Types Of Networks Research Articles

Integrating Radial Basis Networks and Deep Learning for Transportation

Introduction This research focuses on the concept of integrating Radial Basis Function Networks with deep learning models to solve robust regression tasks in both transportation and logistics. Methods It examines such combined models as RNNs with RBFNs, Attention Mechanisms with Radial Basis Function Networks (RBFNs), and Capsule Networks with RBFNs and clearly shows that, in all cases, compared to the others, the former model has a Mean Squared Error (MSE) of 0.010 to 0.013, Mean Absolute Error (MAE) – 0.078 to 0.088, and R-squared (R2) – 0.928 to 0.945, across ten experiments. In the case of Attention Mechanisms with RBFNs, the models also demonstrate strong performance in terms of making predictions. The MSE ranges from 0.012 to 0.015, the MAE from 0.086 to 0.095, and the R2 from 0.914 to 0.933. Results However, it is critical to note that the Capsule Networks with RBFNs outperform other models. In particular, they offer the lowest MSE, which is between 0.009 and 0.012, the smallest MAE, which ranges from 0.075 to 0.083, and the highest R2, from 0.935 to 0.950. Conclusion Overall, the results indicate that the use of RBFNs in combination with different types of deep learning networks can provide highly accurate and reliable solutions for regression problems in the domain of transportation and logistics.

How synchronized human networks escape local minima

Finding the global minimum in complex networks while avoiding local minima is challenging in many types of networks. In human networks and communities, adapting and finding new stable states amid changing conditions due to conflicts, climate changes, or disasters, is crucial. We studied the dynamics of complex networks of violin players and observed that such human networks have different methods to avoid local minima than other non-human networks. Humans can change the coupling strength between them or change their tempo. This leads to different dynamics than other networks and makes human networks more robust and better resilient against perturbations. We observed high-order vortex states, oscillation death, and amplitude death, due to the unique dynamics of the network. This research may have implications in politics, economics, pandemic control, decision-making, and predicting the dynamics of networks with artificial intelligence.

Social participation and depression among resettled Syrian refugees: examining a moderated mediation of social support and bonding or bridging social capital

IntroductionAspects of social capital, including social participation and social support, are among the factors influencing refugee mental health after resettlement. However, the mechanisms by which these aspects interact with one another and affect mental health remain unclear. This study investigates whether social participation influences depressive symptoms via social support and whether this influence is more prominent for Syrian refugees participating primarily in coethnic (bonding) networks compared to cross-ethnic (bridging) networks during the early stages of resettlement.MethodsUsing data from a cohort of 464 Syrian refugees recently resettled in Sweden, a moderated mediation analysis was conducted with multigroup structural equation modelling to investigate the mediatory role of social support in the association between social participation and depressive symptoms as well as the moderating role of bonding networks (social participation with other Syrians) versus bridging networks (social participation with Swedes) in this relationship.ResultsFrequent social participation, compared to rare or no participation, was significantly associated with lower depressive symptoms, regardless of whether participation included a broad or limited range of activities. Social support only mediated this relationship for those with primarily bonding networks, indicating that the mediation itself was moderated by network type. While participating in both bridging and bonding networks was associated with lower depressive symptoms, bonding networks amplified the effect of social participation on depressive symptoms via increased social support, resulting in an overall twofold decrease in depressive symptoms compared to those with bridging networks.DiscussionThese findings indicate that the frequency of social participation may be a more important consideration for fostering mental well-being in recently resettled refugees than the specific types of activities. Furthermore, while both bonding and bridging social networks confer mental health benefits, access to coethnic networks in early resettlement appears to provide a particularly crucial source of social support.

Hybrid Space Calibrated 3D Network of Diffractive Hyperspectral Optical Imaging Sensor

Diffractive multispectral optical imaging plays an essential role in optical sensing, which typically suffers from the image blurring problem caused by the spatially variant point spread function. Here, we propose a novel high-quality and efficient hybrid space calibrated 3D network “HSC3D” for spatially variant diffractive multispectral imaging that utilizes the 3D U-Net structure combined with space calibration modules of magnification and rotation effects to achieve high-accuracy eight-channel multispectral restoration. The algorithm combines the advantages of the space calibrated module and U-Net architecture with 3D convolutional layers to improve the image quality of diffractive multispectral imaging without the requirements of complex equipment modifications and large amounts of data. A diffractive multispectral imaging system is established by designing and manufacturing one diffractive lens and four refractive lenses, whose monochromatic aberration is carefully corrected to improve imaging quality. The mean peak signal-to-noise ratio and mean structural similarity index of the reconstructed multispectral images are improved by 3.33 dB and 0.08, respectively, presenting obviously improved image quality compared with a typical Unrolled Network algorithm. The new algorithm with high space calibrated ability and imaging quality has great application potential in diffraction lens spectroscopy and paves a new method for complex practical diffractive multispectral image sensing.

Advancing Marine Surveillance: A Hybrid Approach of Physics Infused Neural Network for Enhanced Vessel Tracking Using Automatic Identification System Data

In the domain of maritime surveillance, the continuous tracking and monitoring of vessels are imperative for the early detection of potential threats. The Automatic Identification System (AIS) database, which collects vessel movement data over time, including timestamps and other motion details, plays a crucial role in real-time maritime monitoring. However, it frequently exhibits irregular intervals of data collection and intricate, intersecting trajectories, underscoring the importance of analyzing long-term temporal patterns for effective vessel tracking. While Kalman Filters and other physics-based models have been employed to tackle these issues, their effectiveness is limited by their inability to capture long-term dependence and non-linearity in the historical data. This paper introduces a novel approach that leverages Long Short-Term Memory (LSTM), a type of recurrent neural network, renowned for its proficiency in recognizing patterns over extended periods. Recognizing the strengths and limitations of the LSTM model, we propose a hybrid machine-learning algorithm that integrates LSTM with a physics-based model. This combination harnesses the physical laws governing vessel movements alongside data driven pattern mining, thereby enhancing the predictive accuracy of vessel locations. To assess the performance of standalone and hybrid models, various scenarios with different levels of complexity are generated. Furthermore, to simulate real-world data loss conditions often encountered in maritime tracking, temporal data gaps are randomly introduced into the scenarios. The competing approaches are then evaluated using both with time gap and without time gap conditions. Our results show that, although the LSTM model performs better than the physics-based model, the hybrid model consistently outperforms both standalone models across all scenarios. Furthermore, while data gaps negatively impact the accuracy of all models, the performance reduction is minimal for the physics-infused model. In summary, this study not only demonstrates the potential of combining data-driven and physics-based approaches but also sets a new benchmark for maritime vessel tracking.

Error and attack vulnerability of Apollonian networks

Abstract This article examines the resilience of different Apollonian network (AN) types—deterministic, random, and evolutionary—to systematic attacks. ANs, members of the family of maximal planar graphs, possess unique properties such as high clustering coefficients, small-world properties, scale-free behavior, Euclidean and space-filling properties, and modularity. These peculiarities require a thorough investigation of their robustness. This work presents a novel approach to studying ANs by implementing evolutionary Apollonian networks (EANs). These EANs include various probabilities distribution functions, including exponential, degenerate, logistic, Pareto, and stable (Cauchy, Lévy, Normal) distributions. To improve the robustness of these networks, we propose a novel edge rewiring mechanism using a genetic algorithm (GA). The GA aims to optimize a combined metric that includes the Flow Robustness of Degree (SFRD), Betweenness (SFRB), and Dangalchev's closeness (SFRC) centralities while preserving the original degree distribution and structural properties of the network. To evaluate the effectiveness of this approach, we use various robustness measures to assess the resilience of different AN types. The results show that SFRB, SFRD, and SFRC effectively rank ANs based on their robustness.

The application of social network analysis in applied linguistics research: a systematic review

Abstract Social network analysis (SNA) has recently drawn increasing scholarly attention in applied linguistics research in response to the social turn in the field. In this review, we analyze and identify the methodological characteristics and topical concerns of articles addressing SNA in Social Science Citation Index (SSCI) journals. Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, we identify a total of 60 articles published between 1980 and 2023. Our analysis reveals that a growing body of research is adopting qualitative and mixed methods to examine the relationships between social networks and language learning, teaching and use. These findings confirm that social context constitutes an essential part of the ecosystem intertwined with various cognitive, social, and psychological factors, which have a synergistic impact on language learning and teaching. While these studies show that social networks afford learners with valuable linguistic, emotional, and social resources, they reveal that networks may also exert negative influences in their learning behaviors in some contexts. We conclude the review with recommendations for future research to broaden the scope of investigations and consider exploring how different types of social networks at meso- and macro-levels may influence the learning and teaching of language.

SPLANG—a synthetic poisson-lognormal-based abundance and network generative model for microbial interaction inference algorithms

Microbes are pervasive and their interaction with each other and the environment can impact fields as diverse as health and agriculture. While network inference and related algorithms that use abundance data from pyrosequencing can infer microbial interaction networks, the ambiguity surrounding the actual underlying networks hampers the validation of these algorithms. This study introduces a generative model to synthesize both the underlying interactive network and observable abundance data, serving as a test bed for the existing and future network inference algorithms. We tested our generative model with four typical network inference algorithms; our results suggest that none of these algorithms demonstrate adequate accuracy for inferring ecologies of non-commensalistic species, either mutualistic or competitive. We further explored the potential for predictability by combining existing algorithms with an oracle algorithm built by fusing the results of several existing algorithms. The oracle algorithm reveals promising improvements in predictability, although it falls short when applied to networks characterized by dense interspecies taxa interactions. Our work underscores the need for the continued development and validation of algorithms to unravel the intricacies of microbial interaction networks.

Lightweight Advanced Deep Neural Network (DNN) Model for Early-Stage Lung Cancer Detection

Background: Lung cancer, also known as lung carcinoma, has a high mortality rate; however, an early prediction helps to reduce the risk. In the current literature, various approaches have been developed for the prediction of lung carcinoma (at an early stage), but these still have various issues, such as low accuracy, high noise, low contrast, poor recognition rates, and a high false-positive rate, etc. Thus, in this research effort, we have proposed an advanced algorithm and combined two different types of deep neural networks to make it easier to spot lung melanoma in the early phases. Methods: We have used WDSI (weakly supervised dense instance-level lung segmentation) for laborious pixel-level annotations. In addition, we suggested an SS-CL (deep continuous learning-based deep neural network) that can be applied to the labeled and unlabeled data to improve efficiency. This work intends to evaluate potential lightweight, low-memory deep neural net (DNN) designs for image processing. Results: Our experimental results show that, by combining WDSI and LSO segmentation, we can achieve super-sensitive, specific, and accurate early detection of lung cancer. For experiments, we used the lung nodule (LUNA16) dataset, which consists of the patients’ 3D CT scan images. We confirmed that our proposed model is lightweight because it uses less memory. We have compared them with state-of-the-art models named PSNR and SSIM. The efficiency is 32.8% and 0.97, respectively. The proposed lightweight deep neural network (DNN) model archives a high accuracy of 98.2% and also removes noise more effectively. Conclusions: Our proposed approach has a lot of potential to help medical image analysis to help improve the accuracy of test results, and it may also prove helpful in saving patients’ lives.

Sustainable last mile logistics employing drones and e-bikes

Last mile delivery is an important and growing part of the supply chain that has a sizeable negative environmental impact. This paper considers more sustainable approaches to home-delivery that are pragmatic for many non-rural environments. We address the two-echelon, multi-trip, capacitated vehicle routing problem with home-delivery and optional self-pickup services using different combinations of drones, trucks, and electric-assisted bikes (i.e. e-bikes). In the proposed approach, parcels are transported from a depot to parcel lockers by either drones or trucks and are then delivered to customer locations by either e-bikes or trucks. The four approaches range from the most sustainable (drones then e-bikes) to partly green (drone then truck or truck then e-bike) to finally the traditional (truck then truck). We formulate a mathematical model that determines the vehicle routes to minimize the total cost, which consists of vehicle operational cost and operator wages. The four types of delivery networks are assessed and compared for both costs and emissions. Experimental results suggest that with a modest increase in total cost (as little as 13%), emission reductions of up to 92%, on average, can be achieved when using the greenest delivery strategy of drones and e-bikes. The other delivery options have varying tradeoffs between costs and environmental impact. The percentage of self-pickup customers is an influencing factor to consider when choosing the delivery strategy that best meets the organization’s budget and environmental goals, especially when using e-bikes in the second echelon.

How does OTT social viewing relieve pandemic-related depressive symptoms? Investigating the moderated mediation model of social connectedness and network types

ABSTRACT After the outbreak of COVID-19, people have lacked offline social opportunities and had to focus their energy on online social activities. While some researchers have proposed that both anxiety and depression have increased significantly during the COVID-19 pandemic, previous studies have provided evidence that people have mitigated negative emotions during the health crisis by using online services. In this manner, the pandemic-induced increase in online activity has significantly boosted global demand for online video services (Over-the-Top, OTT). OTT social viewing refers to the act of interacting with other users while simultaneously watching content through the social viewing service provided by OTT service providers. Drawing on the social compensation hypothesis and social capital theory, we surveyed people who experienced COVID-19-related depression and used Watch party, a key OTT social viewing service in Korea. The study reveals that while social media alone did not directly alleviate COVID-19-related depression, emotional stability was regained through building social connectedness via online activities. Furthermore, the study highlights that in OTT social viewing, the quality of interactions, rather than the quantity, was more crucial for forming social connectedness.

Contrasting topologies of synchronous and asynchronous functional brain networks

ABSTRACT We generated asynchronous functional networks (aFNs) using a novel method called optimal causation entropy and compared aFN topology with the correlation-based synchronous functional networks (sFNs), which are commonly used in network neuroscience studies. Functional magnetic resonance imaging (fMRI) time series from 212 participants of the National Consortium on Alcohol and Neurodevelopment in Adolescence study were used to generate aFNs and sFNs. As a demonstration of how aFNs and sFNs can be used in tandem, we used multivariate mixed effects models to determine whether age interacted with node efficiency to influence connection probabilities in the two networks. After adjusting for differences in network density, aFNs had higher global efficiency but lower local efficiency than the sFNs. In the aFNs, nodes with the highest outgoing global efficiency tended to be in the brainstem and orbitofrontal cortex. aFN nodes with the highest incoming global efficiency tended to be members of the default mode network in sFNs. Age interacted with node global efficiency in aFNs and node local efficiency in sFNs to influence connection probability. We conclude that the sFN and aFN both offer information about functional brain connectivity, which the other type of network does not.

Implementing Long Short Term Memory (LSTM) in Chatbots for Multi Usaha Raya

The furniture industry is an important sector in Indonesia that supports the economy and provides quality furniture. An in-depth understanding of the furniture business is essential for industry players to improve operational efficiency and customer satisfaction. This research aims to develop a chatbot for Multi Usaha Raya furniture company to improve customer service and operational efficiency. In its development, the Machine Learning Model Development Life Cycle (MDLC) and deep learning approach using the Flask platform are employed. LSTM, a type of recurrent neural network (RNN) architecture capable of handling long-term dependencies, is utilized in this chatbot model. The model training results show an accuracy of 99%, validation accuracy of 96%, loss of 0.1%, and validation loss of 0.2% after 200 epochs, demonstrating the effectiveness of the LSTM algorithm for developing a chatbot in this company.

Spotting Leaders in Organizations with Graph Convolutional Networks, Explainable Artificial Intelligence, and Automated Machine Learning

Over the past few decades, the study of leadership theory has expanded across various disciplines, delving into the intricacies of human behavior and defining the roles of individuals within organizations. Its primary objective is to identify leaders who play significant roles in the communication flow. In addition, behavioral theory posits that leaders can be distinguished based on their daily conduct, while social network analysis provides valuable insights into behavioral patterns. Our study investigates five and six types of social networks frequently observed in different organizations. This study is conducted using datasets we collected from an IT company and public datasets collected from a manufacturing company for the thorough evaluation of prediction performance. We leverage PageRank and effective word embedding techniques to obtain novel features. State-of-the-art performance is obtained using various statistical machine learning methods, graph convolutional networks (GCN), automated machine learning (AutoML), and explainable artificial intelligence (XAI). More specifically, our approach can achieve state-of-the-art performance with an accuracy close to 90% for leaders identification with data from projects of different types. This investigation contributes to the establishment of sustainable leadership practices by aiding organizations in retaining their leadership talent.

The national network of US state legislators on Twitter

Abstract Networks among legislators shape politics and policymaking within legislative institutions. In past work on legislative networks, the ties between legislators have been defined on those who serve in the same legislature or chamber. Online information networks, which have been found to play important roles in legislative communication at the national level, are not bounded by individual legislative bodies. We collect original data for over four thousand US state legislators and study patterns of connection among them on Twitter. We look at three types of Twitter networks—follower, retweets, and mentions. We describe these networks and estimate the relationships between ties and salient attributes of legislators. We find that networks are organized largely along geographic and partisan lines and that identity attributes—namely gender and race—exhibit strong associations with the formation of ties.

Development of Robot Feature for Stunting Analysis Using Long-Short Term Memory (LSTM) Algorithm

Stunting prevalence in Indonesia persists as a significant challenge necessitating concerted efforts from all stakeholders. We developed robot for stunting analysis using deep learning algorithm. It aligns with the Sustainable Development Goal (SDG) agenda, specifically targeting SDG 3, which focuses on ensuring good health and well-being for all. Long Short-Term Memory (LSTM) is a type of Recurrent Neural Network (RNN) designed to overcome the vanishing gradient problem in traditional RNNs. In general, either LSTM can be used in analysis. This study aims to classify stunting based on age and height using LSTM. The LSTM model was trained with 50 epochs using datasets collected from the health office and robots. The evaluation results show training accuracy of 96.65% and training validation of 96.61%, with precision, recall and f1-score varying with relevance to the f1-score and support value. This research illustrates the potential for using data classification methods in stunting diagnosis. However, it is necessary to adjust parameters and increase the amount of training data to improve model performance. With good convergence at epoch 50, these results show the model's ability to classify stunting based on age and height. However, further validation and testing on larger datasets is needed to thoroughly test the reliability and generalization of the model. This research can contribute to the development of deep learning regarding robots as a means of testing stunting. This research provides initial evidence of the potential of stunting classification methods using robots. However, parameter adjustments and increasing the amount of training data need to be done to improve the overall model performance.

Early detection of sepsis using machine learning algorithms: a systematic review and network meta-analysis.

With machine learning (ML) carving a niche in diverse medical disciplines, its role in sepsis prediction, a condition where the 'golden hour' is critical, is of paramount interest. This study assesses the factors influencing the efficacy of ML models in sepsis prediction, aiming to optimize their use in clinical practice. We searched Medline, PubMed, Google Scholar, and CENTRAL for studies published from inception to October 2023. We focused on studies predicting sepsis in real-time settings in adult patients in any hospital settings without language limits. The primary outcome was area under the curve (AUC) of the receiver operating characteristic. This meta-analysis was conducted according to PRISMA-NMA guidelines and Cochrane Handbook recommendations. A Network Meta-Analysis using the CINeMA approach compared ML models against traditional scoring systems, with meta-regression identifying factors affecting model quality. From 3,953 studies, 73 articles encompassing 457,932 septic patients and 256 models were analyzed. The pooled AUC for ML models was 0.825 and it significantly outperformed traditional scoring systems. Neural Network and Decision Tree models demonstrated the highest AUC metrics. Significant factors influencing AUC included ML model type, dataset type, and prediction window. This study establishes the superiority of ML models, especially Neural Network and Decision Tree types, in sepsis prediction. It highlights the importance of model type and dataset characteristics for prediction accuracy, emphasizing the necessity for standardized reporting and validation in ML healthcare applications. These findings call for broader clinical implementation to evaluate the effectiveness of these models in diverse patient groups. https://inplasy.com/inplasy-2023-12-0062/, identifier, INPLASY2023120062.

The Extent and Patterns of Digitalization in Proactive Land Acquisition Strategy (PLAS) Farms in South Africa

This study sought to develop an index for agricultural digitalization by applying composite confirmatory analysis (CCA). Another aim was to determine the factors that affect the development of digitalization in PLAS farms. Data on the indicators of the three dimensions of digitalization were collected from 300 Proactive Land Acquisition Strategy (PLAS) farms in South Africa using semi-structured questionnaires. Confirmatory composite analysis (CCA) was employed to reduce the items into three digitalization dimensions and ultimately to a digitalization index. Standardized digitalization index scores were extracted and fitted to a linear regression model to determine the factors affecting digitalization. The results revealed that the model shows practical validity and can be used to measure digitalization as measures of fit (geodesic distance, standardized root mean square residual, and squared Euclidean distance) were all below their respective 95%quantiles of bootstrap discrepancies (HI95 values). Therefore, digitalization is an emergent variable that can be measured using CCA. The average level of digitalization in PLAS farms was 0.02 and varied significantly across provinces. Although farmers have attempted to digitalise their farms, there are still minimal levels of digitalization in PLAS farms. The results further reveal different digitalization patterns. As judged by the estimated weights of various dimensions of digitalization, the use of digital technologies to collect, store, analyse, and disseminate (CSAD) farm-related data contributed more towards the digitalization index. The second most important component of digitalization was automation digitalization. In contrast, value chain digitalization was the least significant contributor. The factors that significantly influence digitalization were age, gender, farm type, network type, and cellular data type. Since PLAS farmers have not embraced much digitalization, it is important to focus on awareness and capacity building. A balanced approach to digitalization would benefit PLAS farms by ensuring that strategies to integrate digital solutions within the value chain are developed. To foster and support the digitalization in PLAS farms, policymakers and stakeholders should tailor their strategies to fit specific socioeconomic factors.

Measurement-Noise Filtering for Automatic Discovery of Flow Splitting Ratios in ISP Networks

Network telemetry and analytics is essential for providing highly dependable services in modern computer networks. In particular, network flow analytics for ISP networks allows operators to inspect and reason about traffic patterns in their networks in order to react to anomalies. High performance network analytics systems are designed with scalability in mind, and can consequently only observe partial information about the network traffic. Still, they need to provide a holistic view of the traffic, including the distribution of different traffic flows on each link. It is impractical to monitor such fine-grained telemetry, and in large, heterogeneous networks it is often too complex and error-prone, if not impossible, to access and maintain all technical specifications and router-specific configurations needed to determine e.g. the load balancing weights used when traffic is split onto multiple paths. The ratios by which flows are split on the possible paths must be derived indirectly from the measured flow demands and link utilizations. Motivated by a case study provided by a major European ISP, we suggest an efficient method to estimate the flow splitting ratios. Our approach, based on quadratic linear programming, is scalable and achieves robustness to the measurement noise found in a typical network analytics deployment by filtering out certain constraints in the linear program. Finally, we implement an automated tool for estimating the flow splitting ratios and document its applicability on real data from the ISP.

Triangle Centrality

Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none at all. Given a simple, undirected graph \(G=(V,E)\) with \(n=|V|\) vertices and \(m=|E|\) edges, let \(\triangle(v)\) and \(\triangle(G)\) denote the respective triangle counts of \(v\) and \(G\) . Let \(N(v)\) be the neighborhood set of \(v\) . Respectively, \(N_{\triangle}(v)\) and \(N_{\triangle}[v]=\{v\}\cup N_{\triangle}(v)\) denote the set of neighbors that are in triangles with \(v\) and the closed set including \(v\) . Then the triangle centrality for a vertex \(v\) is \(\begin{align*}TC(v)=\frac{\frac{1}{3}\sum_{u\in N_{\triangle}[v]}\triangle(u)+\sum_{w\in\{N(v)\setminus N_{\triangle}(v)\}}\triangle(w)}{\triangle(G)}.\end{align*}\) We show experimentally that triangle centrality is broadly applicable to many different types of networks. Our empirical results demonstrate that 30% of the time triangle centrality identified central vertices that differed with those found by five well-known centrality measures, which suggests novelty without being overly specialized. It is also asymptotically faster to compute on sparse graphs than all but the most trivial of these other measures. We introduce optimal algorithms that compute triangle centrality in \(O(m\overline{\delta})\) time and \(O(m+n)\) space, where \(\overline{\delta}\leq O(\sqrt{m})\) is the average degeneracy introduced by Burkhardt, Faber, and Harris (2020). In practical applications, \(\overline{\delta}\) is much smaller than \(\sqrt{m}\) so triangle centrality can be computed in nearly linear time. On a Concurrent Read Exclusive Write (CREW) Parallel Random Access Machine (PRAM), we give a near work-optimal parallel algorithm that takes \(O(\log n)\) time using \(O(m\sqrt{m})\) CREW PRAM processors. In MapReduce, we show it takes four rounds using \(O(m\sqrt{m})\) communication bits and is therefore optimal. We also derive a linear algebraic formulation of triangle centrality which can be computed in \(O(m\overline{\delta})\) time on sparse graphs.