Network Topological Metrics Research Articles

Network topology metrics explaining enrichment of hybrid epithelial/mesenchymal phenotypes in metastasis.

Epithelial to Mesenchymal Transition (EMT) and its reverse-Mesenchymal to Epithelial Transition (MET) are hallmarks of metastasis. Cancer cells use this reversible cellular programming to switch among Epithelial (E), Mesenchymal (M), and hybrid Epithelial/Mesenchymal (hybrid E/M) state(s) and seed tumors at distant sites. Hybrid E/M cells are often more aggressive and metastatic than the "pure" E and M cells. Thus, identifying mechanisms to inhibit hybrid E/M cells can be promising in curtailing metastasis. While multiple gene regulatory networks (GRNs) based mathematical models for EMT/MET have been developed recently, identifying topological signatures enriching hybrid E/M phenotypes remains to be done. Here, we investigate the dynamics of 13 different GRNs and report an interesting association between "hybridness" and the number of negative/positive feedback loops across the networks. While networks having more negative feedback loops favor hybrid phenotype(s), networks having more positive feedback loops (PFLs) or many HiLoops-specific combinations of PFLs, support terminal (E and M) phenotypes. We also establish a connection between "hybridness" and network-frustration by showing that hybrid phenotypes likely result from non-reinforcing interactions among network nodes (genes) and therefore tend to be more frustrated (less stable). Our analysis, thus, identifies network topology-based signatures that can give rise to, as well as prevent, the emergence of hybrid E/M phenotype in GRNs underlying EMP. Our results can have implications in terms of targeting specific interactions in GRNs as a potent way to restrict switching to the hybrid E/M phenotype(s) to curtail metastasis.

Combined brain network topological metrics with machine learning algorithms to identify essential tremor.

Essential tremor (ET) is a common movement syndrome, and the pathogenesis mechanisms, especially the brain network topological changes in ET are still unclear. The combination of graph theory (GT) analysis with machine learning (ML) algorithms provides a promising way to identify ET from healthy controls (HCs) at the individual level, and further help to reveal the topological pathogenesis in ET. Resting-state functional magnetic resonance imaging (fMRI) data were obtained from 101 ET and 105 HCs. The topological properties were analyzed by using GT analysis, and the topological metrics under every single threshold and the area under the curve (AUC) of all thresholds were used as features. Then a Mann-Whitney U-test and least absolute shrinkage and selection operator (LASSO) were conducted to feature dimensionality reduction. Four ML algorithms were adopted to identify ET from HCs. The mean accuracy, mean balanced accuracy, mean sensitivity, mean specificity, and mean AUC were used to evaluate the classification performance. In addition, correlation analysis was carried out between selected topological features and clinical tremor characteristics. All classifiers achieved good classification performance. The mean accuracy of Support vector machine (SVM), logistic regression (LR), random forest (RF), and naïve bayes (NB) was 84.65, 85.03, 84.85, and 76.31%, respectively. LR classifier achieved the best classification performance with 85.03% mean accuracy, 83.97% sensitivity, and an AUC of 0.924. Correlation analysis results showed that 2 topological features negatively and 1 positively correlated with tremor severity. These results demonstrated that combining topological metrics with ML algorithms could not only achieve high classification accuracy for discrimination ET from HCs but also help us to reveal the potential topological pathogenesis of ET.

An efficient supply management in water flow network using graph spectral techniques.

An efficient way of distributing water in urban cities is one of the major global challenges of our time. A Water Distribution Network (WDN) is a vital infrastructure, intended to provide fresh water to households within a city or designated boundary. Given the WDN's complexity, effective numerical techniques are required to aid in the development of an ideal monitoring system. Flow meters and gate valves should be placed in low-connected areas of the WDN with water flow reaching several regions of the network. This study proposes a general strategy for assisting water utilities in making decisions for effective water supply. The aim of the research is to use weighted spectral clustering algorithms to outline water districts while addressing hydraulic restrictions via weighted adjacency and Laplacian matrices of the weighted network. This work aims to identify influenced nodes in the network based on Eigen centrality and effectively distribute water across those nodes. This project also looks at how to measure the network's connection strength to avoid water leaks. The best clusters are found using Eigenvalues and Eigenvectors of weighted adjacency matrices and Laplacian matrices of the water network in the proposed graph spectral framework. In order to establish the optimum water network division approach, topological and graph metrics were used to compare multiple spectral clustering techniques. The proposed graph spectral approach is tested using a genuine water distribution network serving an urban area of Coimbatore city in India and offering a method for partitioning complex networks that employ the spectral graph partitioning algorithm.

The Network Topology Metrics Contributing to Local-Area Frequency Stability in Power System Networks

The power system network topology influences the system frequency response to power imbalance disturbances. Here, the objective is to find the network metric(s) contributing to frequency transient stability. The graph Laplacians of six 4-node network topologies are analysed using Spectral Graph Theory. For homogeneous network connections, we show that the node degree measure indicates node robustness. Based on these analytical results, the investigation expands to a 10-node network topology consisting of two clusters, which provide further insight into the spectral results. The research then involves a simulation of a power imbalance disturbance on three 20-node networks with different topologies based on node degree, where we link the node degree measure to imbalance disturbance propagation through Wave Theory. The results provide an intuitive understanding of the impact of network topology on power system frequency stability. The analytical and simulation results indicate that a node’s sensitivity to disturbances is partially due to its node degree, reactance from disturbance location, and the link it has to other higher degree nodes (hierarchical position in network topology). Testing of the analytical and simulation results takes place on the nonhomogeneous IEEE-14 bus and IEEE-39 bus networks. These results provide insights into optimal inertia placement to improve the frequency robustness of low-inertia power systems. The network topology, considering node degrees, influences the speed at which the disturbance impact propagates from the disturbance location and how fast-standing waves form. The topology thus contributes to how fast the energy in a disturbance dissipates to zero.

Decline of anterior cingulate functional network efficiency in first-episode, medication-naïve somatic symptom disorder and its relationship with catastrophizing

The high prevalence of somatic symptom disorder (SSD) led to cumulative burdens to the medical system. However, the pathogenesis of this disease still remains unclear. Graph theoretical analysis discovered altered network topology across various psychiatric disorders, yet alteration in the topological structure of brain functional network in SSD patients is still unexplored. Catastrophizing is a common cognitive distortion in SSD. We hypothesize that the network topological metrics of SSD should be altered, and should correlate with catastrophizing scales. 32 medication-naïve, first-episode SSD patients and 30 age, gender matched HCs were recruited. The 17-item Hamilton Depression Rating Scale (HAMD-17), Hamilton Anxiety Rating Scale (HAMA) and Cognitive Emotion Regulation Questionnaire (CERQ) were accessed. Functional MRI were scanned and brain functional networks were constructed based on 166 anatomically cerebrum regions from the automated anatomical labeling 3 (AAL3) template. Network topological metrics were calculated and compared between the two groups. Correlation between these metrics and clinical scales were also calculated. Network global efficiency of SSD was significantly lower than that of HC. Nodal global efficiency of the left subgenual anterior cingulate cortex (sgACC) of SSD was significantly lower than that of HC. FCs between the left sgACC and other 21 seed nodes were significantly declined in SSD in comparison with HC. In SSD group, HAMD total score was significantly negatively correlated with the connection between the left medial superior frontal gyrus and the left sgACC. CERQ catastrophizing score was significantly negatively correlated with nodal global efficiency of left sgACC and with the FCs between the left sgACC and other 13 seed nodes. Catastrophizing could reflect the specific sgACC-centered dysfunction of brain network global efficiency of SSD. The left sgACC may be a future treatment target of dealing with catastrophizing, which is a core cognitive distortion of SSD.

Associations between hemispheric asymmetry and schizophrenia-related risk genes in people with schizophrenia and people at a genetic high risk of schizophrenia.

Schizophrenia is considered a polygenic disorder. People with schizophrenia and those with genetic high risk of schizophrenia (GHR) have presented with similar neurodevelopmental deficits in hemispheric asymmetry. The potential associations between neurodevelopmental abnormalities and schizophrenia-related risk genes in both schizophrenia and those with GHR remains unclear. To investigate the shared and specific alternations to the structural network in people with schizophrenia and those with GHR. And to identify an association between vulnerable structural network alternation and schizophrenia-related risk genes. A total of 97 participants with schizophrenia, 79 participants with GHR and 192 healthy controls, underwent diffusion tensor imaging (DTI) scans at a single site. We used graph theory to characterise hemispheric and whole-brain structural network topological metrics. For 26 people in the schizophrenia group and 48 in the GHR group with DTI scans we also calculated their schizophrenia-related polygenic risk scores (SZ-PRSs). The correlations between alterations to the structural network and SZ-PRSs were calculated. Based on the identified genetic-neural association, bioinformatics enrichment was explored. There were significant hemispheric asymmetric deficits of nodal efficiency, global and local efficiency in the schizophrenia and GHR groups. Hemispheric asymmetric deficit of local efficiency was significantly positively correlated with SZ-PRSs in the schizophrenia and GHR groups. Bioinformatics enrichment analysis showed that these risk genes may be linked to signal transduction, neural development and neuron structure. The schizophrenia group showed a significant decrease in the whole-brain structural network. The shared asymmetric deficits in people with schizophrenia and those with GHR, and the association between anomalous asymmetry and SZ-PRSs suggested a vulnerability imaging marker regulated by schizophrenia-related risk genes. Our findings provide new insights into asymmetry regulated by risk genes and provides a better understanding of the genetic-neural pathological underpinnings of schizophrenia.

Delineating a hierarchical organization of ranked urban clusters using a spatial interaction network

How to reveal the hierarchical structures of urban space has long posed a challenge for researchers. Yet, revealing such structures is of fundamental importance to our understanding of multiscale urban organization. This study, therefore, built a spatial interaction network based on a massive body of human movement data to derive the hierarchical organization of ranked urban clusters. These urban clusters were statistically robust and significant. They were ranked at different levels by fusing network community metrics, urban functional metrics, and road network topological metrics. To verify our methods, experiments were conducted in downtown Wuhan, China, using taxicab trajectory data to construct a spatial interaction network. We derived three levels of urban clusters: (1) geographically cohesive, (2) observable in forms different from government-defined boundaries, and (3) constrained or affected by natural boundaries. We also calculated ranking scores for the urban clusters at different levels based on their structural and functional roles in urban space. Finally, we demonstrate that our ranking scores correlate better with socioeconomic indicators than is the case with other methods. Thus, our method can enrich research on delineating ranked hierarchical urban clusters while the results can provide decision-making support for urban planning and management.

Network Hamiltonian models reveal pathways to amyloid fibril formation

Amyloid fibril formation is central to the etiology of a wide range of serious human diseases, such as Alzheimer’s disease and prion diseases. Despite an ever growing collection of amyloid fibril structures found in the Protein Data Bank (PDB) and numerous clinical trials, therapeutic strategies remain elusive. One contributing factor to the lack of progress on this challenging problem is incomplete understanding of the mechanisms by which these locally ordered protein aggregates self-assemble in solution. Many current models of amyloid deposition diseases posit that the most toxic species are oligomers that form either along the pathway to forming fibrils or in competition with their formation, making it even more critical to understand the kinetics of fibrillization. A recently introduced topological model for aggregation based on network Hamiltonians is capable of recapitulating the entire process of amyloid fibril formation, beginning with thousands of free monomers and ending with kinetically accessible and thermodynamically stable amyloid fibril structures. The model can be parameterized to match the five topological classes encompassing all amyloid fibril structures so far discovered in the PDB. This paper introduces a set of network statistical and topological metrics for quantitative analysis and characterization of the fibrillization mechanisms predicted by the network Hamiltonian model. The results not only provide insight into different mechanisms leading to similar fibril structures, but also offer targets for future experimental exploration into the mechanisms by which fibrils form.

Graph theory and network topological metrics may be the potential biomarker in Parkinson’s disease

This study used Voxel-based morphometry (VBM) and resting-state functional magnetic resonance imaging (rs-fMRI) to investigate changes in brain structure and networks functional connectivity, respectively. We tried to identify the potential biomarkers in Parkinson’s disease (PD) progression. We recruited nine idiopathic PD patients and seven healthy control participants (HC group) who were age-matched to undergo T1-weighted images and rs-fMRI on 1.5 T. Brain structure differences were analyzed by VBM. Topological properties of networks functional connectivity were analyzed by graph theory. Thirty-two nodes of 8 networks and 133 nodes of interest then were identified with graph theory approaches. VBM examinations showed significant decreases of brain gray matter regions including the left temporal lobe, left middle temporal, middle temporal gyrus, parietal lobe, postcentral gyrus, left inferior parietal gyrus, medial frontal gyrus and supplement motor area in PD patients compared to the HC group. The 32 ROI of networks topological metrics measurement in PD demonstrated increases of global efficiency, cost, and degree in frontoparietal PPC (R) network, but decreases of local efficiency, clustering coefficient, and average path length in salience ACC, dorsal attention FEF (L), and salience aInsula (R) networks, respectively. All 165 ROI connectomes showed eight connections intensity changes, that decrease in OP r to frontoparietal PPC, putamen r to cereb11, and SFG l to Ver8 in PD. These results suggest that the graph theory and the network topological metrics measurement may be the potential biomarkers in PD to evaluate the disease progress and to monitor the therapeutic results.

A topological characterization of flooding impacts on the Zurich road network

Infrastructure systems are the structural backbone of cities, facilitating the flow of essential services. Because those systems can be disrupted by natural hazards, risk management has been the prevailing approach for assessing the consequences and expected level of damage. Although this may be a valuable metric, the practice of risk assessment does not represent how hazards affect a network of assets on a larger scale. In contrast, network topology metrics are useful because they evaluate the performance of network infrastructures by looking at the system as a whole. As described here, we began this study to improve our understanding of how flooding events affect the topological properties of road networks, in this case, the urban road infrastructure of Zurich, Switzerland. Using maps of flooding risk, we developed a procedure to extract the damaged networks and analyze the centrality metrics for peak water levels on the surface of the city. Our approach modelled roads as edges and junctions between roads as nodes. The betweenness centrality metric characterizes the importance of nodes or edges for any type of exchange within a network, whereas the closeness centrality metric measures the accessibility of a specific node to all the other nodes. This investigation produced three main findings. First, descriptive analyses showed that the characteristics and patterns of nodes and edges changed under the flooding events. Second, the distribution function of centrality metrics became heavier in the tails as the flood magnitude increased. Third, the associated strain shifted critical nodes to areas in which those nodes would not be important under normal conditions. These findings are essential for identifying crucial locations and devising plans to address risks. Future projects could expand our approach by including traffic flow to move the analysis closer to real-world flows, and by studying the accessibility under emergency conditions at local levels.

Relationship between topological efficiency in white matter structural networks with cerebral oxygen metabolism in young adults

The relationship between the topological characteristics of the white matter (WM) network have been shown to be related to neural development, intelligence, and various diseases; however, few studies have been conducted to explore the relationship between topological characteristics of the WM network and cerebral metabolism. In a recent study we investigated the relationship between WM network topological and metabolic metrics of the cerebral parenchyma in healthy volunteers using the newly developed T2-relaxation-under-spin-tagging (TRUST) magnetic resonance imaging technique and graph theory approaches. Ninety-six healthy adults (25.5 ± 1.8 years of age) were recruited as volunteers in the current study. The cerebral metabolic rate of oxygen (CMRO2), oxygen extraction fraction, and the global topological metrics of the WM network (global efficiency [Eglob], local efficiency, and small-worldliness) were assessed. A stepwise multiple linear regression model was estimated. CMRO2 was entered as the dependent variable. The topological and demographic parameters (age, gender, FIQ, SBP, gray matter volume, and WM volume) were entered as independent variables in the model. The final performing models were comprised of predictors of Eglob, FIQ, and age (adjusted R2 values were 0.489 [L-AAL] and 0.424 [H-1024]). Our study initially revealed a relationship between Eglob and cerebral oxygen metabolism in healthy young adults.

Integrating network topology metrics into studies of catchment-level effects on river characteristics

Abstract. The spatial arrangement of the river network is a fundamental characteristic of the catchment, acting as a conduit between catchment-level effects and reach morphology and ecology. Yet river network structure is often simplified to reflect an upstream-to-downstream gradient of river characteristics, commonly represented by stream order. The aim of this study is to quantify network topological structure using two network density metrics – one that represents network density over distance and the other over elevation – that can easily be extracted from digital elevation models and so may be applied to any catchment across the globe. These metrics should better account for the multi-dimensional nature of the catchment than stream order and be functionally applicable across geomorphological, hydrological and ecological attributes of the catchment. The functional utility of the metrics is assessed by appropriating monitoring data collected for regulatory compliance to explore patterns of river characteristics in relation to network topology. This method is applied to four comparatively low-energy, anthropogenically modified catchments in the UK using river characteristics derived from England's River Habitat Survey database. The patterns in river characteristics explained by network density metrics are compared to stream order as a standard measure of topology. The results indicate that the network density metrics offer a richer and functionally more relevant description of network topology than stream order, highlighting differences in the density and spatial arrangement of each catchment's internal network structure. Correlations between the network density metrics and river characteristics show that habitat quality score consistently increases with network density in all catchments as hypothesized. For other measures of river character – modification score, flow-type speed and sediment size – there are varying responses in different catchments to the two network density metrics. There are few significant correlations between stream order and the river characteristics, highlighting the limitations of stream order in accounting for network topology. Overall, the results suggest that network density metrics are more powerful measures which conceptually and functionally provide an improved method of accounting for the impacts of network topology on the fluvial system.

A topological analysis of growth in the Zurich road network

The functioning of a city depends upon physical structures and services. Over time, a city evolves and the layout of its infrastructure is altered, providing a new arrangement of services for citizens. When designing road infrastructure, planners usually add or change existing roads, looking only at local consequences and ignoring the effects on the whole system. This results in an infrastructure that is developed without a clear understanding of how those alterations affect the global topology. We studied the development of road infrastructure in Zurich, Switzerland, modelled as a network. Our objectives were to 1) assess how non-spatial network topological metrics can identify changes in infrastructure over time and 2) determine any patterns of change in the spatial distribution of those metrics. We analyzed three types of betweenness centrality (BC) metrics with different weighting methods that depended upon structural properties, distance, and population distribution within the urban area. The study resulted in four main findings. First, the number of nodes and edges, together with the network diameter characterized the non-spatial aspect of development. Second, traditional connectivity metrics (alpha, beta, gamma indices) did not yield any changes in time due to their dependence on the average degree, which remained quite constant in infrastructure networks. Third, areas of high BC extended from 1955 to 2012 into a Y-shaped configuration, driven by the development of the main overarching national freeway system. Closeness centrality results show similar patterns. Fourth, the distribution of the 1955 normalized betweenness centrality values transformed into a more heavy-tail distribution in 2012, which implicated that the most critical nodes became even more critical. Future work will enhance this analysis by using more realistic assumptions and incorporating traffic survey data.

Ictal networks of temporal lobe epilepsy: views from high-frequency oscillations in stereoelectroencephalography.

In this study, the authors investigated high-frequency oscillation (HFO) networks during seizures in order to determine how HFOs spread from the focal cerebral cortex and become synchronized across various areas of the brain. All data were obtained from stereoelectroencephalography (SEEG) signals in patients with drug-resistant temporal lobe epilepsy (TLE). The authors calculated intercontact cross-coefficients between all pairs of contacts to construct HFO networks in 20 seizures that occurred in 5 patients. They then calculated HFO network topology metrics (i.e., network density and component size) after normalizing seizure duration data by dividing each seizure into 10 intervals of equal length (labeled I1-I10). From the perspective of the dynamic topologies of cortical and subcortical HFO networks, the authors observed a significant increase in network density during intervals I5-I10. A significant increase was also observed in overall energy during intervals I3-I8. The results of subnetwork analysis revealed that the number of components continuously decreased following the onset of seizures, and those results were statistically significant during intervals I3-I10. Furthermore, the majority of nodes were connected to a single dominant component during the propagation of seizures, and the percentage of nodes within the largest component grew significantly until seizure termination. The consistent topological changes that the authors observed suggest that TLE is affected by common epileptogenic patterns. Indeed, the findings help to elucidate the epileptogenic network that characterizes TLE, which may be of interest to researchers and physicians working to improve treatment modalities for epilepsy, including resection, cortical stimulation, and neuromodulation treatments that are responsive to network topologies.

Grain boundary network evolution in Inconel 718 from selective laser melting to heat treatment

Inconel 718 fabricated by selective laser melting (SLM) was used to investigate the evolution of grain boundary (GB) network structures from as-SLM to heat-treated (HT) samples. Using electron backscatter diffraction (EBSD) data and percolation theory based cluster analysis, GB character distribution and GB network topological metrics were computed at different build locations and directions. The microstructures of the as-SLM samples reveal large spatial heterogeneity in grain morphology and are dominated by general GBs (i.e., ∑> 29), which form one connected cluster spanning across the whole GB network. Heat-treatment homogenizes the microstructure and leads to the formation of annealing twins as a result of recrystallization, which dramatically increases the number of special boundaries (mainly twin ∑3 and twin-related ∑9, ∑27 boundaries with ~ 60% in boundary length fraction). However, these special boundaries have not yet fully connected/merged to form a percolated path throughout the GB network. The triple junction distributions of the HT sample are dominated by J1-type that consists of one special and two general boundaries, further confirming the interweaving GB network made of the general and special boundary clusters. In addition, the implication of applying GB engineering to the SLMed parts is discussed based on the comparison of GB network structures between the SLMed alloys and the conventionally GB engineered metals and alloys.

Lessons from social network analysis to Industry 4.0

With the advent of Industry 4.0, a growing number of sensors within modern production lines generate high volumes of data. This data can be used to optimize the manufacturing industry in terms of complex network topology metrics commonly used in the analysis of social and communication networks. In this work, several such metrics are presented along with their appropriate interpretation in the field of manufacturing. Furthermore, the assumptions under which such metrics are defined are assessed in order to determine their suitability. Finally, their potential application to identify performance limiting resources, allocate maintenance resources and guarantee quality assurance are discussed.

Invasive rodents have multiple indirect effects on seabird island invertebrate food web structure.

Burrowing seabirds that nest on islands transfer nutrients from the sea, disturb the soil through burrowing, damage tree foliage when landing, and thereby modify the surface litter. However, seabirds are in decline worldwide, as are their community- and ecosystem-level impacts, primarily due to invasive predatory mammals. The direct and indirect effects of seabird decline on communities and ecosystems are inherently complex. Here we employed network analysis, as a means of simplifying ecological complexity, to better understand the effects seabird loss may have on island invertebrate communities. Using data on leaf litter communities, we constructed invertebrate food webs for each of 18 offshore oceanic islands in northeastern New Zealand, nine of which have high seabird densities and nine of were invaded by rats. Ten network topological metrics (including entropy, generality, and vulnerability) were compared between rat-invaded and uninvaded (seabird-dominant) islands. We found that, on rat-invaded islands, the invertebrate food webs were smaller and less complex than on their seabird-dominated counterparts, which may be due to the suppression of seabird-derived nutrients and consequent effects on trophic cascades. This decreased complexity of food webs due to the presence of rats is indicative of lower ecosystem resistance via lower trophic redundancy. Our results show that rat effects on island ecosystems are manifested throughout entire food webs, and demonstrate how network analysis may be useful to assess ecosystem recovery status as these invaded islands are restored.

Generic patterns in the evolution of urban water networks: Evidence from a large Asian city.

We examine high-resolution urban infrastructure data using every pipe for the water distribution network (WDN) and sanitary sewer network (SSN) in a large Asian city (≈4 million residents) to explore the structure as well as the spatial and temporal evolution of these infrastructure networks. Network data were spatially disaggregated into multiple subnets to examine intracity topological differences for functional zones of the WDN and SSN, and time-stamped SSN data were examined to understand network evolution over several decades as the city expanded. Graphs were generated using a dual-mapping technique (Hierarchical Intersection Continuity Negotiation), which emphasizes the functional attributes of these networks. Network graphs for WDNs and SSNs are characterized by several network topological metrics, and a double Pareto (power-law) model approximates the node-degree distributions of both water infrastructure networks (WDN and SSN), across spatial and hierarchical scales relevant to urban settings, and throughout their temporal evolution over several decades. These results indicate that generic mechanisms govern the networks' evolution, similar to those of scale-free networks found in nature. Deviations from the general topological patterns are indicative of (1) incomplete establishment of network hierarchies and functional network evolution, (2) capacity for growth (expansion) or densification (e.g., in-fill), and (3) likely network vulnerabilities. We discuss the implications of our findings for the (re-)design of urban infrastructure networks to enhance their resilience to external and internal threats.

Structure and Topology Dynamics of Hyper-Frequency Networks during Rest and Auditory Oddball Performance.

Resting-state and task-related recordings are characterized by oscillatory brain activity and widely distributed networks of synchronized oscillatory circuits. Electroencephalographic recordings (EEG) were used to assess network structure and network dynamics during resting state with eyes open and closed, and auditory oddball performance through phase synchronization between EEG channels. For this assessment, we constructed a hyper-frequency network (HFN) based on within- and cross-frequency coupling (WFC and CFC, respectively) at 10 oscillation frequencies ranging between 2 and 20 Hz. We found that CFC generally differentiates between task conditions better than WFC. CFC was the highest during resting state with eyes open. Using a graph-theoretical approach (GTA), we found that HFNs possess small-world network (SWN) topology with a slight tendency to random network characteristics. Moreover, analysis of the temporal fluctuations of HFNs revealed specific network topology dynamics (NTD), i.e., temporal changes of different graph-theoretical measures such as strength, clustering coefficient, characteristic path length (CPL), local, and global efficiency determined for HFNs at different time windows. The different topology metrics showed significant differences between conditions in the mean and standard deviation of these metrics both across time and nodes. In addition, using an artificial neural network approach, we found stimulus-related dynamics that varied across the different network topology metrics. We conclude that functional connectivity dynamics (FCD), or NTD, which was found using the HFN approach during rest and stimulus processing, reflects temporal and topological changes in the functional organization and reorganization of neuronal cell assemblies.

Network topological effects on the macroscopic Bureau of Public Roads function

Cost flow functions are a central class of models in the transport field because they are an essential ingredient of static user equilibrium traffic assignment and transport policy and planning analysis. Macroscopic cost flow (MCF) functions, which model travel cost at different levels of network use, have gained much attention in recent decades due to their potential applications in area-wide traffic management and control, and initial land-use planning. They are the collective outcomes of the responses of road users to the existing transportation network and the interactions between road users at different levels of traffic demand. Network topological effects have long been anticipated to be the primary factors governing the shape and performance of a network. However, few studies have investigated network topology. This paper aims to unveil the direct link between network topological metrics and the parameters of a specific MCF, in the form of macroscopic Bureau of Public Roads (MBPR) function, with the support of real-world data. Seventy-one 1 km × 1 km urban built-up regions were sampled in Hong Kong. The MBPR functions of the selected regions were calibrated using taxi global positioning system data. Intensive investigations revealed that the average number of junctions per unit distance and the road density were topological features correlating with the free-flow travel time and congestion sensitivity parameters of the MBPR function, respectively. A spatially variable MBPR function was established.