized networks that preserve weighted degree (strength) sequences. We show that the procedure outperforms other rewiring algorithms and generalizes to multiple network formats, including directed and signed networks, as well as diverse real-world networks. Throughout, we use morphospace representation to assess the sampling behavior of the algorithm and the variability of the resulting ensemble. Finally, we show that accurate strength preservation yields different inferences about brain network organization. Collectively, this work provides a simple but powerful method to analyze richly detailed next-generation connectomics datasets.

Aberrant network topological structure of sensorimotor superficial white-matter system in major depressive disorder.

White-matter tracts play a pivotal role in transmitting sensory and motor information, facilitating interhemispheric communication and integrating different brain regions. Meanwhile, sensorimotor disturbance is a common symptom in patients with major depressive disorder (MDD). However, the role of aberrant sensorimotor white-matter system in MDD remains largely unknown. Herein, we investigated the topological structure alterations of white-matter morphological brain networks in 233 MDD patients versus 257 matched healthy controls (HCs) from the DIRECT consortium. White-matter networks were derived from magnetic resonance imaging (MRI) data by combining voxel-based morphometry (VBM) and three-dimensional discrete wavelet transform (3D-DWT) approaches. Support vector machine (SVM) analysis was performed to discriminate MDD patients from HCs. The results indicated that the network topological changes in node degree, node efficiency, and node betweenness were mainly located in the sensorimotor superficial white-matter system in MDD. Using network nodal topological properties as classification features, the SVM model could effectively distinguish MDD patients from HCs. These findings provide new evidence to highlight the importance of the sensorimotor system in brain mechanisms underlying MDD from a new perspective of white-matter morphological network.

Effects of higher-order interactions and impulsive vaccination for rumor propagation.

This paper introduces a rumor propagation model with saturation incidence, based on hypergraph theory. Hypergraphs can capture the higher-order interactions between nodes in a social network, where the node degree is substituted with hyperdegree. First, the threshold for rumor spreading model is obtained, the global asymptotically stable of the rumor-free equilibrium, and the global attractive and global asymptotically stable of the rumor-prevailing equilibrium are proved. Then, we incorporate impulsive vaccination into the model to represent the guided effect, simulating the periodic educational activities organized by official institutions to counteract rumor dissemination. By employing the comparison theorem, the paper demonstrates the global attractiveness of the rumor-free periodic solution and the persistence of the model. Finally, through numerical simulations, the paper compares the effects of higher-order and pairwise interactions on rumor spreading, validating the theoretical conclusions. The results indicate that higher-order interactions can promote rumor spreading, while impulsive vaccination can effectively decrease the scale of rumor spreading.

Risk evolution and prevention and control strategies in emergency responses for Arctic maritime transportation

The intertwined and complex risks involved in the various stages of the Arctic maritime transportation emergency response severely hinder the response's effectiveness. The present study aims to develop a risk coupling network involved in the Arctic maritime transportation emergency response. First, an Arctic maritime transportation emergency response scenario is defined by reviewing SAR manuals and agreements, emergency guidelines of ships, and emergency drill videos. Second, the control structure of the emergency response process is systematically analyzed through Systems-theoretic process analysis, and a risk coupling network with task-layer, unsafe control actions-layer, and risk-layer is developed. Third, the robustness of the risk coupling network is stimulated by random and deliberate attacks, where deliberate attacks are based on the measured results of node degree, betweenness centrality, and integrated values. Finally, critical risk factors are determined based on the results of the network robustness analysis, and targeted prevention and control strategies of critical risk factors for the Arctic maritime transportation emergency response are proposed. The research findings suggest that equipment/system failures, personnel experience and expression capabilities, the effects of high-latitude magnetic fields, response times to assistance requests, and the preparedness of emergency resources should be focused on during Arctic maritime transportation emergency response.

A Niche Quantum Ant Colony Multifaceted Routing Algorithm for WSN-based IoT Networks in the Emerging Quantum Industry

Quantum computing (QC) is an important area of technological study. The ever-growing network size and complexity in quantum computation research are the cause of evolutionary dynamics in QC. The Internet of Things (IoT) is a paradigm shift in thinking; it advances many forms of communication that rely on WSNs to gather data, and it has the potential to be even more effective with the help of quantum computing. Network congestion results in lost packets, delayed transmissions, and wasted effort during recovery. In an attempt to improve the efficiency and velocity of the route, the proposed method considers a number of objectives. Since quantum computers leverage the characteristics of quantum states to do certain computations at orders of magnitude quicker than classical computers, this is an exciting new direction to investigate. This study introduced the Niche Quantum Ant Colony Multifaceted Routing Algorithm (NQAC-MRA), a method for optimizing wireless distributed networks in IoT routes that combines quantum computation, an optimization function for several objectives, and monitoring. Producing cost-effective routing that is congestion-aware for alarm message transmission over WSN-IoT and for alert message transmission utilizing IoT devices to their respective destinations with the lowest latency is the primary goal of this study. To be more specific, the quantum bits stand in for the node pheromone, and turning quantum gates modifies the search path's pheromone. Nodes' power consumption, communication delay, and degree of network load-balancing serve as fitness metrics to find the best communication path. According to the results of the performance analysis, the suggested scheme is both lightweight and more effective than the alternatives. The performance research showed that the proposed approach outperformed the alternatives while being significantly lighter. The suggested NQAC-MRA beat its competitors in terms of total simulation results thanks to its reduced energy usage and enhanced performance.

A Multivariate and Network Analysis Uncovers a Long-Term Influence of Exclusive Breastfeeding on the Development of Brain Morphology and Structural Connectivity.

Exclusive breastfeeding (eBF) in infancy appears to offer a developmental advantage for children's brains compared to formula-fed counterparts. Existing research has predominantly focused on global brain measures (i.e., total white/grey matter volumes) or on limited sets of specific brain regions, in selected age groups, leaving uncertainties about the impact of eBF on the overall structural connectomes. In this cross-sectional study encompassing participants from childhood to adulthood, partial least squares correlations (PLSC) were employed to assess white and grey matter volumes. Furthermore, a network analytic approach was used to estimate the structural connectome based on cortical thickness data. The results revealed that eBF duration correlated with increased white matter volumes in children and with the volume of the medial orbital gyrus in adults. Structural connectome analyses demonstrated heightened anatomical connectivity in eBF children, evidenced by enhanced network density and local/global efficiency, along with increased node degree and local efficiency in frontal and temporal lobes. Similarly, eBF in adults was associated to an improved node connectivity in the frontal lobe. These findings imply a lasting impact of eBF on brain morphometry and structural connectivity. Childhood benefits include heightened white matter development, while in adulthood, eBF may contribute to reduced neural loss associated with aging and enhanced connectivity, particularly in frontal regions.

Advances in the application of network analysis methods in traditional Chinese medicine research

ObjectiveThis review aims at evaluating the role and potential applications of network analysis methods in the medicinal substances of traditional Chinese medicine (TCM), theories of TCM compatibility, properties of herbs, and TCM syndromes. MethodsLiterature was retrieved from databases, such as CNKI, PubMed, and Web of Science, using keywords, including "network analysis," "network biology," "network pharmacology," and "network medicine." The extracted literature included the biological network construction (including ingredient-target and target-disease relations), analysis of network topology characteristics (including node degree, clustering coefficient, and path length), network modularization analysis, functional annotation and so on. These studies were categorized and organized based on their research methods, application domains, and other relevant characteristics. ResultsNetwork analysis algorithms, such as network distance, random walk, matrix factorization, graph embedding, and graph neural networks, are widely applied in fields related to the properties, compatibility, and mechanisms of TCM. They effectively reflect the interactive relations within the complex systems of TCM and elucidate and clarify theories, such as the effective substances, the principles of TCM compatibility, the TCM syndromes, and the properties of TCM. ConclusionThe network analysis method is a powerful mathematical and computational tool that reveals the structure, dynamics, and functions of complex systems by analyzing the elements and their relations. This approach has effectively promoted the modernization of TCM, providing essential theoretical and practical tools for personalized treatment and scientific research on TCM. It also offers a significant methodological framework for the modernization and internationalization of TCM.

Network analysis of lawyer referral markets: Evidence from Indiana

AbstractUsing network analysis, we study referrals among plaintiff‐side lawyers handling medical malpractice cases in Indiana. The referral network is stratified, with a few highly connected “hub” firms. Firm connectivity follows a power law distribution—suggesting that new entrants tend to associate with already well‐connected firms, rather than starting a new network. Regression analysis shows that, for a given firm, connectivity (i.e., node degree) in the referral network and being loyal to a smaller number of firms both lead to better outcomes in non‐referred cases. The referral network also became more concentrated over time. The stratification of the market for plaintiff‐side representation is reinforced through these processes.

Unsupervised definition of two clinical subtypes of Essential tremor and the underlying brain topology

BackgroundEssential tremor (ET) is one of the most prevalent neurological diseases varying considerably in clinical manifestations and prognosis, which indicates the existence of subtypes. Identifying ET subtypes is crucial for explaining clinical heterogeneity. This study aimed to identify ET subtypes using unsupervised clustering analysis based on clinical manifestations and explore underlying brain topology within both functional and structural networks. MethodsWe recruited 103 ET patients and 43 healthy control subjects. K-means clustering analysis was performed to identify ET subtypes based on age of onset, motor and non-motor symptoms. Functional MRI and diffusion tensor imaging data were used to construct functional and structural networks. Global attributes (clustering coefficient, characteristic path length, global efficiency, and local efficiency) and nodal attributes (nodal clustering coefficient, nodal efficiency, and nodal degree centrality) were calculated for topological analysis. ResultsWe identified two subtypes: Subtype 1 (earlier age of onset – without nonmotor symptoms subtype) and Subtype 2 (later age of onset – with nonmotor symptoms subtype). Decreased clustering coefficient and global efficiency, increased characteristic path length were observed in Subtype 2 compared to NC, while only decreased global efficiency was observed in Subtype 1. More widespread brain regions with decreased nodal clustering coefficient were specifically observed in Subtype 2. ConclusionWe identified two ET subtypes based on comprehensive clinical information and revealed that Subtype 2 may be a more malignant subtype. Our study firstly unsupervisedly identifies the clinical heterogeneity of ET and provides neuroimaging evidence for better understanding the underlying disease biology.

Atypical brain network topology of the triple network and cortico-subcortical network in autism spectrum disorder

The default mode network (DMN), salience network (SN), and central executive control network (CEN) form the well-known triple network, providing a framework for understanding various neurodevelopmental and psychiatric disorders. However, the topology of this network remains unclear in autism spectrum disorder (ASD). To gain a more profound understanding of ASD, we explored the topology of the triple network in ASD. Additionally, the striatum and thalamus are pivotal centres of information transmission within the brain, and the realization of various brain functions requires the coordination of cortical and subcortical structures. Therefore, we also investigated the topology of the cortico-subcortical network in ASD, which consists of the DMN, SN, CEN, striatum, and thalamus. Resting-state functional magnetic resonance imaging data on 208 ASD patients and 278 typically developing (TD) controls (8–18 years old) were obtained from the Autism Brain Imaging Data Exchange database. We performed graph theory analysis on the triple network and the cortico-subcortical network. The results showed that the triple network’s clustering coefficient, lambda, and network local efficiency values were significantly lower in ASD, and the nodal degree and efficiency of the medial prefrontal cortex also decreased. For the cortico-subcortical network, the sigma, clustering coefficient, gamma, and network local efficiency showed the same reduction, and the altered clustering coefficient negatively correlated with ASD manifestations. In addition, the interaction between the DMN and CEN was more robust in ASD patients. These findings enhance our understanding of ASD and suggest that subcortical structures should be more considered in future ASD related studies.

Fast Identification of Critical Nodes in Complex Network Based on Improved Greedy Algorithm

Abstract Over the past decades, many critical and complex systems, such as power grid, transportation network, and information network, have been effectively modeled using complex network. However, these networks are susceptible to cascading failure, triggered by minor failure, leading to partial or total collapse. Preventing cascading failure necessitates the protection of critical nodes within the network, making the identification of these nodes particularly crucial. In this paper, we introduce an Improved Greedy Algorithm (IGA), inspired by the traditional greedy algorithm and the relationship between the propagation mechanism of cascading failure and N-K failure. This algorithm gets rid of the shortcomings of traditional recognition algorithms for dealing with large-scale networks with long time and low accuracy, and evaluates the critical degree of nodes based on network connectivity and overload rate. The simulation is carried out in Barabsi-Albert (BA) network and IEEE 39-, 118-bus systems, and make comparisons with other different algorithms. The results show that IGA not only has low computational complexity, but also has high accuracy in identifying critical nodes in complex networks.

Exponential growth rate of lattice comb polymers

Abstract We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of t teeth, also modelled as mutually and self-avoiding walks, attached to the backbone at vertices or nodes of degree 3. Each tooth of the comb has ma edges and there are mb edges in the backbone between adjacent degree 3 vertices and between the first and last nodes of degree 3 and the end vertices of degree 1 of the backbone. We are interested in the exponential growth rate as t → ∞ with ma and mb fixed. We prove upper bounds on this growth rate and show that for small values of ma the growth rate is strictly less than that of self-avoiding walks.

Comparing random walks in graph embedding and link prediction.

Random walks find extensive applications across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding generation from sequence data and their subsequent effects on link prediction remain elusive. We conduct a comparative analysis of several random walk strategies, including the true self-avoiding random walk and the traditional random walk. We also analyze walks biased towards node degree and those with inverse node degree bias. Diverse adaptations of the node2vec algorithm to induce distinct exploratory behaviors were also investigated. Our empirical findings demonstrate that despite the varied behaviors inherent in these embeddings, only slight performance differences manifest in the context of link prediction. This implies the resilient recovery of network structure, regardless of the specific walk heuristic employed to traverse the network. Consequently, the results suggest that data generated from sequences governed by unknown mechanisms can be successfully reconstructed.

Meadow degradation reduces microbial β diversity and network complexity while enhancing network stability

Continuing meadow degradation under the dual impacts of climate change and human activities has altered microbially-mediated biogeochemical cycles. However, microbial diversity and network stability in response to meadow degradation and their relationships to environmental variables remain insufficiently understood. This study focused on alpine meadows with varying degrees of degradation in the hinterland of the Qinghai-Tibetan Plateau. It analyzed the soil microbial diversity (α and β diversity) and ecological network topology characteristics under the degradation of alpine meadows. Furthermore, the extent to which these factors elucidate the environmental changes observed during degradation was explored. The results demonstrated that: (1) the α diversity of soil microbial under degradation of alpine meadows exhibited an increasing trend, although not significantly. The β diversity (community dissimilarity) exhibited a significant decreasing trend. These indicated that meadow degradation resulted in microbial homogenization intra- and inter-community. In the light degradation stage, the β diversity of bacteria and fungi significantly increased with geographic and environmental distance rise. Only bacterial β diversity significantly increased with geographical distance in the moderate degradation stage and environmental distance in the heavy degradation stage, respectively. This indicated that meadow degradation possibly altered microbial assembly, especially for fungi. (2) The degree of soil bacterial nodes exhibited a significant decreasing trend with degradation and fungal eigencentrality demonstrated a significant decreasing trend. After removing the identical nodes, the natural connectivity of the fungal network exhibited a significant decreasing trend with degradation. This suggested that the stability of the soil microbial network increased while the network complexity decreased under meadow degradation. These changes possibly marked the irreversible course of alpine meadow degradation. (3) The Mantel test indicated that bacterial diversity and network topological features were more strongly associated with environmental factors than those of fungi. Akaike information criterion (AIC) values and the upset matrix plots of variance partitioning based on Redundancy analysis (RDA) indicated that higher rates of soil factors, such as soil pH, organic carbon (SOC) content, and total potassium (TK), elucidated changes in microbial community diversity and network topological features. This study highlights the importance of soil microorganisms for ecological stability and the role of microorganisms should be emphasized in future efforts to restore alpine grasslands.

Analysis of transmission dynamics of dengue fever on a partially degenerated weighted network

In this paper, we propose a partially degenerated weighted network dynamical model for dengue fever transmission to study its spatial transmission dynamics, in which population mobility are characterized by the weighted graph Laplacian diffusion. Firstly, we establish the comparison principle for general reaction–diffusion differential equations defined on finite weighted network. Next, the well-posedness of solutions is established for the model. Then the basic reproduction number of the model is calculated, and then the stability of disease-free and endemic equilibria is investigated by means of the upper and lower solutions method and the construction of Lyapunov function. Furthermore, the uniform persistence of the model also is demonstrated. Finally, we apply the generalized weighted graph to the Watts–Strogatz network and present several numerical examples to verify theoretical results and obtain some interesting conclusions: the peak numbers of infected human population and infected mosquito populations depending on the node degree, even though the equations for the mosquito population in the model has no diffusion term.

Disrupted White Matter Topology Organization in Preschool Children with Tetralogy of Fallot.

Cognitive impairment is the most common long-term complication in children with congenital heart disease (CHD) and is closely related to the brain network. However, little is known about the impact of CHD on brain network organization. This study aims to investigate brain structural network properties that may underpin cognitive deficits observed in children with Tetralogy of Fallot (TOF). In this prospective study, 29 preschool-aged children diagnosed with TOF and 19 without CHD (non-CHD) were enrolled. Participants underwent diffusion tensor imaging (DTI) scans alongside cognitive assessment using the Chinese version of the Wechsler Preschool and Primary Scale of Intelligence-fourth edition (WPPSI-IV). We constructed a brain structural network based on DTI and applied graph analysis methodology to investigate alterations in diverse network topological properties in TOF compared with non-CHD. Additionally, we explored the correlation between brain network topology and cognitive performance in TOF. Although both TOF and non-CHD exhibited small-world characteristics in their brain networks, children with TOF significantly demonstrated increased characteristic path length and decreased clustering coefficient, global efficiency, and local efficiency compared with non-CHD (p < 0.05). Regionally, reduced nodal betweenness and degree were found in the left cingulate gyrus, and nodal efficiency was decreased in the right precentral gyrus and cingulate gyrus, left inferior frontal gyrus (triangular part), and insula (p < 0.05). Furthermore, a positive correlation was identified between local efficiency and cognitive performance (p < 0.05). This study elucidates a disrupted brain structural network characterized by impaired integration and segregation in preschool TOF, correlating with cognitive performance. These findings indicated that the brain structural network may be a promising imaging biomarker and potential target for neurobehavioral interventions aimed at improving brain development and preventing lasting impairments across the lifetime.

Altered structural covariance of the cortex and hippocampal formation in patients with lung cancer after chemotherapy

ObjectiveIn this retrospective study, we aimed to investigate changes in brain morphology and structural topological networks in patients with lung cancer (LC) with or without chemotherapy. MethodsWe retrospectively recruited 191 participants for this cross-sectional study, including 113 patients with LC without chemotherapy (Ch-), 38 patients with LC with chemotherapy (Ch+), and 40 healthy controls (HC) matched for age, sex, and education. The gray matter volume (GMV) and cortical properties were compared among the three groups. We constructed the structural covariant network (SCN) based on cortical thickness, volumes of subcortical structures, and volumes of hippocampal subfields and the amygdala in all participants. The global and nodal topological properties of SCN were compared among groups. In addition, 23 patients with LC (8 Ch+ and 15 Ch-) who received two identical brain magnetic resonance scans were enrolled in the follow-up study. The paired t-test was used to compare group differences in brain morphology and topological properties in the structural network. ResultsThe GMV of the bilateral caudate and thalamus were smaller in the Ch- and Ch+ groups compared to the HC group using threshold-free cluster enhancement and permutation (P < 0.05, 5000 times permutations) for multiple comparison correction. The cortical SCN analysis suggested multiple enhanced nodal properties in several brain areas in Ch+ and Ch- compared to HC, mainly in the temporal gyrus, using permutations test and false discovery rate (FDR) (P < 0.05) corrections. Moreover, an increased sigma was found in the Ch+ compared with HC (P = 0.0238). The reduced nodal degree (P = 0.0002) and betweenness (P = 0.0008) in the right amygdala of Ch+ compared to HC were detected by subcortical SCN analysis. Furthermore, reduced gamma (P = 0.0342) and sigma (P < 0.0001) were found in Ch- compared with HC in the SCN analysis of subfields of the amygdala-hippocampal complex. In the follow-up study, reduced nodal degree (P < 0.0001) was found in the right anterior amygdala, and reduced clustering coefficient and local efficiency were found in patients with LC after the permutation test. ConclusionsOur study showed GMV defects and structural topological property abnormalities related to LC and chemotherapy. Such morphological changes associated with LC and chemotherapy could be used as imaging markers for clinical assessments and pathological indicators.

Superradiant phase transitions in ultrastrong coupling regime

Abstract One of the long-standing problems in quantum optics and laser physics is the observation of both equilibrium and non-equilibrium (Dicke) superradiant states in two-level (qubit) systems interacting with the quantized electromagnetic (EM) field. We demonstrate that the superradiant phase transition (PT) at thermal equilibrium in such a system is close to ultrastrong light–matter coupling (USC) condition, which is currently available for superconducting devices. We examine the USC regime for EM fields interacting with two-level systems located in highly connected graph nodes of photonic networks beyond the rotating wave approximation. We find that a critical matter–field coupling parameter reduces ⟨ k ⟩ times due to network peculiarities providing suitable conditions for equilibrium PT observation; ⟨ k ⟩ is a network average node degree. We study the non-equilibrium (Dicke) superradiance for the same network system and show that superradiance appears as a non-equilibrium PT to the superradiant laser operating within a bad cavity limit. We show that population inversion in this case plays the same role as the reciprocal temperature inherent to the equilibrium superradiant PT. Our results open new perspectives for experimental observation of superradiance in cavity-free systems in the gigahertz photonic regime and beyond.

ADRP-DQL: An adaptive distributed routing protocol for underwater acoustic sensor networks using deep Q-learning

Underwater Wireless Sensor Networks (UWSNs) face unique constraints due to their unstructured and dynamic underwater environment. Data gathering from these networks is crucial as energy resources are limited. In this regard, efficient routing protocols are needed to optimize energy consumption, increase the network lifetime, and enhance data delivery in these networks. In this work, we develop an Adaptive Distributed Routing Protocol for UWSNs using Deep Q-Learning (ADRP-DQL). This protocol employs the ability of reinforcement learning to dynamically learn the best routing decisions based on the network’s state and action-value estimates. It allows nodes to make intelligent routing decisions, considering residual energy, depth and node degree. A Deep Q-Network (DQN) is employed as the function approximator to estimate action values and choose the optimal routing decisions. The DQN is trained using off-policy and on-policy strategies and the neural network model. Simulation results demonstrate that ADRP-DQL performs well regarding energy efficiency (EE), data delivery ratio, and network lifetime. The results highlight the proposed protocol’s effectiveness and adaptability to UWSNs. The ADRP-DQL protocol contributes to intelligent routing for UWSNs, offering a promising approach to enhance performance and optimize energy utilization in these demanding environments.