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Nowadays, there are positive and negative relationships among individuals in social networks, which can be abstracted as a signed network with two edge attributes. These two different attributes between individuals are usually used to infer the underlying attitudes of others and modeled as the edge signs in the complex network. Recently, many studies apply local path information to predict edge signs, ignoring the effect of the clustering coefficient of nodes in the three-hop path when determining signs of links. We believe that clustering coefficients of nodes on paths with different lengths reflect the node connecting tightness and contribute significantly to predicting potential relationships. Therefore, we propose a sign prediction algorithm based on the node Connecting Tightness (CT). First, influences of the connection tightness of first- and second-order common neighbors, i.e. nodes on two- and three-hop paths between target nodes, are calculated. Second, based on these influences, the similarity of target node pairs is modeled, and the link sign is predicted by combining the structural balance theory. Finally, node degrees are used to predict directly when there are no common neighbors between the target nodes. Experiments in real-world and artificial networks demonstrate that CT achieves better accuracy and F1 performances in sign prediction. [ABSTRACT FROM AUTHOR]

In the pursuit of graph processing performance, graph partitioning, as a crucial preprocessing step, has been widely concerned. Based on an in-depth analysis of Neighbor Expansion (NE) graph partitioning algorithm, we propose Parallel Expansion based on Clustering Coefficient (PECC). Firstly, to address the partition disturbance caused by internal structural changes during the process of vertex neighborhood expansion in the traditional NE algorithm, we perform a formal redefinition of the vertex state during the partitioning process and introduce the concept of clustering coefficient. Then, PECC uses the clustering coefficient as a metric to measure the closeness between vertices and potential partitions. Based on this metric, a novel parallel partitioning strategy in the distributed environment is proposed. This strategy consists of two core steps: the expansion process and the allocation process. Through two steps, PECC can effectively improve the operating efficiency of programs and significantly reduce the partitioning time. In addition, to ensure data consistency during parallel expansion, we adopt a distributed locking engine to solve concurrency management problems. Our evaluations on large real-world graphs show that in many cases, PECC achieves a balance between partitioning quality and computational efficiency. Finally, we show that PECC integrated on GraphX outperforms the built-in native algorithms. [ABSTRACT FROM AUTHOR]

A network is a crucial asset in biology for capturing and exploring interaction data in biological systems of many types, such as protein-protein communications, amino acid associations, gene regulation, and cellular metabolism. In this article, we constructed an amino acid distance matrix by considering each base's positional relevance in a codon, chemical types: Purine and Pyrimidine, and H-bonding count. Based on the amino acid distance matrix, we eventually generated a twenty amino acid network having evolutionary significance. We reviewed multiple centrality metrics to assess the relative importance of amino acids in the proposed network: Degree Centrality, Closeness Centrality, Betweenness Centrality, Eigenvector Centrality, Eccentricity Centrality, and Radiality Centrality. We also looked at the correlation coefficients between the different centrality measures to figure out whether the network is assortative or disassortative. Furthermore, we examined the Clustering Coefficient and Degree Distribution as two effective network measures, and the results seem noteworthy.

The reliable prediction of streamflow is crucial for various water resources, environmental, and ecosystem applications. The current study employs a complex networks-based approach for the prediction of streamflow. The approach consists of three major steps: (1) the formation of a network using streamflow time series; (2) the calculation of the clustering coefficient (CC) as a network measure; and (3) the use of a clustering coefficient-based nearest neighbor search procedure for streamflow prediction. For network construction, each timestep is considered as a node and the existence of link between any node pair is identified based on the difference (distance) between the streamflow values of the nodes. Different distance threshold values are used to identify the critical distance threshold to form the network. The complex networks-based approach is implemented for the prediction of daily streamflow at 142 stations in the contiguous United States. The prediction accuracy is quantified using three statistical measures: correlation coefficient (R), normalized root mean square error (NRMSE), and Nash–Sutcliffe efficiency (NSE). The influence of the number of neighbors on the prediction accuracy is also investigated. The results, obtained with the critical distance threshold, reveal that the clustering coefficients for the 142 stations range from 0.799 to 0.999. Overall, the prediction approach yields reasonably good results for all 142 stations, with R values ranging from 0.05 to 0.99, NRMSE values ranging from 0.1 to 12.3, and the NSE values ranging from −0.89 to 0.99. An attempt is also made to examine the relationship between prediction accuracy and the catchment characteristics/streamflow statistical properties (drainage area, mean flow, coefficient of variation of flow). The results suggest that the prediction accuracy does not have much of a relationship with the drainage area and the mean streamflow values, but with the coefficient of variation of flow. The outcomes from this study are certainly promising regarding the application of complex networks-based concepts for the prediction of streamflow (and other hydrologic) time series. [ABSTRACT FROM AUTHOR]

Dimension reduction is an effective method for system's resilience analysis. In this paper, we investigate the effect of network structure on the accuracy of resilience dimension reduction. First, we introduce the resilience dimension reduction method and define the evaluation indicator of the resilience dimension reduction method. Then, by adjusting node connections, preferential connection mechanisms, and connection probabilities, we generate artificial networks, small-world networks and social networks with tunable assortativity coefficients, average clustering coefficients, and modularities, respectively. Experimental results for the gene regulatory dynamics show that the network structures with positive assortativity, large clustering coefficient, and significant community can enhance the accuracy of resilience dimension reduction. The result of this paper indicates that optimizing network structure can enhance the accuracy of resilience dimension reduction, which is of great significance for system resilience analysis and provides a new perspective and theoretical basis for selecting dimension reduction methods in system resilience analysis. [ABSTRACT FROM AUTHOR]

Theories to maximise influence in social networks have been investigated vastly by researchers in recent times. Various strategies have been proposed to identify initial seed node set to diffuse the information in the network. In this manuscript, a seed node selection strategy has been proposed based on the clustering coefficient and betweenness centrality scores of the nodes in the graph (CLUS-BET). The influence spread (in the underlying network) is measured using Independent Cascade Model (ICM) by selecting top k seed nodes having high CLUS-BET score. The network coverage obtained are 72.48 % , 65.85 % , 51.12 % and 53.15 % for CORA, Citeseer, PubMed and Amazon Computers network respectively. The results obtained are better in comparison to any of the classical centrality algorithms'-based seed node selection. Also, the results are compared with a recent state of art method GRAIN based seed selection strategy. The manuscript further testifies that the quality of nodes selected based on CLUS-BET property improves the Graph Convolution Network (GCN) based node classification accuracy. CLUS-BET based GCN produces a node classification accuracy of 90 % , 77 % and 89.2 % for CORA, Citeseer and PubMed networks respectively. The results surpass the classification accuracy of base GCN model and its variations in contemporary state of art. Also, the property helps in identifying the most prominent influential clusters or groups of the network responsible for spreading the information in the network to a vast majority. The analytical explanation suggests that these are the groups having most number of nodes with high CLUS-BET score. The proposed idea is scalable with the graphical network as it avoids Monte Carlo simulation rounds with Greedy method for information cascade to identify seed nodes. The metric calculation for CLUS-BET is simple, less time consuming and effective. [ABSTRACT FROM AUTHOR]

Objective: Genetic generalized epilepsy (GGE) accounts for approximately 20% of adult epilepsy cases and is considered a disorder of large brain networks, involving both hemispheres. Most studies have not shown any difference in functional whole‐brain network topology when compared to healthy controls. Our objective was to examine whether this preserved global network topology could hide local reorganizations that balance out at the global network level. Methods: We recorded high‐density electroencephalograms from 20 patients and 20 controls, and reconstructed the activity of 118 regions. We computed functional connectivity in windows free of interictal epileptiform discharges in broad, delta, theta, alpha, and beta frequency bands, characterized the network topology, and used the Hub Disruption Index (HDI) to quantify the topological reorganization. We examined the generalizability of our results by reproducing a 25‐electrode clinical system. Results: Our study did not reveal any significant change in whole‐brain network topology among GGE patients. However, the HDI was significantly different between patients and controls in all frequency bands except alpha (p <.01, false discovery rate [FDR] corrected, d < −1), and accompanied by an increase in connectivity in the prefrontal regions and default mode network. This reorganization suggests that regions that are important in transferring the information in controls were less so in patients. Inversely, the crucial regions in patients are less so in controls. These findings were also found in delta and theta frequency bands when using 25 electrodes (p <.001, FDR corrected, d < −1). Significance: In GGE patients, the overall network topology is similar to that of healthy controls but presents a balanced local topological reorganization. This reorganization causes the prefrontal areas and default mode network to be more integrated and segregated, which may explain executive impairment associated with GGE. Additionally, the reorganization distinguishes patients from controls even when using 25 electrodes, suggesting its potential use as a diagnostic tool. [ABSTRACT FROM AUTHOR]

The association between immune checkpoint inhibitors (ICIs) and immune gene networks in squamous lung cancer (LUSC) and lung adenocarcinoma (LUAD) was studied. Immune gene networks were constructed using RNA-seq data from the gene expression omnibus (GEO) database. Datasets with more than 10 samples of normal control and tumor tissues were selected; of these, GSE87340, GSE120622, and GSE111907 were suitable for analysis. Gene set enrichment for pathway analysis was performed. For immune gene network construction, 998 unique immune genes were selected from 21 pathways in the Kyoto Encyclopedia of Genes and Genomes (KEGG). Gene function annotation was performed based on the KEGG, Gene Ontology, and Reactome databases. Tumor tissues showed decreased coagulation, hematopoiesis, and innate immune pathways, whereas complement- and coagulation-related genes were prominent in the tumor immune gene network. The average numbers of neighbors, clustering coefficients, network diameters, path lengths, densities, and heterogeneities were highest for normal tissue, followed by LUAD and LUSC. Decreased coagulation genes, which were prominent in tumor immune networks, imply functional attenuation. LUAD was deviated from normal tissue, based on network parameters. Tumor tissues showed decreased immune function, and the deviation of LUSC from normal tissue might explain LUSC's better therapeutic response to ICI treatment. [ABSTRACT FROM AUTHOR]

The detection and ranking of influential nodes in complex networks are crucial for various practical applications such as identifying potential drug targets in protein-to-protein interaction networks, critical devices in communication networks, key people in social networks, and transportation hubs in logistics networks. The knowledge of influential spreaders in complex networks is extremely useful for controlling the spread of information. Centrality measures are known for effectively quantifying the influential nodes information in large-scale complex networks. Researchers have proposed different centrality measures in the literature, including Degree, Betweenness, Closeness, and Clustering coefficient centralities. However, these measures have certain limitations when implemented over large-scale complex networks. Most of these measures can be classified as global and local structural approaches. The global structure based algorithms are too complex to evaluate key nodes, particularly in large-scale networks, whereas the local measures overlook the essential global network information. To address these challenges, an extended clustering coefficient local global centrality (ECLGC) is proposed, which combines the local and global structural information to measure the node’s influence in large-scale networks. The effectiveness and computational efficiency of the proposed measure are compared with existing centrality measures on real-world network datasets. Susceptible-Infected-Recovered (SIR) model is utilized to evaluate the performance of the ECLGC to capture the high-information dissemination compared to conventional measures. Further, we demonstrate that the proposed measure outperforms the conventional measures in terms of spreading efficiency.

Ranking influential nodes within complex networks offers invaluable insights into a wide array of phenomena ranging from disease management to information dissemination and optimal routing in real-time networking applications. Centrality measures, which quantify the importance of nodes based on network properties and relationships of nodes within the network, are instrumental in achieving this task. These measures are typically classified into local and global centralities. Global measures consider the overall structure and connectivity patterns. However, they often suffer from high computational complexity in large-scale networks. On the other hand, local measures focus on the immediate neighborhood of each node, potentially overlooking global information. To address these challenges, we propose a novel metric called Isolating Clustering Centrality (ISCL), which leverages a convex combination approach. By introducing a convex tuning parameter, ISCL enhances the applicability and adaptability of centrality measures across a wide range of real-world network applications. In this study, we assess the efficacy of the proposed measure using real-world network datasets and simulate the spreading process using susceptible-infected-removed (SIR) and independent cascade (IC) models. Our extensive results demonstrate that ISCL significantly improves spreading efficiency compared to conventional and recent centrality measures, while also maintaining better computational efficiency in large-scale complex networks.

Abstract.In this work, we consider a randomized version of the deterministic pseudofractal graph model, which was first proposed in the physical literature. Our model is a sequence of dynamic networks, in which the increment of network size at each time depends on the current size and a sequence of evolving parameters. We first show that the network size is closely related to a branching process in the varying environment. Under a mild assumption, we then prove that the asymptotic degree distribution in our model obeys the power law with an exponent three. Based on this asymptotic degree distribution, we show that the clustering coefficient of our network model converges to a given constant in probability. [ABSTRACT FROM AUTHOR]

INTRODUCTION: The retina may provide non‐invasive, scalable biomarkers for monitoring cerebral neurodegeneration. METHODS: We used cross‐sectional data from The Maastricht study (n = 3436; mean age 59.3 years; 48% men; and 21% with type 2 diabetes [the latter oversampled by design]). We evaluated associations of retinal nerve fiber layer, ganglion cell layer, and inner plexiform layer thicknesses with cognitive performance and magnetic resonance imaging indices (global grey and white matter volume, hippocampal volume, whole brain node degree, global efficiency, clustering coefficient, and local efficiency). RESULTS: After adjustment, lower thicknesses of most inner retinal layers were significantly associated with worse cognitive performance, lower grey and white matter volume, lower hippocampal volume, and worse brain white matter network structure assessed from lower whole brain node degree, lower global efficiency, higher clustering coefficient, and higher local efficiency. DISCUSSION: The retina may provide biomarkers that are informative of cerebral neurodegenerative changes in the pathobiology of dementia. [ABSTRACT FROM AUTHOR]

We provide a novel approach for analysing the financial resilience of the insurance sector during coronavirus pandemic. To this end, we build temporal directed and weighted networks where the weights on the arcs take into account the tail dependence between couple of firms. To assess the resilience of the network, we provide a new global indicator, aimed at capturing the impact on the clustering coefficient of a shock affecting in turn each firm and diffusing in the network via shortest paths. A local measure of resilience is also provided by quantifying the contribution of each firm to the global indicator. In this way, we are able to detect most critical firms in the system. A numerical application has been developed in order to test the proposed approach. The results show that the proposed resilience measure appears able to detect main periods of financial crises. The first wave of COVID-19 pandemic results as a extreme phenomenon in the market and the lowest resilience is associated to the period in which COVID-19 has been declared pandemic. [ABSTRACT FROM AUTHOR]

Identifying key spreaders in a network is one of the fundamental problems in the field of complex network research, and accurately identifying influential propagators in a network holds significant practical implications. In recent years, numerous effective methods have been proposed and widely applied. However, many of these methods still have certain limitations. For instance, some methods rely solely on the global position information of nodes to assess their propagation influence, disregarding local node information. Additionally, certain methods do not consider clustering coefficients, which are essential attributes of nodes. Inspired by the quality formula, this paper introduces a method called Structural Neighborhood Centrality (SNC) that takes into account the neighborhood information of nodes. SNC measures the propagation power of nodes based on first and second-order neighborhood degrees, local clustering coefficients, structural hole constraints, and other information, resulting in higher accuracy. A series of pertinent experiments conducted on 12 real-world datasets demonstrate that, in terms of accuracy, SNC outperforms methods like CycleRatio and KSGC. Additionally, SNC demonstrates heightened monotonicity, enabling it to distinguish subtle differences between nodes. Furthermore, when it comes to identifying the most influential Top-k nodes, SNC also displays superior capabilities compared to the aforementioned methods. Finally, we conduct a detailed analysis of SNC and discuss its advantages and limitations. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, contact tracing was used to identify individuals who had been in contact with a confirmed case so that these contacted individuals could be tested and quarantined to prevent further spread of the SARS-CoV-2 virus. Many countries developed mobile apps to find these contacted individuals faster. We evaluate the epidemiological effectiveness of the Dutch app CoronaMelder, where we measure effectiveness as the reduction of the reproduction number R. To this end, we use a simulation model of SARS-CoV-2 spread and contact tracing, informed by data collected during the study period (December 2020 - March 2021) in the Netherlands. We show that the tracing app caused a clear but small reduction of the reproduction number, and the magnitude of the effect was found to be robust in sensitivity analyses. The app could have been more effective if more people had used it, and if notification of contacts could have been done directly by the user and thus reducing the time intervals between symptom onset and reporting of contacts. The model has two innovative aspects: i) it accounts for the clustered nature of social networks and ii) cases can alert their contacts informally without involvement of health authorities or the tracing app.

During the translation process, the genetic code is the nucleotide sequence that determines the amino acid sequence of protein molecules. A codon is a universal triplet of nucleotides that codes for an amino acid. A group G's identity graph is a graph in which the vertex set is the set of all group elements and two vertices in G are adjacent if a.b = e, where e is the group's identity element. In this study, we looked at the identity graph in the genetic code algebra. In our current study, we have thoroughly discussed various measures of centrality. In addition to this analysis, the correlation coefficients between various centrality measures, clustering coefficient, degree of distribution, and skewness are all examined.

The reliable prediction of streamflow is crucial for various water resources, environmental, and ecosystem applications. The current study employs a complex networks-based approach for the prediction of streamflow. The approach consists of three major steps: (1) the formation of a network using streamflow time series; (2) the calculation of the clustering coefficient (CC) as a network measure; and (3) the use of a clustering coefficient-based nearest neighbor search procedure for streamflow prediction. For network construction, each timestep is considered as a node and the existence of link between any node pair is identified based on the difference (distance) between the streamflow values of the nodes. Different distance threshold values are used to identify the critical distance threshold to form the network. The complex networks-based approach is implemented for the prediction of daily streamflow at 142 stations in the contiguous United States. The prediction accuracy is quantified using three statistical measures: correlation coefficient (R), normalized root mean square error (NRMSE), and Nash–Sutcliffe efficiency (NSE). The influence of the number of neighbors on the prediction accuracy is also investigated. The results, obtained with the critical distance threshold, reveal that the clustering coefficients for the 142 stations range from 0.799 to 0.999. Overall, the prediction approach yields reasonably good results for all 142 stations, with R values ranging from 0.05 to 0.99, NRMSE values ranging from 0.1 to 12.3, and the NSE values ranging from −0.89 to 0.99. An attempt is also made to examine the relationship between prediction accuracy and the catchment characteristics/streamflow statistical properties (drainage area, mean flow, coefficient of variation of flow). The results suggest that the prediction accuracy does not have much of a relationship with the drainage area and the mean streamflow values, but with the coefficient of variation of flow. The outcomes from this study are certainly promising regarding the application of complex networks-based concepts for the prediction of streamflow (and other hydrologic) time series.

The use of emerging technologies to construct an interactive academic field of Li Zehou’s aesthetic theory aims to promote the study of Li Zehou’s aesthetic thought and the development of contemporary Chinese aesthetics. Based on the content and characteristics of Li Zehou’s aesthetics theory, the article describes the innovative application of emerging technology in academic communication, constructs the academic field of Li Zehou’s aesthetics theory on the basis of Bourdieu’s field theory, and designs the framework of the interactive academic field by combining with emerging technology. Relying on Li Zehou’s interactive academic field for the construction of a multi-layer innovation network model and providing relevant quantitative methods for interactive academic field network metrics. The dataset is constructed with the relevant literature of Li Zehou’s aesthetics theory from 2005 to 2022 as the search target, and the network density, central potential, clustering coefficients, and path lengths of the interactive field are analyzed, and the evolution characteristics of the multilayer field network are explored. The cross-border innovation multilayer network density of the interactive field of Li Zehou’s aesthetic thought fluctuates around 0.092, approaching the mean value of central potential up to 65.76%, and the average clustering coefficient fluctuates in the range of [0.25,0.35]. The cooperative sub-network and the technology sub-network have smaller path lengths with larger clustering coefficients, indicating small-worldness. The interactive academic field combining emerging technologies can promote the widespread dissemination of Li Zehou’s aesthetic ideas.

In the context of digital technological change and media convergence, how to quantitatively analyze the digital communication path of contemporary politics and Marxist thought has become a new problem to be solved. The objective of this paper is to create a model for analyzing the digital communication path of political information and Marxist thought. The degree correlation in the social network algorithm is used to analyze the correlation between the information nodes of contemporary politics and Marxist thought, and the clustering coefficients are used to predict the behavior and evolution of the nodes in the dissemination network. The dissemination model of contemporary politics and Marxist ideology can be explored by combining the infectious disease information dissemination model on the network platform. After the construction has been completed, the model is employed to evaluate the relevant information of a network platform. The early stages of the spread of political and Marxist-related information resulted in 180,000 crowd contacts becoming information exposers and quickly reaching the peak point. The peak point of 119,800 people is quickly reached when both intentional and unintentional communicators of political messages increase. Node density reaches 0.94 and then declines roughly 24 hours after the political message is released. The model employed in this paper is capable of effectively analyzing the digital dissemination path of politics and Marxist ideology and providing a reference for exploring the digital dissemination of political information.

Concurrent extreme rainfall events, or synchronous extremes, during Indian Summer Monsoon Rainfall (ISMR), cause significant damage, but their spatiotemporal evolution remains unclear. Using the event synchronization approach to examine the synchronicity of extreme rainfall events from 1901 to 2019, we find that Central India consistently hosts strongly connected synchronous extreme hubs with localized connections, indicating the geographical trapping of these concurrent events in the region. We observe a moderate positive correlation between network cohesiveness and El Niño Southern Oscillations (ENSO), and a negative correlation between ENSO and link lengths, suggesting localized synchronicity during El Niño dominant decades and opposite patterns in La Niña periods. Despite increasing ISMR variability and spatial nonuniformity, the persistence of hubs and network attributes could offer insights for predicting synchronous extremes, informing effective adaptation and risk management strategies during the monsoon season. Plain Language Summary: Synchronous extreme rainfall events during the India monsoon season have been persistent over the past century, tending to concentrate in Central India and remaining highly localized. These events are correlated with El Niño Southern Oscillations (ENSO), with more synchronization during strong El Niño periods and less during La Niña conditions. The networks representing these synchronous extremes at various levels of severity exhibit key attributes that are time‐invariant with minimal divergence. These properties demonstrate a significant correlation with recurring climate patterns such as ENSO and Tropical Sea‐Surface Temperature Anomalies. Understanding these time‐invariant characteristics and their links to larger climate patterns is essential for infrastructure planning and design, given the persistent challenges posed by these synchronous extremes. Key Points: Despite growing spatial non‐uniformity, synchronous monsoon rainfall extremes confine to nearly the same geographical regionHighly connected locations persist in Central India and synchronize locally, indicating a stable network of extreme rainfall eventsTime‐invariant network properties linked to ocean‐atmosphere processes could serve as key covariates for predicting synchronous extremes [ABSTRACT FROM AUTHOR]

Complex networks are pervasive in the real world, capturing dyadic interactions between pairs of vertices, and a large corpus has emerged on their mining and modeling. However, many phenomena are comprised of polyadic interactions between more than two vertices. Such complex hypergraphs range from emails among groups of individuals, scholarly collaboration, or joint interactions of proteins in living cells. Complex hypergraphs and their models form an emergent topic, requiring new models and techniques. A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. The previously proposed Iterated Local Transitivity (ILT) model incorporated transitivity as an evolutionary mechanism. The ILT model provably satisfies many observed properties of social networks, such as densification, low average distances, and high clustering coefficients. We propose a new, generative model for complex hypergraphs based on transitivity, called the Iterated Local Transitivity Hypergraph (or ILTH) model. In ILTH, we iteratively apply the principle of transitivity to form new hypergraphs. The resulting model generates hypergraphs simulating properties observed in real-world complex hypergraphs, such as densification and low average distances. We consider properties unique to hypergraphs not captured by their 2-section. We show that certain motifs, which are specified subhypergraphs of small order, have faster growth rates in ILTH hypergraphs than in random hypergraphs with the same order and expected average degree. We show that the graphs admitting a homomorphism into the 2-section of the initial hypergraph appear as induced subgraphs in the 2-section of ILTH hypergraphs. We consider new and existing hypergraph clustering coefficients, and show that these coefficients have larger values in ILTH hypergraphs than in comparable random hypergraphs. [ABSTRACT FROM AUTHOR]

The clustering coefficient of a vertex v, of degree at least 2, in a graph Γ is obtained using the formula C (v) = 2 t (v) deg (v) (deg (v) − 1) , where t (v) denotes the number of triangles of the graph containing v as a vertex, and the clustering coefficient of Γ is defined as the average of the clustering coefficient of all vertices of Γ , that is, C (Γ) = 1 | V | ∑ v ∈ V C (v) , where V is the vertex set of the graph. In this paper, we give explicit expressions for the clustering coefficient of corona and lexicographic products, as well as for the Cartesian sum; such expressions are given in terms of the order and size of factors, and the degree and number of triangles of vertices in each factor. [ABSTRACT FROM AUTHOR]

We propose a novel algorithm called Unique Brain Network Identification Number (UBNIN) for encoding the brain networks of individual subjects. To realize this objective, we employed structural MRI on 180 Parkinson's disease (PD) patients and 70 healthy controls (HC) from the National Institute of Mental Health and Neurosciences, India. We parcellated each subject's brain volume and constructed an individual adjacency matrix using the correlation between the gray matter volumes of every pair of regions. The unique code is derived from values representing connections for every node (i), weighted by a factor of 2−(i−1). The numerical representation (UBNIN) was observed to be distinct for each individual brain network, which may also be applied to other neuroimaging modalities. UBNIN ranges observed for PD were 15,360 to 17,768,936,615,460,608, and HC ranges were 12,288 to 17,733,751,438,064,640. This model may be implemented as a neural signature of a person's unique brain connectivity, thereby making it useful for brainprinting applications. Additionally, we segregated the above datasets into five age cohorts: A: ≤32 years (n1 = 4, n2 = 5), B: 33–42 years (n1 = 18, n2 = 14), C: 43–52 years (n1 = 42, n2 = 23), D: 53–62 years (n1 = 69, n2 = 22), and E: ≥63 years (n1 = 46, n2 = 6), where n1 and n2 are the number of individuals in PD and HC, respectively, to study the variation in network topology over age. Sparsity was adopted as the threshold estimate to binarize each age-based correlation matrix. Connectivity metrics were obtained using Brain Connectivity toolbox (Version 2019-03-03)-based MATLAB (R2020a) functions. For each age cohort, a decreasing trend was observed in the mean clustering coefficient with increasing sparsity. Significantly different clustering coefficients were noted in PD between age-cohort B and C (sparsity: 0.63, 0.66), C and E (sparsity: 0.66, 0.69), and in HC between E and B (sparsity: 0.75 and above 0.81), E and C (sparsity above 0.78), E and D (sparsity above 0.84), and C and D (sparsity: 0.9). Our findings suggest network connectivity patterns change with age, indicating network disruption may be due to the underlying neuropathology. Varying clustering coefficients for different cohorts indicate that information transfer between neighboring nodes changes with age. This provides evidence of age-related brain shrinkage and network degeneration. We also discuss limitations and provide an open-access link to software codes and a help file for the entire study. [ABSTRACT FROM AUTHOR]

A simple but powerful network model with n$$ n $$ nodes and m$$ m $$ partly overlapping layers is generated as an overlay of independent random graphs G1,...,Gm$$ {G}_1,\dots, {G}_m $$ with variable sizes and densities. The model is parameterized by a joint distribution Pn$$ {P}_n $$ of layer sizes and densities. When m$$ m $$ grows linearly and Pn→P$$ {P}_n\to P $$ as n→∞$$ n\to \infty $$, the model generates sparse random graphs with a rich statistical structure, admitting a nonvanishing clustering coefficient together with a limiting degree distribution and clustering spectrum with tunable power‐law exponents. Remarkably, the model admits parameter regimes in which bond percolation exhibits two phase transitions: the first related to the emergence of a giant connected component, and the second to the appearance of gigantic single‐layer components. [ABSTRACT FROM AUTHOR]

In this paper we deal with a network analysis of interconnected cabinets in Greece for an extended time period. In parallel, we present a small review of the economic crises that have occurred in Greece over this period. More particularly, we used historical sources to locate all different Greek governments and all economic crises starting from the 1821 Greek revolution to the present days. We also formed a two-mode (also known as affiliation) network of ministers and cabinets and subsequently created a network of interconnected cabinets. We used dedicated software to visualize this network and used Social Network Analytical procedures in order to calculate its properties. Finally, in an attempt to investigate possible relations between network metrics and economic crises, we note and discuss an interesting observation between a specific metrics and such major economic events. In our paper, we firstly introduce the context and present our research questions. We then present the relevant literature, mainly discussing the extent to which Social Network Analysis has been used to investigate patterns of behaviors in politics. We then proceed to presenting and applying our methodology on network creation, visualization and metrics computations. The following section discusses the longitudinal evolution of our network and the relation between its clustering coefficient and the emergence of economic crises. We then finalize our paper with some conclusions.

Abstract Concurrent extreme rainfall events, or synchronous extremes, during Indian Summer Monsoon Rainfall (ISMR), cause significant damage, but their spatiotemporal evolution remains unclear. Using the event synchronization approach to examine the synchronicity of extreme rainfall events from 1901 to 2019, we find that Central India consistently hosts strongly connected synchronous extreme hubs with localized connections, indicating the geographical trapping of these concurrent events in the region. We observe a moderate positive correlation between network cohesiveness and El Niño Southern Oscillations (ENSO), and a negative correlation between ENSO and link lengths, suggesting localized synchronicity during El Niño dominant decades and opposite patterns in La Niña periods. Despite increasing ISMR variability and spatial nonuniformity, the persistence of hubs and network attributes could offer insights for predicting synchronous extremes, informing effective adaptation and risk management strategies during the monsoon season.

Link prediction is one of the most important and challenging tasks in complex network analysis, which aims to predict the existence of unknown links based on the known information in the network. As critical topological properties in the network, node's degree and clustering coefficient are well-suited for describing the tightness of connection between nodes. The importance of node can affect the possibility of link existence to a certain extent. By analyzing the impact of different centrality on links, which concluded that the degree centrality and proximity centrality have the greatest influence on network link prediction. A link prediction algorithm combines importance of node and network topological properties, called DCCLP, is proposed in this paper, the symmetry of the adjacency matrix is considered in the DCCLP link prediction algorithm to further describe the structural similarity of network nodes. In the training phase of the DCCLP algorithm, the maximized AUC indicator in the training set as the objective, and the optimal parameters are estimated by utilizing the White Shark Optimization algorithm. Then the prediction accuracy of the DCCLP algorithm is evaluated in the test set. By experimenting on twenty-one networks with different scales, and comparing with existing algorithms, the experimental results show that the effectiveness and feasibility of DCCLP algorithm, and further illustrate the importance of the degree centrality of node pairs and proximity centrality of nodes to improve the prediction accuracy of link prediction. [ABSTRACT FROM AUTHOR]

The structure of a model has an important impact on information dissemination. Many information models of hypernetworks have been proposed in recent years, in which nodes and hyperedges represent the individuals and the relationships between the individuals, respectively. However, these models select old nodes based on preference attachment and ignore the effect of aggregation. In real life, friends of friends are more likely to form friendships with each other, and a social network should be a hypernetwork with an aggregation phenomenon. Therefore, a social hypernetwork evolution model with adjustable clustering coefficients is proposed. Subsequently, we use the SIS (susceptible–infectious–susceptible) model to describe the information propagation process in the aggregation-phenomenon hypernetwork. In addition, we establish the relationship between the density of informed nodes and the structural parameters of the hypernetwork in a steady state using the mean field theory. Notably, modifications to the clustering coefficients do not impact the hyperdegree distribution; however, an increase in the clustering coefficients results in a reduced speed of information dissemination. It is further observed that the model can degenerate to a BA (Barabási–Albert) hypernetwork by setting the clustering coefficient to zero. Thus, the aggregation-phenomenon hypernetwork is an extension of the BA hypernetwork with stronger applicability. [ABSTRACT FROM AUTHOR]

Sleep disorders affect more than one-quarter of the world's population, resulting in reduced daytime productivity, impaired immune function, and an increased risk of cardiovascular disease. It is important to identify the physiological and psychological factors related to sleep for the prevention and treatment of sleep disorders. In this study, we correlated measurements of emotional state, sleep quality, and some brain neural activity parameters to better understand the brain and psychological factors related to sleep. Resting-state functional magnetic resonance imaging (rs-fMRI) of 116 healthy undergraduates were analyzed using graph theory to assess regional topological characteristics. Among these, the left thalamic cluster coefficient proved to be the ablest to reflect the characteristics of the sleep neural graph index. The Profile of Mood States (POMS) was used to measure vigor, and the Pittsburgh Sleep Quality Index (PSQI) to assess sleep quality. The results showed that the left thalamic clustering coefficient was negatively correlated with sleep quality and vigor. Further, the left thalamic clustering coefficient moderated the relationship between vigor and sleep quality. When the left thalamic clustering coefficient was very low, there was a significant positive correlation between vigor and sleep quality. However, when the left thalamic clustering coefficient was high, the correlation between vigor and sleep quality became insignificant. The relationship between vigor and sleep quality is heterogeneous. Analyzing the function of the left thalamic neural network could help understand the variation in the relationship between vigor and sleep quality in different populations. Such observations may help in the development of personalized interventions for sleep disorders. [ABSTRACT FROM AUTHOR]

The exponential growth of social media platforms has led to a demand for applications related to social network analysis. One major challenge in social network analysis is identifying communities within the network. In this work, a novel QST-ClustNet is proposed in which the sooty tern optimization algorithm is integrated with the quantum behavior to identify the communities within the social network by clustering the user profiles. Initially, the LinkedIn dataset is pre-processed using natural language processing (NLP) techniques such as data extraction, removal of stop words handling the missing data or values, and data stemming for removing irrelevant data. After preprocessing the feature are extracted using bag of words for the creation on user profiles. These created features are given as an input to frequency probability-based similarity measures to find similarities between users. Finally, quantum-inspired Sooty tern optimization is utilized for clustering the user profile in social networks. The effectiveness of the proposed strategy is examined using several parameters, such as Davies Bouldin score, Calinski Harabasz score, and Silhouette score. The proposed QST-ClustNet improves the silhouette score 22.48, 16.25, and 11.081 better than K mean clustering, C mean clustering, and fuzzy C mean clustering respectively. This approach helps examine and comprehend the structure of professional networks of online social networks, which can be applied for multiple applications such as job recommendation, talent acquisition, and many more. [ABSTRACT FROM AUTHOR]

Complex networks in reality are not just single-layer networks. The connection of nodes in an urban metro network includes two kinds of connections: line and passenger flow. In fact, it is a multilayer network. The line network constructed by the Space L model based on a complex network reflects the geographical proximity of stations, which is an undirected and weightless network. The passenger flow network constructed with smart card big data reflects the passenger flow relationship between stations, which is a directed weighted network. The construction of a line-flow multilayer network can reflect the actual situation of metro traffic passenger flow, and the node clustering coefficient can measure the passenger flow clustering effect of the station on adjacent stations. Combined with the situation of subway lines in Nanjing and card-swiping big data, this research constructs the line network with the Space L model and the passenger flow network with smart card big data, and uses these two networks to construct the multilayer network of line flow. This research improves the calculation method of the clustering coefficient of weighted networks, proposes the concept of node group, distinguishes the inflow and outflow, and successively calculates the clustering coefficient of nodes and the whole network in the multilayer network. The degree of passenger flow activity in the network thermal diagram is used to represent the passenger flow activity of the line-flow network. This method can be used to evaluate the clustering effect of metro stations and identify the business districts in the metro network, so as to improve the level of intelligent transportation management and provide a theoretical basis for transportation construction and business planning. [ABSTRACT FROM AUTHOR]

Over the past decade, there has been extensive research conducted on complex networks, primarily driven by their crucial role in understanding the various real-world networks such as social networks, communication networks, transportation networks, and biological networks. Ranking influential nodes is one of the fundamental research problems in the areas of rumor spreading, disease research, viral marketing, and drug development. Influential nodes in any network are used to disseminate the information as fast as possible. Centrality measures are designed to quantify the node’s significance and rank the influential nodes in complex networks. However, these measures typically focus on either the local or global topological structure within and outside network communities. In particular, many measures limit their ability to capture the node’s overall impact on small-scale networks. To address these challenges, we develop a novel centrality measure called Isolating Clustering Distance Centrality (ICDC) by integrating the isolating and clustering coefficient centrality measures. The proposed metric gives a more thorough assessment of the node’s importance by integrating the local isolation and global topological influence in large-scale complex networks. We employ the SIR and ICM epidemic models to study the efficiency of ICDC against traditional centrality measures across real-world complex networks. Our experimental findings consistently highlight the superior efficacy of ICDC in terms of fast spreading and computational efficiency when compared to existing centrality measures.

For the comparative analysis of proteins, their proper clustering, and evolutionary relationships require analysis of their sequences. We used a mathematical parameter termed a similar factor to create a similar degree matrix of ND6 protein sequences taken from eight different species in this paper. We built a network out of the matrix to analyze their evolutionary and similarity trends with each other. By observing the various centrality measures, the correlation between multiple centrality measures and different network parameter shows that our network is consistent with the known evolution fact of ND6 protein sequences.

Studies of brain network organisation have swiftly adopted graph theory-based quantitative analysis of complicated networks. Small-world topology, densely connected hubs, and modularity characterise the brain's structural and functional systems. Many measures quantify graph topology. It has not yet been determined which measurements are most appropriate for brain network analysis. This work introduces a new parameter applicable to brain network analysis. This parameter may help in the identification of symmetry and the study of symmetry breakdown in the brain. This is important because decreased symmetry in the brain is associated with a decreased chance of developing neurodevelopmental and psychiatric disorders. This work is to study brain networks using maximal independent set-based topological indices. These indices seem to depict significant properties of brain networks, such as clustering, small-worldness, etc. One new parameter introduced in this paper for brain network analysis depends on Zagreb topological indices and independence degree. This parameter is useful for analyzing clusters, rich clubs, small-worldness, and connectivity in modules. [ABSTRACT FROM AUTHOR]

When an individual is socially connected to two others, the resulting triplet can be closed (if the two social partners are themselves connected) or open (if they are not connected). The proportion of closed triplets, referred to as the binary network transitivity, is a classic measure of the level of interconnectedness of a social network. However, in any given triplet, if the closing link is weak, or indeed if any of the links in the triplet is weak, then the triplet should not contribute as much to network transitivity as if all three links were equally strong. I propose two ways to weight the contribution of each triplet according to the dissimilarity between the three links in the triplet. Empirically, the resulting new metrics conveyed information not picked up by any other network-level metric. I envision that this approach could prove useful in studies of triadic mechanisms, i.e., situations where pre-existing social ties influence the interactions with third parties. These metrics could also serve as repeatable synthetic variables that summarize information about the variability of the strength of social connections. • The transitivity of social networks is classically computed by summing over "triplet" contributions. • I weight the contribution of each triplet using the three links inside of it. • The resulting new metrics effectively captured information otherwise conveyed by 8 metrics, and more. • The new metrics are particularly geared towards studies into triadic mechanisms. [ABSTRACT FROM AUTHOR]

Meaningful representation of large-scale non-Euclidean structured data, especially in complex domains like network security and IoT system, is one of the critical problems of contemporary machine learning and deep learning. Many successful cases of graph-based models and algorithms deal with non-Euclidean structured data. However, It is often undesirable to derive node representations by walking through the complete topology of a system or network (graph) when it has a very big or complicated structure. An important issue is using neighborhood knowledge to deduce the symmetric network's topology or graph. The traditional approach to solving the graph representation learning issue is surveyed from machine learning and deep learning perspectives. Second, include local neighborhood data encoded to the attention mechanism to define node solidarity and enhance node capture and interactions. The performance of the proposed model is then assessed for transduction and induction tasks that include downstream node categorization. The attention model taking clustering into account has successfully equaled or reached the state-of-the-art performance of several well-established node classification benchmarks and does not depend on previous knowledge of the complete network structure, according to experiments. Following a summary of the research, we discuss problems and difficulties that must be addressed for developing future graph signal processing algorithms and graph deep learning models, such as graph embeddings' interpretability and adversarial resilience. At the same time, it has a very positive impact on network security and artificial intelligence security. [ABSTRACT FROM AUTHOR]

In this paper we deal with a network analysis of interconnected cabinets in Greece for an extended time period. In parallel, we present a small review of the economic crises that have occurred in Greece over this period. More particularly, we used historical sources to locate all different Greek governments and all economic crises starting from the 1821 Greek revolution to the present days. We also formed a two-mode (also known as affiliation) network of ministers and cabinets and subsequently created a network of interconnected cabinets. We used dedicated software to visualize this network and used Social Network Analytical procedures in order to calculate its properties. Finally, in an attempt to investigate possible relations between network metrics and economic crises, we note and discuss an interesting observation between a specific metrics and such major economic events. In our paper, we firstly introduce the context and present our research questions. We then present the relevant literature, mainly discussing the extent to which Social Network Analysis has been used to investigate patterns of behaviors in politics. We then proceed to presenting and applying our methodology on network creation, visualization and metrics computations. The following section discusses the longitudinal evolution of our network and the relation between its clustering coefficient and the emergence of economic crises. We then finalize our paper with some conclusions. [ABSTRACT FROM AUTHOR]

Link prediction finds the future or the missing links in a social–biological complex network such as a friendship network, citation network, or protein network. Current methods to link prediction follow the network properties, such as the node's centrality, the number of edges, or the weights of the edges, among many others. As the properties of the networks vary, the link prediction methods also vary. These methods are inaccurate since they exploit limited information. This work presents a link prediction method based on the stochastic block model. The novelty of our approach is the three-step process to find the most-influential nodes using the m-PageRank metric, forming blocks using the global clustering coefficient and, finally, predicting the most-optimized links using maximum likelihood estimation. Through the experimental analysis of social, ecological, and biological datasets, we proved that the proposed model outperforms the existing state-of-the-art approaches to link prediction. [ABSTRACT FROM AUTHOR]

Abstract Multiple network embedding algorithms have been proposed to perform the prediction of missing or future links in complex networks. However, we lack the understanding of how network topology affects their performance, or which algorithms are more likely to perform better given the topological properties of the network. In this paper, we investigate how the clustering coefficient of a network, i.e., the probability that the neighbours of a node are also connected, affects network embedding algorithms’ performance in link prediction, in terms of the AUC (area under the ROC curve). We evaluate classic embedding algorithms, i.e., Matrix Factorisation, Laplacian Eigenmaps and node2vec, in both synthetic networks and (rewired) real-world networks with variable clustering coefficient. Specifically, a rewiring algorithm is applied to each real-world network to change the clustering coefficient while keeping key network properties. We find that a higher clustering coefficient tends to lead to a higher AUC in link prediction, except for Matrix Factorisation, which is not sensitive to the change of clustering coefficient. To understand such influence of the clustering coefficient, we (1) explore the relation between the link rating (probability that a node pair is the missing link) derived from the aforementioned algorithms and the number of common neighbours of the node pair, and (2) evaluate these embedding algorithms’ ability to reconstruct the original training (sub)network. All the network embedding algorithms that we tested tend to assign higher likelihood of connection to node pairs that share an intermediate or high number of common neighbours, independently of the clustering coefficient of the training network. Then, the predicted networks will have more triangles, thus a higher clustering coefficient. As the clustering coefficient increases, all the algorithms but Matrix Factorisation could also better reconstruct the training network. These two observations may partially explain why increasing the clustering coefficient improves the prediction performance.

The genetic code is a series of codons that stores genetic information about protein molecule formation. The identity graph of a group G is a graph in which the vertex set is the set of all elements of the group and two vertices in G are adjacent if a.b = e, where e is the group's identity element. Let H be a subgroup of G then the identity graph drawn for the subgroup H is known as the identity special subgraph of G (special identity subgraph of G). In this study, we looked at the special identity graph in the genetic code algebra. Different measures of centrality have been thoroughly discussed in our current study. Aside from this investigation, research is being conducted on the correlation coefficients between different measures of centrality, as well as the clustering coefficient, degree of distribution, and skewness.