Node Betweenness Centrality Research Articles

Robustness analysis of edge-coupled interdependent networks under different attack strategies

The robustness of interdependent networks has been a focus of research on complex networks, and the issue of attacks has become a popular research topic. However, some existing works have revealed significant vulnerabilities in interdependent networks, and the research on its robustness has been limited to node-coupled networks. While in reality, many networks are edge-coupled, and their robustness analysis has been overlooked. This paper constructs edge-coupled networks with positive, negative and random coupling based on the characteristics of edge-coupled interdependent networks. The sublayers use Erdös–Rényi (ER) random networks and scale-free (SF) networks, and four attack strategies, which includes intentional node/edge attack and random node/edge attack, are used to analyze the robustness of different edge-coupled interdependent networks. Seven edge/node importance indicators are proposed by considering node betweenness centrality, degree and eigenvector centrality, and these indicators are applied to attack strategies for result analysis, corresponding methods for enhancing robustness are proposed. The analysis results indicate that under intentional attacks, networks with negative coupling exhibit the strongest robustness, and its robustness can be influenced by their sublayers. In an environment with 500 nodes and an average degree of 4, when there is an ER network in the sublayer, protecting nodes/edges with high degree can improve the robustness of networks. If the sublayers are only composed of many SF networks, the betweenness centrality will have a greater impact when attacking most edges. While under random attacks, the networks with positive coupling exhibit the strongest robustness.

Estimation and update of betweenness centrality with progressive algorithm and shortest paths approximation

Betweenness centrality is one of the key measures of the node importance in a network. However, it is computationally intractable to calculate the exact betweenness centrality of nodes in large-scale networks. To solve this problem, we present an efficient CBCA (Centroids based Betweenness Centrality Approximation) algorithm based on progressive sampling and shortest paths approximation. Our algorithm firstly approximates the shortest paths by generating the network centroids according to the adjacency information entropy of the nodes; then constructs an efficient error estimator using the Monte Carlo Empirical Rademacher averages to determine the sample size which can achieve a balance with accuracy; finally, we present a novel centroid updating strategy based on network density and clustering coefficient, which can effectively reduce the computation burden of updating shortest paths in dynamic networks. The experimental results show that our CBCA algorithm can efficiently output high-quality approximations of the betweenness centrality of a node in large-scale complex networks.

The recoverability of network controllability with respect to node additions

Network controllability is a critical attribute of dynamic networked systems. Investigating methods to restore network controllability after network degradation is crucial for enhancing system resilience. In this study, we develop an analytical method based on degree distributions to estimate the minimum fraction of required driver nodes for network controllability under random node additions after the random removal of a subset of nodes. The outcomes of our method closely align with numerical simulation results for both synthetic and real-world networks. Additionally, we compare the efficacy of various node recovery strategies across directed Erdös–Rényi (ER) networks, swarm signaling networks (SSNs), and directed Barabàsi Albert (BA) networks. Our findings indicate that the most efficient recovery strategy for directed ER networks and SSNs is the greedy strategy, which considers node betweenness centrality. Similarly, for directed BA networks, the greedy strategy focusing on node degree centrality emerges as the most efficient. These strategies outperform recovery approaches based on degree centrality or betweenness centrality, as well as the strategy involving random node additions.

Potential biomarker for early detection of ADHD using phase-based brain connectivity and graph theory.

This research investigates an efficient strategy for early detection and intervention of attention-deficit hyperactivity disorder (ADHD) in children. ADHD is a neurodevelopmental condition characterized by inattention and hyperactivity/impulsivity symptoms, which can significantly impact a child's daily life. This study employed two distinct brain functional connectivity measurements to assess our approach across various local graph features. Six common classifiers are employed to distinguish between children with ADHD and healthy control. Based on the phase-based analysis, the study proposes two biomarkers that differentiate children with ADHD from healthy control, with a remarkable accuracy of 99.174%. Our findings suggest that subgraph centrality of phase-lag index brain connectivity within the beta and delta frequency bands could be a promising biomarker for ADHD diagnosis. Additionally, we identify node betweenness centrality of inter-site phase clustering connectivity within the delta and theta bands as another potential biomarker that warrants further exploration. These biomarkers were validated using a t-statistical test and yielded a p-value of under 0.05, which approved their significant difference in these two groups. Suggested biomarkers have the potential to improve the accuracy of ADHD diagnosis and could help identify effective intervention strategies for children with the condition.

Effective Brain Connectivity Extraction by Frequency-Domain Convergent Cross-Mapping (FDCCM) and Its Application in Parkinson's Disease Classification.

Inferring causal or effective connectivity between measured timeseries is crucial to understanding directed interactions in complex systems. This task is especially challenging in the brain as the underlying dynamics are not well-understood. This paper aims to introduce a novel causality measure called frequency-domain convergent cross-mapping (FDCCM) that utilizes frequency-domain dynamics through nonlinear state-space reconstruction. Using synthesized chaotic timeseries, we investigate general applicability of FDCCM at different causal strengths and noise levels. We also apply our method on two resting-state Parkinson's datasets with 31 and 54 subjects, respectively. To this end, we construct causal networks, extract network features, and perform machine learning analysis to distinguish Parkinson's disease patients (PD) from age and gender-matched healthy controls (HC). Specifically, we use the FDCCM networks to compute the betweenness centrality of the network nodes, which act as features for the classification models. The analysis on simulated data showed that FDCCM is resilient to additive Gaussian noise, making it suitable for real-world applications. Our proposed method also decodes scalp-EEG signals to classify the PD and HC groups with approximately 97% leave-one-subject-out cross-validation accuracy. We compared decoders from six cortical regions to find that features derived from the left temporal lobe lead to a higher classification accuracy of 84.5% compared to other regions. Moreover, when the classifier trained using FDCCM networks from one dataset was tested on an independent out-of-sample dataset, it attained an accuracy of 84%. This accuracy is significantly higher than correlational networks (45.2%) and CCM networks (54.84%). These findings suggest that our spectral-based causality measure can improve classification performance and reveal useful network biomarkers of Parkinson's disease.

Functional connectivity analysis on electroencephalography signals reveals potential biomarkers for treatment response in major depression

BackgroundThe treatment efficacy varies across individual patients with major depressive disorder (MDD). It lacks robust electroencephalography (EEG) markers for an antidepressant-responsive phenotype.MethodThis is an observational study enrolling 28 patients with MDD and 33 healthy controls (mean age of 40.7 years, and 71.4% were women). Patients underwent EEG exams at baseline (week0) and week1, while controls’ EEG recordings were acquired only at week0. A resting eye-closing EEG segment was analyzed for functional connectivity (FC). Four parameters were used in FC analysis: (1) node strength (NS), (2) global efficiency (GE), (3) clustering coefficient (CC), and (4) betweenness centrality (BC).ResultsWe found that controls had higher values in delta wave in the indices of NS, GE, BC, and CC than MDD patients at baseline. After treatment with antidepressants, patients’ FC indices improved significantly, including GE, mean CC, and mean NS in the delta wave. The FC in the alpha and beta bands of the responders were higher than those of the non-responders.ConclusionsThe FC of the MDD patients at baseline without treatment was worse than that of controls. After treatment, the FC improved and was close to the values of controls. Responders showed better FC in the high-frequency bands than non-responders, and this feature exists in both pre-treatment and post-treatment EEG.

Enhancing the Robustness of Scale-Free Networks: The Simulation of Cascade Failures with Adjustable Initial Load Parameters

A reasonable definition of nodes load and capacity is essential for improving the robustness of scale-free networks against cascading failure, which has gained significant attention over recent years. This paper presents two methods for defining the load-capacity model: a degree-based method and a betweenness-based method. In these methods, the initial load and capacity of nodes were determined by considering the degrees and betweenness centrality of nodes and their neighbors. These values could be adjusted using both global and local parameters. This paper achieved load redistribution during cascading failures through targeted attacks on network nodes. In addition, this study applied load redistribution to cascading failure processes in networks by targeting network nodes. In order to evaluate the effectiveness of the proposed approach, this paper examines the impact of adjusting two parameters on the minimum critical tolerance coefficient and network robustness. Computer-generated scale-free networks and a real network were used for evaluation purposes. The findings indicated that higher global parameters resulted in a lower average robustness index. Moreover, our degree-based method demonstrated a smaller minimum critical tolerance coefficient and average robustness index compared to existing load definition methods. Therefore, the proposed methods enhanced the robustness and integrity of scale-free networks against attacks.

A novel method to assess urban multimodal transportation system resilience considering passenger demand and infrastructure supply

With the continuous construction of urban infrastructure, urban multi-modal transportation system (UMTS) has gradually become complex and intertwined, which makes the system more uncertain and vulnerable, especially under disruptions. Improving the resilience of UMTS is critical to maintaining urban reliability and sustainability. This paper aims to build effective models to assess the resilience of UMTS. To develop the resilience assessment model, we provide a comprehensive, dynamic index that considers passenger demand and infrastructure supply. Three transportation modes are considered: bus, subway and taxi, and a cascading failure model is simulated. Data from Singapore are collected to analyse resilience indicators’ characteristics and explore relationship between resilience indicators and node measures. The results indicate that 1) when stations experience failure, it has the greatest impact on the accessibility of the transportation network, followed by efficiency and connectivity; 2) system resilience is negatively related to the node degree and node betweenness centrality of the attacked station; 3) beyond a certain threshold, continuing to increase stations’ additional capacity does not significantly increase system resilience. The proposed resilience index can be used as an optimization goal during system design and recovery. The conclusions and recommendations can inform the management and improvement of urban transportation system resilience.

Disrupted topological organization of white matter structural networks in high myopia patients revealed by diffusion kurtosis imaging and tractography.

High myopia (HM) is a public health issue that can lead to severe visual impairment. Previous studies have exhibited widespread white matter (WM) integrity damage in HM patients. However, how these WM damages are topologically related, and the network-level structural disruptions underlying HM has not been fully defined. We aimed to assess the alterations of brain WM structural networks in HM patients using diffusion kurtosis imaging (DKI) and tractography in the present study. Individual whole-brain and ROI-level WM networks were constructed using DKI tractography in 30 HM patients and 33 healthy controls. Graph theory analysis was then applied to explore the altered global and regional network topological properties. Pearson correlations between regional properties and disease duration in the HM group were also assessed. For global topology, although both groups showed a small-world network organization, HM patients exhibited significant decreased local efficiency and clustering coefficient compared with controls. For regional topology, HM patients and controls showed highly similar hub distributions, except for three additional hub regions in HM patients including left insula, anterior cingulate and paracingulate gyri (ACG), and median cingulate and paracingulate gyri (DCG). In addition, HM patients showed significantly altered nodal betweenness centrality (BC) mainly in the bilateral inferior occipital gyrus (IOG), left superior occipital gyrus (SOG), caudate nucleus, rolandic operculum and right putamen, pallidum, and gyrus rectus compared with controls. Intriguingly, the nodal BC of left IOG was negatively correlated with disease duration in HM patients. Our findings suggest that HM exhibited alterations in WM structural networks as indicated by decreased local specialization. This study may advance the current understanding of the pathophysiological mechanisms underlying HM.

Functional brain network based multi-domain feature fusion of hearing-Impaired EEG emotion identification

In the past, Electroencephalography (EEG)-based emotion identification research mainly focused on healthy, disordered, or depressed subjects. Due to the lack of an emotion acquisition and expression channel, there may be a bias in affective cognition for the hearing impaired. In this work, 15 hearing-impaired subjects were recruited to participate in an emotional movie-induced experiment, while their EEG signals were collected for emotion recognition. Four types of movie clips, which contained happiness, calmness, sadness, and fear, were selected. We fused three kinds of features, differential entropy (DE), power spectral density (PSD), and functional brain network to integrate the frequency domain and the spatial domain information of EEG signals. To find the brain region connections of different emotions, different coupling methods, and binarization methods were explored. Moreover, the combination of different brain network attributes was used to find the representativeness of emotional information in the spatial domain. The experimental results show that the combination of phase-locked value (PLV) & 20% sparsity with four brain network attributes (clustering coefficient (CC), node degree (ND), node betweenness centrality (NBC), and node strength (NS)) achieved a higher accuracy of 94.17% for functional brain network-based emotion recognition. In addition, the method of feature fusion obtained a classification accuracy of 95.91% with an SVM-Linear classifier. Moreover, by constructing functional brain network, the key connectivity paths of different emotions are explored, which may provide insights into understanding the emotional processing of the hearing-impaired.

A routing method with adaptively adjusting memory information based on local routing history.

Finding the shortest paths for packets from sources to destinations in packet-switched communication networks is an inevitable problem in building a future high-speed information society. A routing method with memory information has already been proposed to alleviate the congestion of large volumes of packet flow. This routing method shows a high transmission completion rate even for large volumes of packet flows in communication networks with scale-free properties. However, the method exhibits poor performance for networks with local triangular connections and long distances between nodes. To overcome these problems, in this study, we first enhanced the routing performance of the conventional communication network models by using the betweenness centrality of nodes, which is one of the network centralities that measures the number of shortest paths that pass through each node in the networks. Subsequently, we adaptively changed the transmitting paths of packets by using only local information. Numerical simulations indicated that our routing method performs successfully for various topologies of communication networks by avoiding the congested node, and effectively using the memory information.

Network analysis of pore structure of coral reef limestone and its implications for seepage flow

Determining the seepage characteristics of coral reef limestone is highly significant for engineering activities on relevant strata. In this paper, the pore structure information of two types of coral reef limestones with distinct pore characteristics was obtained by combining computed tomography (CT) scanning technology and pore network modeling. We regarded the pore structure of coral reef limestone as a complex network, and the seepage inside is analogous to information transmission. Network analysis was performed on this network considering both global and individual network indicators. It was shown that the pore network of coral reef limestones has a short seepage distance and strong connectivity, and exhibits a prominent clustering effect. The centrality of network nodes indicated that very few pore nodes have extremely high centrality. Based on the Dijkstra algorithm, the shortest percolation paths along three orthogonal directions were obtained and visualized for both samples. This showed that the shortest percolation paths always converge to a few paths in all directions for a pore network of coral reef limestone with coarse pores. There existed a preferential seepage path characterized by more intensive shortest percolated paths. Some pore nodes with higher betweenness centrality were located at a crucial location in a few shortest percolation paths. A new indicator VB considering both the volume and betweenness centrality of the pore node was proposed. Those pore nodes with large VB values were identified as key pore nodes in the network, as seepage simulations showed that blockage of these key nodes causes a dramatic decrease in permeability.

Electricity-Related Water Network Analysis in China Based on Multi-Regional Input–Output Analysis and Complex Network Analysis

The transfer of electricity-related water across regions and sectors provides an opportunity to alleviate water stress and make the development of the power system sustainable. Yet, the key node identification and properties of the electricity-related water network have not been studied. In this study, the properties and key nodes of the regional sectoral electricity-related water network in China were analyzed based on a multi-regional input–output model and complex network analysis. An iterative method was proposed to calculate the water consumption index inventory. The results showed electricity transmission can affect the regional water consumption index. Degree, intensity, betweenness centrality, and closeness centrality indicators of nodes were used to identify the key nodes. Sector 24 in Shandong was the key node with the largest closeness centrality. Sector 9 in Xinjiang was the key node with the largest betweenness centrality. They were the best choice for establishing points to observe and control flows, respectively. The transfer network did not have the small-world nature with the average clustering coefficient being 0.478 and the average path length being 2.327. It is less likely to cause large-scale clustering change in the network. This study can provide references for the common sustainable development of power systems and water resources.

Habitats Within the Plant Root Differ in Bacterial Network Topology and Taxonomic Assortativity.

The root microbiome is composed of distinct epiphytic (rhizosphere) and endophytic (endosphere) habitats. Differences in abiotic and biotic factors drive differences in microbial community diversity and composition between these habitats, though how they shape the interactions among community members is unknown. Here, we coupled a large-scale characterization of the rhizosphere and endosphere bacterial communities of 30 plant species across two watering treatments with co-occurrence network analysis to understand how root habitats and soil moisture shape root bacterial network properties. We used a novel bootstrapping procedure and null network modeling to overcome some of the limitations associated with microbial co-occurrence network construction and analysis. Endosphere networks had elevated node betweenness centrality versus the rhizosphere, indicating greater overall connectivity among core bacterial members of the root endosphere. Taxonomic assortativity was higher in the endosphere, whereby positive co-occurrence was more likely between bacteria within the same phylum while negative co-occurrence was more likely between bacterial taxa from different phyla. This taxonomic assortativity could be driven by positive and negative interactions among members of the same or different phylum, respectively, or by similar niche preferences associated with phylum rank among root inhabiting bacteria across plant host species. In contrast to the large differences between root habitats, drought had limited effects on network properties but did result in a higher proportion of shared co-occurrences between rhizosphere and endosphere networks. Our study points to fundamentally different ecological processes shaping bacterial co-occurrence across root habitats. [Formula: see text] Copyright © 2023 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license.

Evaluation Method for Node Importance of Urban Rail Network Considering Traffic Characteristics

As a sustainable means of public transport, the safety of the urban rail transit is a significant section of public safety and is highly important in urban sustainable development. Research on the importance of urban rail stations plays an important role in improving the reliability of urban rail networks. This paper proposed an improved method for evaluating the importance of urban rail stations in a topology network, which was used to identify the key stations that affect the urban rail network performance. This method was based on complex network theory, considering the traffic characteristics of the urban rail network that runs on specific lines and integrating the structural characteristics and interrelationship of the lines where the stations are located. Hereafter, this method will be abbreviated as CLI. In order to verify that the high importance stations evaluated by this method were the key stations that had a great impact on the urban rail network performance, this paper designed a comparative attack experiment of betweenness centrality and CLI. The experiment was carried out by taking the Suzhou Rail Transit (SZRT) network as an example and the largest connected subgraph as well as the network efficiency as indicators to measure the network performance. The results showed that CLI had a greater impact on network performance and could better evaluate the key stations in the urban rail network than node degree and betweenness centrality.

Altering patterns of sensorimotor network in patients with different pathological diagnoses and glioma-related epilepsy under the latest glioma classification of the central nervous system.

We aimed to clarify the relationship between alterations in functional networks and glioma-related epilepsy (GRE) in patients with different molecular diagnoses. We enrolled 160 patients with prefrontal gliomas and different histories of GRE. The patients were grouped based on the latest pathological glioma classification and GRE history. Graph theory analysis was applied to reveal alterations in the sensorimotor networks among various subgroups. Binary logistic regression was used to identify risk factors for preoperative GRE onset. Decreasing shortest path length was found in patients with GRE, regardless of the chromosome 1p/19q status. Nodes located in the premotor and supplementary motor areas showed decreased nodal betweenness centrality and vulnerability in patients with GRE and chromosome 1p/19q intact. Additionally, the node on the primary motor area showed decreased nodal vulnerability but the node on the sensory-related thalamus increased in patients with GRE and chromosome 1p/19q co-deletion. Decreased shortest path length, grade 2, and decreased nodal betweenness centrality of the premotor area were risk factors for GRE. Decreased shortest path length was a characteristic alteration in GRE and prefrontal glioma. Alterations in global properties were similar, but nodal properties were different in patients with GRE and different chromosome 1p/19q statuses.

C3P-RPL: A collaborative and proactive approach for optimal peer to peer path selection and sustenance

Internet of Things is evolving from information gathering platforms into collaborative systems wherein, smart devices actively interact with each other in a seamless manner. For instance, Internet of Robotic Things is envisioned to provide augmented solutions through collaboration of varied smart devices and robots. These visions revolve around the ability of smart devices to directly communicate and cooperate with each other in real time. In this context, this paper is an attempt to study RPL’s (Routing Protocol for Low-power Lossy Networks) point to point routing that creates multi-hop paths between peer nodes. This standard routing protocol is known for robust and failsafe upward paths but its peer to peer (P2P) routes are reported to be suboptimal. This work assesses P2P performance of RPL’s storing mode in a network of new generation devices having higher memory. Further, a Collaborative and Proactive Peer to Peer (C3P) path selection and sustenance approach is proposed where, root node collates incremental topology from collaborative nodes and disseminates optimal single source shortest path trees SPT(n). A progressive node betweenness centrality score ensures spread out paths. Minor topology changes are accommodated through incremental node and edge updates to targeted SPT(n) locally. Storing SPTs in intermediate nodes reduces storage and packet size. Through simulations and testbed experiments, it is proven that C3P-RPL improves simultaneous peer to peer communication between all the nodes. Specifically, the path length is reduced by 30% and subsequently the network latency drops by 65% in an experimental testbed of 47 nodes, making it suitable for collaborations.

Influence of link-addition strategies on network balance and passenger experience in rail networks

The performance of a network can be enhanced by adding links. The importance of the rail network augmentation scheme comparison is brought into the forefront because of the long lead time and disproportionate high cost. This work focuses on the influence of the addition link among the initial railway stations on passenger flow. The effectiveness of the network was evaluated by flow imbalance (FIB), average transfer times (ATT), average path length (APL), and the combined evaluation using three different strategies, namely, passenger flow load — subgraphs highest node (PFL-S), passenger flow load — least load (PFL-L), and node degree and betweenness centrality (Degree-BC). The case study on the real urban rail network with 2,211,468 trip records a day at 339 stations show that PFL-S and PFL-L have better performance than Degree-BC. Simulation experiments reveal that the link construction investment at the early stage during the expanding or in the network with less existing transfer stations for the same size can receive greater returns than those nearly completed networks. The proposed method not only provides a policy guidance for the sustainable development of rail networks but also offers a reference for other networks with limited flow loading capacity and high-cost constraints.

Meta-governance, uncertainty and self-organization in corporatist social service sectors: The case of Hong Kong

This article explores the relationship between meta-governance, uncertainty and governance network responses. A social network analysis was conducted on the interlocking directorate network among nonprofits before and after a market-oriented collibration triggered by a new public management reform to the corporatist social service provision system in Hong Kong. By unpacking and showing the distinct processes of network formation in response to substantive and strategic uncertainty arising from the market-oriented collibration, the study shows that although more nonprofit actors were directly included in the formalized policy venues after the reform, the network density and clustering coefficient dropped after the reform, potentially reducing the self-coordinating capacity of the governance network. However, for some nonprofit actors, node betweenness centrality increased and node degree centrality decreased, creating an enabling condition for adaption. Points for practitioners The uncertainties in meta-governance may bring about network processes at variance with the original intentions of public meta-governors that actors with complementary resources and competences combine their efforts in the provision of services and service innovation. To manage substantive and strategic uncertainties, public meta-governors need to find ways to increase the shared understandings of social problems, enhance the clarity of policy goals, and find a balance when collaborating between collaborative and market modes of governance.

Altered whole-brain resting-state functional connectivity and brain network topology in typhoon-related post-traumatic stress disorder.

Altered resting-state functional connectivity has been found in patients with post-traumatic stress disorder (PTSD). However, the alteration of resting-state functional connectivity at whole-brain level in typhoon-traumatized individuals with PTSD remains largely unknown. To investigate changes in whole-brain resting-state functional connectivity and brain network topology in typhoon-traumatized subjects with and without PTSD. Cross-sectional study. Twenty-seven patients with typhoon-related PTSD, 33 trauma-exposed controls (TEC), and 30 healthy controls (HC) underwent resting-state functional MRI scanning. The whole brain resting-state functional connectivity network was constructed based on the automated anatomical labeling atlas. The graph theory method was used to analyze the topological properties of the large-scale resting-state functional connectivity network. Whole-brain resting-state functional connectivity and the topological network property were compared by analyzing the variance. There was no significant difference in the area under the curve of γ, λ, σ, global efficiency, and local efficiency among the three groups. The PTSD group showed increased dorsal cingulate cortex (dACC) resting-state functional connectivity with the postcentral gyrus (PoCG) and paracentral lobe and increased nodal betweenness centrality in the precuneus relative to both control groups. Compared with the PTSD and HC groups, the TEC group showed increased resting-state functional connectivity between the hippocampus and PoCG and increased connectivity strength in the putamen. In addition, compared with the HC group, both the PTSD and TEC groups showed increased connectivity strength and nodal efficiency in the insula. Aberrant resting-state functional connectivity and topology were found in all trauma-exposed individuals. These findings broaden our knowledge of the neuropathological mechanisms of PTSD.