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Surfacic networks are structures built upon a 2D manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations from typical plane networks and require specific tools to understand their impact. Here, we present such tools, including lazy paths that minimize elevation differences, graph arduousness which measures the tiring nature of shortest paths (SPs), and the excess effort, which characterizes positive elevation variations along SPs. We illustrate these measures using toy models of surfacic networks and empirically examine pedestrian networks in selected cities. Specifically, we examine how changes in elevation affect the spatial distribution of betweenness centrality. We also demonstrate that the excess effort follows a nontrivial power law distribution, with an exponent that is not universal, which illustrates that there is a significant probability of encountering steep slopes along SPs, regardless of the elevation difference between the starting point and the destination. These findings highlight the significance of elevation fluctuations in shaping network characteristics. Surfacic networks offer a promising framework for comprehensively analyzing and modeling complex systems that are situated on or constrained to a surface environment.

Multiple chronic diseases in the elderly significantly impact health and quality of life. Identifying key comorbidities and their formation can aid in controlling their progression. Using two follow-up datasets from CHARLS, we constructed a dependency network of disease progression and applied multi-centrality indicators to analyze relationships among chronic disease comorbidities. (1) Chronic disease comorbidities follow a power-law distribution. (2) Common chronic disease comorbidities include heart disease and stroke, dyslipidemia and stroke, dyslipidemia and chronic liver disease, and chronic liver disease and stroke. (3) Key states in comorbidity formation include complete health, only asthma, only arthritis, and stomach disease with arthritis. (4) Controlling a single disease state does not alter the final distribution of comorbidities. The formation of chronic disease comorbidities show complexity. Reducing individual comorbidity prevalence requires intervention across the entire formation process, as targeting single diseases has limited impact on the overall population distribution. [ABSTRACT FROM AUTHOR]

Biodiversity, which underpins the resilience of ecosystems, has declined sharply as the global species extinction rates have accelerated. Current biodiversity conservation cannot meet the needs of all species, and keystone species provide a key entry point for maximizing their conservation benefits. However, identifying specific keystone species remains challenging, and their roles in ecosystems need further analysis. In this study, the linear inverse model—Markov Chain Monte Carlo—was constructed by simulating the removal of candidate keystone species in Haizhou Bay ecosystem of China. Using the percentage changes of energy flows and ecological network analysis (ENA) in food web as evaluation indicators, specific keystone species were identified, and their roles in the ecosystem were comprehensively analyzed. The results showed that the keystone species identified based on energy flows and ENA were Johnius belangerii, Alpheus distinguendus, and Larimichthys polyactis. Energy flow was more responsive to simulated keystone species removal than ENA analysis, with higher percentage changes in energy flow to detritus and respiration than those to predators. In addition, the five ENA indicators responded differently to simulated removal scenarios, with HP and i/d responding most extensively to these scenarios. These findings will contribute to a comprehensive understanding of the role of keystone species in marine ecosystems and improve the understanding of biodiversity conservation. This work will guide the selection of priority conservation species and provide essential information for ecosystem-based fisheries management. [ABSTRACT FROM AUTHOR]

The literature on algorithmic fairness has examined exogenous sources of biases such as shortcomings in the data and structural injustices in society. It has also examined internal sources of bias as evidenced by a number of impossibility theorems showing that no algorithm can concurrently satisfy multiple criteria of fairness. This paper contributes to the literature stemming from the impossibility theorems by examining how informational richness affects the accuracy and fairness of predictive algorithms. With the aid of a computer simulation, we show that informational richness is the engine that drives improvements in the performance of a predictive algorithm, in terms of both accuracy and fairness. The centrality of informational richness suggests that classification parity, a popular criterion of algorithmic fairness, should be given relatively little weight. But we caution that the centrality of informational richness should be taken with a grain of salt in light of practical limitations, in particular, the so-called bias-variance trade off. [ABSTRACT FROM AUTHOR]

We developed a portable microfluidic system that combines spontaneous lumen formation from human umbilical endothelial cells (HUVECs) in fibrin–collagen hydrogels with active perfusion controlled by a braille actuator. Adaptive interstitial flow and feedthrough perfusion switching enabled the successful culture of spontaneously formed naturally branched lumens for more than one month. We obtained many large-area (2 mm × 3 mm) long-term (more than 30 days per run) time-lapse image datasets of the in vitro luminal network using this microfluidic system. We also developed an automatic image analysis pipeline to extract the morphology of the lumen network and node–edge network structure weighted with segmentwise flow parameters. The automatic lumen area measurements revealed that almost all lumens were successfully cultured in this system for approximately 50 days, following the meshwork, sprouting, remodeling, stability, and erosion stages. We found that the optimization of the lumen network during the remodeling stage can be explained by the decrease in the betweenness centrality of the WSS-weighted network and the increase in the strength centrality of the flow-rate-weighted network. [ABSTRACT FROM AUTHOR]

Driven by the substantial profits, the evolution of Portable Executable (PE) malware has posed persistent threats. PE malware classification has been an important research field, and numerous classification methods have been proposed. With the development of machine learning, learning-based static classification methods achieve excellent performance. However, most existing methods cannot meet the requirements of industrial applications due to the limited resource consumption and concept drift. In this article, we propose a fast, high-accuracy, and robust FCG-based PE malware classification method. We first extract precise function call relationships through code and data cross-referencing analysis. Then we normalize function names to construct a concise and accurate function call graph. Furthermore, we perform topological analysis of the function call graph using social network analysis techniques, thereby enhancing the program function call features. Finally, we use a series of machine learning algorithms for classification. We implement a prototype system named MalSensor and compare it with nine state-of-the-art static PE malware classification methods. The experimental results show that MalSensor is capable of classifying a malicious file in 0.7 seconds on average with up to 98.35% accuracy, which represents a significant advantage over existing methods. [ABSTRACT FROM AUTHOR]

Abstract This study analyzes the status, trends, and future directions in wood science research using text-mining techniques. We applied these techniques to a textual dataset constructed from metadata of six major wood science journals, covering the period from 2002 to 2024. The research explores publication trends, international collaborations, keywords, and research networks, and it employs topic modeling using the Latent Dirichlet Allocation model. The descriptive analysis reveals a consistent increase in publication volume throughout the study period, unaffected by the COVID-19 pandemic. In contrast, international collaboration declined after 2020, likely due to the pandemic. In addition, a network analysis identified key research areas, including surface treatments, structural composites, and high-performance wood products, with lignin, mechanical properties, and moisture content emerging as central keywords. Topic modeling reveals a growing interest in wood modification technologies and an increased focus on studying wood as a sustainable material. The study confirms a shift of the field towards sustainable innovations while also highlighting the enduring relevance of traditional research areas. Future research should adapt to these evolving trends and address emerging challenges to maximize the potential of wood for carbon neutrality and sustainable development. This analysis provides a concise overview of current research trends and future directions in wood science.

Spectral analysis of networks states that many structural properties of graphs, such as the centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher-order networks is strongly limited by the fact that a given hypergraph could have several different adjacency hypermatrices, and hence the results obtained so far are mainly restricted to the class of uniform hypergraphs, which leaves many real systems unattended. A new method for analyzing non-linear eigenvector-like centrality measures of non-uniform hypergraphs was presented in this paper that could be useful for studying properties of $ \mathcal{H} $-eigenvectors and $ \mathcal{Z} $-eigenvectors in the non-uniform case. In order to do so, a new operation——the uplift——was introduced, incorporating auxiliary nodes in the hypergraph to allow for a uniform-like analysis. We later argued why this was a mathematically sound operation, and we furthermore used it to classify a whole family of hypergraphs with unique Perron-like $ \mathcal{Z} $-eigenvectors. We supplemented the theoretical analysis with several examples and numerical simulations on synthetic and real datasets: On the latter, we find a clear improvement over the existing methods, specially in cases where there is a huge disparity between the structure at each order, and on the former, we find that regardless of the chosen uniformization scheme, the nodes were similarly ranked.

Abstract This paper establishes a symmetric matrix based on the coopetition relationships among global automobile enterprises, and uses Ucinet software to obtain the visualization chart of the coopetition network of global automobile enterprises. Then, the multiple moderating effect method and two-stage least squares method are adopt to reveal the interaction between structural hole and centrality on enterprise market performance, and how the ego-network characteristics affect this interaction. The results show that structural hole and centrality have a positive interaction on market performance. Compared with high ego-network stability, the positive interaction between structural hole and centrality on enterprise market performance is stronger under the condition of low ego-network stability. And compared with low ego-network density, the positive interaction between structural hole and centrality on market performance is stronger under the condition of high ego-network density. These new findings further strengthen the connection between the overall network and ego-network.

Traffic flow prediction, crucial for traffic management, relies on spatial and temporal data to achieve high accuracy. However, standard performance metrics only measure the average prediction errors and overlook the spatiotemporal aspects. To address this gap, this study introduces three simple spatial key performance indicators (KPIs): Global Moran's I, Getis-Ord General G, and Adapted PageRank Algorithm Modified (APAM). We evaluated the traffic prediction results for synthetic clustering scenarios and four different prediction methods applied to the PeMSD8 dataset using spatial KPIs. Spatial KPIs are calculated based on traffic prediction errors and the adjacency matrix of the traffic network. Our results demonstrate that spatial KPIs can effectively differentiate between synthetic clustering scenarios. Global Moran's I measures the spatial autocorrelation, Getis-Ord General G measures the spatial clustering of high/low values, and the univariate analysis of APAM deduces the distribution of node importance by considering node centrality and node values. Getis-Ord General G showed the highest sensitivity, being capable of distinguishing between methods with similar average RMSE, whereas Global Moran's I and APAM univariate analysis revealed subtle differences between methods. Spatial KPIs serve as important complementary metrics for performance evaluation in the design of robust traffic management systems. [ABSTRACT FROM AUTHOR]

This article examined the attitudes of Hungarian Jews towards Israel using two databases that were collected in 1999 and 2017 in a quasi-representative sample. The findings indicate that 1) Perception of Israel's central role depends on age and the level of Jewish affiliation; 2) One's perception of Israel's centrality for diasporic life and one's feeling of belonging to Israel do not necessarily coincide; and 3) The younger generations and the more secularised Jews are more critical of Israeli policies. [ABSTRACT FROM AUTHOR]

Using computational Social Network Analysis (SNA), this longitudinal study investigates the development of the interaction network and its influence on the second language (L2) gains of a complete cohort of 41 U.S. sojourners enrolled in a 3‐month intensive study‐abroad Arabic program in Jordan. Unlike extant research, our study focuses on students' interactions with alma mater classmates, reconstructing their complete network, tracing the impact of individual students' positions in the social graph using centrality metrics, and incorporating a developmental perspective with three measurement points. Objective proficiency gains were influenced by predeparture proficiency (negatively), multilingualism, perceived integration of the peer learner group (negatively), and the number of fellow learners speaking to the student. Analyses reveal relatively stable same‐gender cliques, but with changes in the patterns and strength of interaction. We also discuss interesting divergent trajectories of centrality metrics, L2 use, and progress; predictors of self‐perceived progress across skills; and the interplay of context and gender. A one‐page Accessible Summary of this article in nontechnical language is freely available in the Supporting Information online and at https://oasis‐database.org [ABSTRACT FROM AUTHOR]

This study examined the hypothesis that the network of citation in biomechanics journals would change over the last decade and specifically the centrality of the journal Sports Biomechanics. Top 20 cited biomechanics journals identified using the 'Journal Citation Relationships' feature from Journal Citation Reports were extracted for 12 'seed' biomechanics journals in 2011, 2016, and 2021. From 2011 till 2021 the total number of top cited biomechanics journals in Journal Citation Reports decreased (17%) from 90 to 74, while the citations to these journals nearly increased 5-fold (8,051 to 39,574). Top Journal Citation Reports cited biomechanics journals changed over time, indicating variability in the centrality of many journals in the biomechanics citation network based on this prestigious database. Over time there were decreasing citation of medical journals, as well as increasing citation of open access mega journals and the journal Sports Biomechanics. Citation network analysis provides insight into the changing structure of knowledge creation in biomechanics, with recent trends towards applied research particularly on wearable sensors published in mega journals. [ABSTRACT FROM AUTHOR]

Yang Shi initiated the Neo-Confucian methodology of self-cultivation centered on quiet-sitting, and focusing on Yang Shi may shift the study of Confucian quiet-sitting to a more chronologically appropriate "beginning-forward" approach. Incorporating techniques such as breathing and calming the mind, Yang's approach to self-cultivation follows a model of returning to the state of centrality through quiet-sitting, and then preserving and expanding that state in moments of everyday life. This model is based on a moral psychology and metaphysics that views the comprehensive pattern-principle of the universe, Tianli, as fully manifest in the vital state of the human heartmind achievable through the practice of quiet-sitting. This view inherits major features of Cheng Hao's philosophy while distinguishing itself from Cheng Yi's. Yang Shi's reflections on the differences between Confucian and Buddhist contemplative practices also indicate, despite his view being closer to the Huayan Buddhist metaphysical perspective of perfect fusion between pattern-principle and things compared to Cheng Yi, an insistence on characterizing his quiet-sitting philosophy as distinctively Confucian. [ABSTRACT FROM AUTHOR]

In this article, we examine the contours of the Association of Southeast Asian Nations' (ASEAN) response to the latest regional challenge from Myanmar, the 2021 coup. Scholars and practitioners alike often portray ASEAN as a relatively cohesive community of states united in adherence to a long-held and comparatively stable set of norms within the so-called "ASEAN way." Core among these norms has been domestic non-interference. However, we argue that rather than being determined by a coherent set of agreed norms, ASEAN's response to this crisis has been shaped by intra-regional contestation and division around how ASEAN ought to enact its particular "way" of regional governance. More narrowly, we show that the ASEAN response has been shaped by contestation over competing normative impulses in the organization--centrality and non-interference--which have developed in increasing tension since the humanitarian disaster after Cyclone Nargis in 2008 and the Rohingya crisis after 2016. We show that in response to these crises, officials from the organization and its member states advanced divergent accounts of what ASEAN ought to do and why, given competing normative commitments to centrality and non-interference. By showing how ASEAN's response to the 2021 coup is the result of internal contestation within the organization, we support accounts of regional governance in Southeast Asia that stress less the fixity of ASEAN norms than their contestation in practice. To make our argument we analyze more than 250 documents and draw on interviews with regional officials. [ABSTRACT FROM AUTHOR]

This study analyzes the status, trends, and future directions in wood science research using text-mining techniques. We applied these techniques to a textual dataset constructed from metadata of six major wood science journals, covering the period from 2002 to 2024. The research explores publication trends, international collaborations, keywords, and research networks, and it employs topic modeling using the Latent Dirichlet Allocation model. The descriptive analysis reveals a consistent increase in publication volume throughout the study period, unaffected by the COVID-19 pandemic. In contrast, international collaboration declined after 2020, likely due to the pandemic. In addition, a network analysis identified key research areas, including surface treatments, structural composites, and high-performance wood products, with lignin, mechanical properties, and moisture content emerging as central keywords. Topic modeling reveals a growing interest in wood modification technologies and an increased focus on studying wood as a sustainable material. The study confirms a shift of the field towards sustainable innovations while also highlighting the enduring relevance of traditional research areas. Future research should adapt to these evolving trends and address emerging challenges to maximize the potential of wood for carbon neutrality and sustainable development. This analysis provides a concise overview of current research trends and future directions in wood science. [ABSTRACT FROM AUTHOR]

Henri Grivois has posited that psychosis involves the subjective experience of oneself as the center or focal point of the world. In this experience, the world that is typically unrelated to oneself becomes incomprehensible, and in its place is the sense that all life events are directly related to oneself or that one is perpetually at the center of all noteworthy activity. We suggest that this experience of centrality can be understood through the lens of the integrated model of metacognition. Specifically, we explore the idea that the metacognitive domain of decentration, or the ability to form ideas about the larger community one is a part of, can be used to operationalize and measure centrality. We propose a three-phase approach to addressing centrality within an integrative psychotherapy focused on subjective and experiential aspects of recovery. These phases focus on the patient's experience of centrality and include (1) inviting the therapist to join one's centrality, (2) acknowledging others as different from oneself, and (3) recognizing alternative perspectives in the world. We provide case examples and explore the metacognitive tasks and potential barriers associated with each phase. [ABSTRACT FROM AUTHOR]

Based on the world vegetable oilseeds trade data, the topology, overall structural characteristics, individual centrality and community layout evolution of the global vegetable oilseeds trade network from 2003 to 2021 were studied by using social network analysis methods. The results reveal that: 1) with the passage of time, the global trade volume of vegetable oilseeds continues to grow, the formed trade network is more closely interconnected, showing a trend of centralization, and the characteristics of "small world" and scale-free nature become more prominent; 2) The distribution pattern of the community of the global vegetable oilseeds trade network has been deeply adjusted, and the community structure is closer and the geographical distance is more likely to form associations; 3) Countries such as China and India in Asia, France, Germany and the Netherlands in Europe, Brazil and Argentina in South America, the United States and Canada in North America, and Australia in Oceania hold high core positions in the trade of vegetable oilseeds. Additionally, Turkey, Mexico and Paraguay also hold pivotal position in the international trade of vegetable oilseeds; 4) China's dependence on vegetable oilseeds imports has decreased significantly, but it is still mainly concentrated in Brazil and the United States. In this regard, it is suggested that China should promote diversified development of vegetable oilseeds import products and markets, expand export income generation, and make full use of the international trade platform mechanism to promote the high-quality development of China's vegetable oilseeds trade. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Informatics, Media & Communication Technology (IJIMCT) is the property of Beni Suef University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Shanghai Jiaotong University (Science) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In addition to considering the influence of a species on other species (centrality), the identification of keystone species should also consider whether it has a unique network position (uniqueness). Clarifying the correlation between species centrality and uniqueness, or whether central species exhibit positional redundancy in food webs, can enhance the understanding of mechanisms stabilizing food webs. However, the findings from analyses utilizing different measures of uniqueness are contentious. In this study, we constructed the food web of the eutrophic Zhangze Lake (northern China) using stable isotopes to estimate the contribution of food sources to consumers. We then calculated trophic field overlap index to assess the uniqueness of species using this quantified food web information. Additionally, we analyzed how the weak interaction and the threshold value under which interactions are considered as weak influence the relationship between species uniqueness and centrality. The findings revealed that, in contrast to the traditional trophic field overlap index, the improved index identified the basal species with the strongest trophic interactions with other species and the filter‐feeding fishes with the fewest interactors as the most unique species, while the basal species were considered the least unique under the traditional index. The ranking results of the traditional index and the centrality showed a significant negative correlation, whereas the improved index displayed a positive correlation, which was caused by the comprehensive consideration of threshold and weak interaction. In addition, based on the data analysis, the suggestion was given for the selection of indices used to identify unique species, and whether central species have positional redundancy was explored. The methodology used in study provides a practical solution for the identification of the most unique species, points out and solves the problems faced in the uniqueness analysis, and advances the understanding of the mechanisms underlying food web robustness. [ABSTRACT FROM AUTHOR]

We studied spatial variation in the effects of environment and network size on species positions and roles in multiple flea–mammal networks from four biogeographic realms. We asked whether species positions (measured as species strength [SS], the degree of interaction specialization [d′], and the eigenvector centrality [C]) or the roles of fleas and their hosts in the interaction networks: (a) are repeatable/conserved within a flea or a host species; (b) vary in dependence on environmental variables and/or network size; and (c) the effects of environment and network size on species positions or roles in the networks depend on species traits. The repeatability analysis of species position indices for 441 flea and 429 host species, occurring in at least two networks, demonstrated that the repeatability of SS, d′, and C within a species was significant, although not especially high, suggesting that the indices' values were affected by local factors. The majority of flea and host species in the majority of networks demonstrated a peripheral role. A value of at least one index of species position was significantly affected by environmental variables or network size in 41 and 36, respectively, of the 52 flea and 52 host species that occurred in multiple networks. In both fleas and hosts, the occurrence of the significant effect of environment or network size on at least one index of species position, but not on a species' role in a network, was associated with some species traits. [ABSTRACT FROM AUTHOR]

The Fast Economic Growth Indicator, a newly developed metric leveraging big data, provides policymakers with timely insights crucial for assessing the economic impact of policies or events. Among various open-source datasets, aviation data stands out as a potential indicator of rapid economic growth, given its inherent graph structure with airports as nodes and flight connections as edges. However, global flight data, being dynamic and complex, poses challenges in analysis. To glean comprehensive insights, it's imperative to condense this graph data into representative vector values while preserving node relationships. In this study, we utilize the dynamic graph node embedding method to quantify the influence levels of airports relative to each other. Traditional node embedding methods often prioritize homophily over structural equivalence, challenging directly extracting influence levels. To address this limitation, we introduce anchored dynamic graph node embedding, employing a virtual node as a reference point in embedding space to enable direct calculation of influence levels. These influence metrics are then compared to the GDP of airport regions. Using USA domestic flight data from 1988 to 2021 as a case study, our methodology demonstrates promising results, boasting a 0.94 correlation coefficient with national GDP and a 0.9 correlation coefficient with state Gross State Product (GSP). This research aims to advance dynamic graph node embedding methods towards structural equivalence rather than homophily, enhancing applicability to tasks emphasizing node structure over neighborhood proximity. An example of the benefits of this research is its utility in addressing Influence Maximization Problems within dynamic graphs. [ABSTRACT FROM AUTHOR]

Water system connectivity is an important measure to optimize the balanced spatial allocation of water resources and water security patterns. Inland river basins in arid zones are generally insufficiently connected, so the scientific evaluation of the current status of water system connectivity and the centrality of its nodes in the water system network has practical significance for the scientific construction of regional water networks. Taking the Tarim River Basin in Xinjiang, China, as an object, this study conducted a comprehensive evaluation of basin water system connectivity by constructing a water system connectivity evaluation system with a total of 12 indicators for the three aspects of pattern connectivity, structural connectivity and functional connectivity. Subsequently, the TOPSIS model, with combined weights of the analytic hierarchy process and the entropy weight method, was used to comprehensively evaluate the connectivity of the watershed's water system. The research evaluated the node centrality of the water system network that was closely related to the basin water system connectivity by using complex network analyses. The study results indicated the following: (1) among the source streams in the Tarim River Basin, the connectivity of the Aksu Basin was the best and that of the Keriya Basin was the worst and (2) the distribution patterns of the eigenvector centrality and betweenness centrality of the basin hydrological network nodes were similar, with nodes of highest centrality concentrated in the vicinity of the mainstems and the source–mainstem intersections. This work provides a basis and reference for the construction of water system connectivity and the selection of key control sections for ecological flow in the Tarim River Basin. [ABSTRACT FROM AUTHOR]

Micro-level internationalization offers possibilities to explore different human experiences in international higher education. This is especially crucial given well-reported issues of racism, micro-aggression, and underrepresentation of racially minoritized international academic staff, whose voices remain mostly invisible in internationalization discourses. Previous research connects these issues to the continuing legacy of colonial logic, that privileges hegemonic Westerncentric knowledge systems. In this paper, centrality is proposed as a conceptual framework that offers a direct response to the question of epistemicide which Santos (2014) explains as the exclusion of the knowledges of racially marginalized persons [in or with origins] from the Global South. It draws attention to how epistemicide and historicide (erasure of cultural history) impinge their agentic capabilities, drawing on their lived experiences and cognitive epistemological and ontological frames of knowing and being. Centrality, therefore, reiterates the need to center marginalized voices as legitimate and knowledgeable contributors to conversations and research on decolonizing internationalization, drawing on their knowledge, capabilities, and lived experience. This calls on Global North allies to not only articulate their positionality, acknowledging the inequities inherent in the hegemonic Western-centric epistemology paradigm but to contribute to dismantling persisting structural coloniality and embedded hierarchies in teaching, research, and international partnerships. Centrality thus offers a framework for: i) dismantling the persisting pernicious legacy of colonialization by working collaboratively to undo the epistemic hegemony that perpetuates the universality of Eurocentric knowledge and subalternity of the Global South, and ii) advancing access to ecologies of knowledge that affirms rather than disparages our shared humanity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]