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The best known solutions for k-message broadcast in dynamic networks of size n require Ω (nk) rounds. In this article, we see if these bounds can be improved by smoothed analysis. To do so, we study perhaps the most natural randomized algorithm for disseminating tokens in this setting: at every timestep, choose a token to broadcast randomly from the set of tokens you know. We show that with even a small amount of smoothing (i.e., one random edge added per round), this natural strategy solves k-message broadcast in \(\tilde{O}(n+k^3)\) rounds, with high probability, beating the best known bounds for \(k=o(\sqrt {n})\) and matching the Ω (n+k) lower bound for static networks for k=O(n1/3) (ignoring logarithmic factors). In fact, the main result we show is even stronger and more general: Given ℓ-smoothing (i.e., ℓ random edges added per round), this simple strategy terminates in \(O(kn^{2/3}\log ^{1/3}(n)\ell ^{-1/3})\) rounds. We then prove this analysis close to tight with an almost-matching lower bound. To better understand the impact of smoothing on information spreading, we next turn our attention to static networks, proving a tight bound of \(\tilde{O}(k\sqrt {n})\) rounds to solve k-message broadcast, which is better than what our strategy can achieve in the dynamic setting. This confirms the intuition that although smoothed analysis reduces the difficulties induced by changing graph structures, it does not eliminate them altogether. Finally, we apply tools developed to support our smoothed analysis to prove an optimal result for k-message broadcast in so-called well-mixed networks in the absence of smoothing. By comparing this result to an existing lower bound for well-mixed networks, we establish a formal separation between oblivious and strongly adaptive adversaries with respect to well-mixed token spreading, partially resolving an open question on the impact of adversary strength on the k-message broadcast problem. [ABSTRACT FROM AUTHOR]

The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, we still have a limited understanding of maximal matching which is one of the central problems of parallel and distributed computing. All known MPC algorithms for maximalmatching either take polylogarithmic time which is considered inefficient, or require a strictly superlinear space of n1+Ω(1) per machine. In this work, we close this gap by providing a novel analysis of an extremely simple algorithm, which is a variant of an algorithm conjectured to work by Czumaj, Lacki, Madry, Mitrovic, Onak, and Sankowski [15]. The algorithm edge-samples the graph, randomly partitions the vertices, and finds a random greedy maximal matching within each partition.We show that this algorithm drastically reduces the vertex degrees. This, among other results, leads to an O(log log Δ) round algorithm for maximal matching with O(n) space (or even mildly sublinear in n using standard techniques). As an immediate corollary, we get a 2 approximate minimum vertex cover in essentially the same rounds and space, which is the optimal approximation factor under standard assumptions. We also get an improved O(log log Δ) round algorithm for 1 + ε approximate matching. All these results can also be implemented in the congested clique model in the same number of rounds. [ABSTRACT FROM AUTHOR]

We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any \(\gamma›0\) and \(k\ge3\), we show that asymptotically almost surely, every subgraph of the binomial random \(k\)-uniform hypergraph \(G^{(k)}\big(n,n^{\gamma-1}\big)\) in which all \((k-1)\)-sets are contained in at least \(\big(\tfrac12+2\gamma\big)pn\) edges has a tight Hamilton cycle. This is a cyclic ordering of the \(n\) vertices such that each consecutive \(k\) vertices forms an edge.Mathematics Subject Classifications: 05C80, 05C35Keywords: Random graphs, hypergraphs, tight Hamilton cycles, resilience

This article discusses random hypergraphs with varying hyperedge sizes, admitting large hyperedges with size tending to infinity, and heavy-tailed limiting hyperedge size distributions. The main result describes a threshold for the random hypergraph to be connected with high probability, and shows that the average hyperedge size suffices to characterise connectivity under mild regularity assumptions. Especially, the connectivity threshold is in most cases insensitive to the shape and higher moments of the hyperedge size distribution. Similar results are also provided for related random intersection graph models. [ABSTRACT FROM AUTHOR]

Digital service trade has become an important engine of world economic growth, and its competitive landscape is also evolving. We construct domestic value-added networks of digital service exports (DVAN-DSEs) from 1995 to 2018 based on the world input-output table, and explores their structural evolution and determinants using Temporal Exponential Random Graph Model. We find that (a) the DVAN-DSEs present the features of agglomeration, heterogeneity, reciprocity and unevenness. (b) The United States and European countries are the core in DVAN-DSEs. (c) Preference attachment, structural embeddedness, delayed reciprocity, stability, variability, Matthew effect in GDP, population and Internet coverage, geographical proximity, cultural similarities, and regional trade agreements play important roles in the evolution of DVAN-DSEs. (d) Structural embeddedness and geographic proximity only facilitate new relationship construction, while other factors influence both relationship establishment and maintenance. Countries should build network facilities, expand trading partners and promote trade agreement negotiations to facilitate the development of digital service trade. [ABSTRACT FROM AUTHOR]

We develop a model of market entry under social learning through word of mouth (WOM). The success of an entrant depends on consumer awareness generated via WOM, modeled as a percolation process on a random graph. The likelihood of an entrant gaining significant awareness depends on network structure, characterized by the first three factorial moments of the degree distribution. We identify three pricing equilibria: blockaded, deterred, and accommodated entry. The model demonstrates that increased network density can shift equilibria from blockaded to deterred and eventually to accommodated entry. Numerical simulations suggest that consumer surplus may be nonmonotonic with respect to network density. Additionally, if incumbents can charge personalized prices based on consumers' connectivity, they may optimally set lower prices for highly connected consumers. [ABSTRACT FROM AUTHOR]

Summary: This article designs and implements a runtime library for general dataflow programming, DFCPP (Luo Q, Huang J, Li J, Du Z. Proceedings of the 52nd International Conference on Parallel Processing Workshops. ACM; 2023:145‐152.), and builds upon it to design and implement a multi‐machine C++ dataflow library, M‐DFCPP. In comparison to existing dataflow programming environments, DFCPP features a user‐friendly interface and richer expressive capabilities (Luo Q, Huang J, Li J, Du Z. Proceedings of the 52nd International Conference on Parallel Processing Workshops. ACM; 2023:145‐152.), enabling the representation of various types of dataflow actor tasks (static, dynamic and conditional task). Besides that, DFCPP addresses the memory management and task scheduling for non‐uniform memory access architectures, while other dataflow libraries lack attention to these issues. M‐DFCPP extends the capability of current dataflow runtime libraries (DFCPP, taskflow, openstream, etc.) and capable of multi‐machine computing, while maintains the API compatible with DFCPP. M‐DFCPP adopts the concepts of master and follower (Dean J, Ghemawat S. Commun ACM. 2008;51(1):107‐113; Ghemawat S, Gobioff H, Leung ST. ACM SIGOPS Operating Systems Review. ACM; 2003:29‐43.), which form a worksharing framework as many multi‐machine system. To shift to the M‐DFCPP framework, a filtering layer is inserted to the original DFCPP, transforming it into followers that can cooperate with each other. The master is made of modules for scheduling, data processing, graph partition, state management and so forth. In benchmark tests with workload with directed acyclic graph topology of binary trees and random graphs, DFCPP demonstrated performance improvements of 20% and 8%, respectively, compared to the second fastest library. M‐DFCPP consistently exhibits outstanding performance across varying levels of concurrency and task workloads, achieving a maximum speedup of more than 20 over DFCPP, when the task parallelism exceeds 5000 on 32 nodes. Moreover, M‐DFCPP, as a runtime library supporting multi‐node dataflow computation, is compared with MPI, a runtime library supporting multi‐node control flow computation. [ABSTRACT FROM AUTHOR]

AbstractThe configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network’s structure can be explained by its degree structure alone. A Markov chain Monte Carlo (MCMC) algorithm, based on a degree-preserving double-edge swap, provides an asymptotic solution to sample from the configuration model. However, accurately and efficiently detecting when this Markov chain is sufficiently close to its stationary distribution remains an unsolved problem. Here, we provide a solution to sample from the configuration model using this standard MCMC algorithm. We develop an algorithm, based on the assortativity of the sampled graphs, for estimating the gap between effectively independent MCMC states, and a computationally efficient gap-estimation heuristic derived from analyzing a corpus of 509 empirical networks. We provide a convergence detection method based on the Dickey-Fuller Generalized Least Squares test, which we show is more accurate and efficient than three alternative Markov chain convergence tests. Supplementary materials for the proposed methods can be found here. [ABSTRACT FROM AUTHOR]

Building upon Li & Britz (Li NZ, Britz T. 2024 On the scale-freeness of random colored substitution networks. Proc. Amer. Math. Soc. 152, 1377–1389 (doi: 10.1090/proc/16604)), this study aims to introduce fractal geometry into graph theory and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore fractal-like graphs, termed iterated graph systems (IGS) for the first time. While the concept of substitution is commonplace in fractal geometry and dynamical systems, its analysis in the context of graph theory remains a nascent field. By delving into the properties of these systems, including distance and diameter, we derive two primary outcomes. Firstly, within the deterministic IGS, we establish that the Minkowski dimension and Hausdorff dimension align through explicit formulae. Secondly, in the case of random IGS, we demonstrate that almost every Gromov–Hausdorff scaling limit exhibits identical Minkowski and Hausdorff dimensions analytically by their Lyapunov exponents. The exploration of IGS holds the potential to unveil novel directions. These findings not only, mathematically, contribute to our understanding of the interplay between fractals and graphs, but also, physically, suggest promising avenues for applications for complex networks. [ABSTRACT FROM AUTHOR]

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of selforganization because energy is a local property of configurations. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent empirical results has shown that a local property of configurations called "rattling" predicts the steady states of some nonequilibrium systems, leading to claims of a far-reaching principle of nonequilibrium self-organization. But for which nonequilibrium systems is rattling accurate, and why? Wedevelop a theory of rattling in terms of Markov processes that gives simple and precise answers to these key questions. Our results show that rattling predicts a broader class of nonequilibrium steady states than has been claimed and for different reasons than have been suggested. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global "parts" of a steady state. We show how these quantities characterize the local-global relationships of various random walks on random graphs, spin-glass dynamics, and models of animal collective behavior. Surprisingly, we find that the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike. [ABSTRACT FROM AUTHOR]

We initiate the study of a generalization of Kim-independence, Conant-independence, based on the notion of strong Kim-dividing of Kaplan, Ramsey and Shelah. A version of Conant-independence was originally introduced to prove that all NSOP2 theories are NSOP1. We introduce an axiom on stationary independence relations, essentially generalizing the “freedom” axiom in some of the free amalgamation theories of Conant, and show that this axiom provides the correct setting for carrying out arguments of Chernikov, Kaplan and Ramsey on NSOP1 theories relative to a stationary independence relation. Generalizing Conant’s results on free amalgamation to the limits of our knowledge of the NSOPn hierarchy, we show using methods from Conant as well as our previous work that any theory where the equivalent conditions of this local variant of NSOP1 holds is either NSOP1 or SOP3 and is either simple or TP2. We observe that these theories give an interesting class of examples of theories where Conant-independence is symmetric. This includes all of Conant’s examples, the small cycle-free random graphs of Shelah, and the (finite-language) ω-categorical Hrushovski constructions of Evans and Wong. We then answer Conant’s question on the existence of non-modular free amalgamation theories. We show that the generic functional structures of Kruckman and Ramsey are examples of non-modular free amalgamation theories. We also show that any free amalgamation theory is NSOP1 or SOP3, while an NSOP1 free amalgamation theory is simple if and only if it is modular. Finally, we show that every theory where Conant-independence is symmetric is NSOP4. Therefore, symmetry for Conant-independence gives the next known neostability-theoretic dividing line on the NSOPn hierarchy beyond NSOP1. We explain the connection to some established open questions. [ABSTRACT FROM AUTHOR]

In analyzing collected network data, measurement error is a common concern. One of the current research interests is to study robustness of network properties to measurement error. In this work, we analytically study the impact of measurement error on the global clustering coefficient and the average clustering coefficient of a network. Two types of common measurement errors are considered: (I) each node is randomly removed with probability β and (II) each edge is randomly removed with probability γ. We analytically derive the limits of the clustering coefficients of an inhomogeneous Erdös-Rényi random graph or a power-law random graph with the above two measurement errors. The limits can be used to quantify robustness of the coefficients: if the limits do not depend on β or γ, the coefficients can be considered as robust. Based on our results, the global clustering coefficient and the average clustering coefficient are robust to random removal of nodes but vulnerable to random removal of edges. Extensive experiments validate our theoretical results. [ABSTRACT FROM AUTHOR]

Safeguarding important links is a useful way to promote network vulnerability, especially in sparse networks where random link failures can disconnect the network. Sustaining network connectivity is the main goal of safeguarding and can be handled by selectively safeguarding links belonging to certain cuts of a network. However, due to the inherent high complexity of cut enumeration, existing algorithms can only handle small‐scale networks with limited nodes. It is important to find practical algorithms that are feasible for large‐scale graphs, as a significant portion of real‐world graphs under investigation are not as small as dozens of nodes. To address the problem, we propose to use a high‐precision approximate approach to accelerate the first step of the two‐step safeguard process and thus accelerate the whole process. A Monte Carlo algorithm is proposed to exploit efficient random paths for small cuts enumeration, which can help locate important edges with high probability in large‐scale sparse networks. These edges will then be utilized to find the approximated minimum cost edge set whose safeguarding can sustain the expected network connectivity. The algorithm is validated using various sizes of graphs of random/Barbasi–Albert scale‐free/Clustered scale‐free/unit disk/Watts–Strogatz small‐world and real‐world graphs. The experimental results show that the algorithm can perfectly sustain the network connectivity, and the acceleration ratio of more than 105 can be achieved with a little additional overhead. Specifically, in large graphs of one million nodes, approximated safeguard solutions survive at least 99.9% random link failures, and the solution time can be further reduced to dozens of seconds when the algorithm steps are easily implemented in full parallel. [ABSTRACT FROM AUTHOR]

We study SIR‐type epidemics (susceptible‐infected‐resistant) on graphs in two scenarios: (i) when the initial infections start from a well‐connected central region and (ii) when initial infections are distributed uniformly. Previously, Ódor et al. demonstrated on a few random graph models that the expectation of the total number of infections undergoes a switchover phenomenon; the central region is more dangerous for small infection rates, while for large rates, the uniform seeding is expected to infect more nodes. We rigorously prove this claim under mild, deterministic assumptions on the underlying graph. If we further assume that the central region has a large enough expansion, the second moment of the degree distribution is bounded and the number of initial infections is comparable to the number of vertices, the difference between the two scenarios is shown to be macroscopic. [ABSTRACT FROM AUTHOR]

Central nodes, also known as vital or critical nodes, play a unique role in networks of various domains. To date, numerous centrality evaluation methods have been proposed to identify central nodes from different types of networks. However, most of existing methods did not address this issue from a rigorous significance testing perspective. As a result, it is hard for us to judge whether an identified central node is true or not and control the quality of reported nodes in a statistically sound manner. In this paper, we propose a centrality evaluation method based on hypothesis testing, where the test statistic is the degree sum of the neighbors of the node. We further derive an analytical p value and its upper bound under the Erdös–Rényi model, which can be employed as the centrality score for vital node recognition. To demonstrate the effectiveness of our method, extensive experiments are conducted on both simulated and real networks. The experimental results show that (1) our testing‐based centrality measure in terms of p value is capable of distinguishing central nodes from non‐central ones effectively and (2) our method is able to identify central nodes more accurately than those classic centrality measures and state‐of‐the‐art (SOTA) centrality evaluation methods. [ABSTRACT FROM AUTHOR]

In efforts to address the far-reaching effects of climate change and associated impacts in communities, research on environmental philanthropy suggests that more resources are being allocated to environmental societal challenges. However, understandings about which environmental nonprofits benefit from these funding flows is limited. This study integrates resource dependency theory with elitism and pluralism perspectives to analyze a network of environmental nonprofits and their funders in Texas. Resource dependency and a network-analytic approaches share underlying relationality principles, and we connect those dots by conceptualizing the funding dynamics in Texas as a network of funder-grantee relations. Drawing on statewide survey data (n = 114), we use a network analysis technique – exponential random graph modeling (ERGM) – to analyze funding allocations in Texas through the organizational attributes of environmental nonprofits, their funder-grantee relations, and their community context. We specifically observe elitism in funding allocations in Texas, which is evident in network effects (preferential attachment) and the focal areas of environmental work. However, we find limited evidence that age or resources of the nonprofit are predictive of funding and the most influential factor determining a funder-grantee relationship is the natural hazard risk of the community served by the nonprofit. Our findings suggest interconnected funding dynamics of pluralism and elitism in the Texas environmental philanthropy landscape, prompting further discussion about the potential synergies of these patterns and the implications for environmental funding practices. [ABSTRACT FROM AUTHOR]

The Katz centrality of a node in a complex network is a measure of the node's importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its "global" character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P(K) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank-1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way. [ABSTRACT FROM AUTHOR]

The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent "bias events," whose realizations enhance reciprocity, transitivity, or other structural features. Subsequent developments have introduced local specifications of biased nets, which reduce the need for approximations required in early specifications based on tracing processes. Here, we show that while one such specification leads to inconsistencies, a closely related Markovian specification both evades these difficulties and can be extended to incorporate new types of effects. We introduce the notion of inhibitory bias events, with satiation as an example, which are useful for avoiding degeneracies that can arise from closure bias terms. Although our approach does not lead to a computable likelihood, we provide a strategy for approximate Bayesian inference using random forest prevision. We demonstrate our approach on a network of friendship ties among college students, recapitulating a relationship between the sibling bias and tie strength posited in earlier work by Fararo. [ABSTRACT FROM AUTHOR]

The Swift–Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger and Holzer (SIAM J Math Anal 55(3):2150–2185, 2023), we consider discrete SHE on deterministic and random graphs. The two families of the discrete models share the same continuum limit in the form of a nonlocal SHE on a circle. The analysis of the continuous system, parallel to the analysis of the classical SHE, shows bifurcations of spatially periodic solutions at critical values of the control parameters. However, the proximity of the discrete models to the continuum limit does not guarantee that the same bifurcations take place in the discrete setting in general, because some of the symmetries of the continuous model do not survive discretization. We use the center manifold reduction and normal forms to obtain precise information about the number and stability of solutions bifurcating from the homogeneous state in the discrete models on deterministic and sparse random graphs. Moreover, we present detailed numerical results for the discrete SHE on the nearest-neighbor and small-world graphs. [ABSTRACT FROM AUTHOR]

The paper builds on the framework proposed by Pattison and Snijders (2012) for specifying exponential random graph models (ERGMs) for social networks. We briefly review the two-dimensional hierarchy of potential dependence structures for network tie variables that they outlined and provide proofs of the relationships among the model forms and of the nature of their sufficient statistics, noting that models in the hierarchy have the potential to reflect the outcome of processes of cohesion, closure, boundary and bridge formation and path creation over short or longer network distances. We then focus on the so-called partial inclusion dependence assumptions among network tie variables and the pendant-triangle , or paw , statistics to which they give rise, and illustrate their application in an empirical setting. We argue that the partial inclusion assumption leads to models that can reflect processes of boundary and bridge formation and that the model hierarchy provides a broad and useful framework for the statistical analysis of network data. We demonstrate in the chosen setting that pendant-triangle (or paw) effects, in particular, lead to a marked improvement in goodness-of-fit and hence add a potentially valuable capacity for modelling social networks. • The paper provides a principled basis for some new effects for exponential random graph models for social networks • We describe how these new terms can be used to understand processes of boundary and bridge formation in networks • We demonstrate that these new terms improve goodness-of-fit in an illustrative application [ABSTRACT FROM AUTHOR]

This research examines whether categorical closure – an increased tendency for closure in homogeneous triads – matters for tie formation and tie persistence. We utilized 2019–2020 panel data on students' networks at three law schools and employed separable temporal exponential random graph models to examine whether closed triads with shared identities were more likely to form and to persist over time. We also investigated whether closed triads based on shared organizational assignments were associated with lower likelihoods of tie formation and tie persistence over time. Results supported the notion that law students were more likely to form homogeneous closed triads based on shared categories, particularly family background, gender, and race, while closed triads based on organizational assignments were less likely. Closed triads tended to persist over time, but there was some support for the notion that homogeneous closed triads based on family background, college rank, and sexuality were more durable. This study highlights categorical closure as an additional network mechanism giving rise to homogenous groups. • This research examines whether categorical closure – an increased tendency for closure in homogeneous triads – matters for social networks. • This research utilizes longitudinal network data and separable temporal exponential random graph models to test for categorical closure. • Results supported the notion that law students were more likely to form homogeneous closed triads based on some shared categories. • This study highlights categorical closure as an additional network mechanism giving rise to homogenous groups. [ABSTRACT FROM AUTHOR]

In light of the crucial role of collaborative R&D in advancing technology within the new energy vehicle industry, this study seeks to explore ways to overcome the barriers to technological innovation by establishing an effective collaborative innovation network. Utilizing joint patent-authorized data from China's new energy vehicles between 2005 and 2019, the collaborative innovation network was developed, and the Exponential Random Graph Model (ERGM) was employed to analyze its formation and evolution mechanisms. The results indicate that the network has undergone significant expansion, closely linked to strong national policy support and the active involvement of innovation participants. The network exhibits effects of expansion, transfer, and closure. External attribute analysis revealed the Matthew effect and geographical compatibility effect and found that organizational compatibility tends to foster complementary cooperation. The findings offer insights into optimizing collaborative innovation networks in the NEVs industry and suggest strategies for policymakers and industry players to promote collaborative innovation. [ABSTRACT FROM AUTHOR]

We consider an infinite planar Delaunay graph Gϵ which is obtained by locally deforming the coordinate embedding of a general isoradial graph Gcr, with respect to a real deformation parameter ϵ. Using Kenyon's exact and asymptotic results for the critical Green's function on an isoradial graph, we calculate the leading asymptotics of the first- and second-order terms in the perturbative expansion of the log-determinant of the Laplace-Beltrami operator Δ(ϵ), the David-Eynard Kähler operator D(ϵ), and the conformal Laplacian Δ ​(ϵ) on the deformed Delaunay graph Gϵ. We show that the scaling limits of the second-order bi-local term for both the Laplace-Beltrami and David-Eynard Kähler operators exist and coincide, with a shared value independent of the choice of the initial isoradial graph Gcr. Our results allow us to define a discrete analog of the stress-energy tensor for each of the three operators. Furthermore, we can identify a central charge (c=-2) in the case of both the Laplace-Beltrami and David-Eynard Kähler operators. While the scaling limit is consistent with the stress-energy tensor and the value of the central charge for the Gaussian free field (GFF), the discrete central charge value of c=-2 for the David-Eynard Kähler operator is, however, at odds with the value of c=-26 expected by Polyakov's theory of 2D quantum gravity; moreover, there are problems with convergence of the scaling limit of the discrete stress-energy tensor for the David-Eynard Kähler operator. The second-order bi-local term for the conformal Laplacian involves anomalous terms corresponding to the creation of discrete curvature dipoles in the deformed Delaunay graph Gϵ; we examine the difficulties in defining a convergent scaling limit in this case. Connections with some discrete statistical models at criticality are explored. [ABSTRACT FROM AUTHOR]

We show that, in almost every n$$ n $$‐vertex random directed graph process, a copy of every possible n$$ n $$‐vertex oriented cycle will appear strictly before a directed Hamilton cycle does, except of course for the directed cycle itself. Furthermore, given an arbitrary n$$ n $$‐vertex oriented cycle, we determine the sharp threshold for its appearance in the binomial random directed graph. These results confirm, in a strong form, a conjecture of Ferber and Long. [ABSTRACT FROM AUTHOR]

The Erdös–Rényi graph is a popular choice to model network data as it is parsimoniously parameterized, straightforward to interpret and easy to estimate. However, it has limited suitability in practice, since it often fails to capture crucial characteristics of real‐world networks. To check its adequacy, we propose a novel class of goodness‐of‐fit tests for homogeneous Erdös–Rényi models against heterogeneous alternatives that permit nonconstant edge probabilities. We allow for both asymptotically dense and sparse networks. The tests are based on graph functionals that cover a broad class of network statistics for which we derive limiting distributions in a unified manner. The resulting class of asymptotic tests includes several existing tests as special cases. Further, we propose a parametric bootstrap and prove its consistency, which avoids the often tedious variance estimation for asymptotic tests and enables performance improvements for small network sizes. Moreover, under certain fixed and local alternatives, we provide a power analysis for some popular choices of subgraph counts as goodness‐of‐fit test statistics. We evaluate the proposed class of tests and illustrate our theoretical findings by simulations. [ABSTRACT FROM AUTHOR]

Information exchange is critical to the functionality of governance networks. Traditionally, it has been argued that actors within governance networks tend to engage in information exchange with others who share similar beliefs and motivations, as these are deemed catalysts for achieving collective objectives. An alternative viewpoint posits that actors may prioritize strategies aimed at minimizing transaction costs and maximizing returns when selecting their partners. This paper proposes that information exchange predominantly occurs with partners who are easily accessible (i.e., where transaction costs are low) and with partners who are perceived as influential (i.e., where benefits are high). To investigate these alternative propositions, we examine three distinct opportunity structures that actors may utilize, which are based on their preferences for (1) partners with similar participatory motivations, (2) partners who co‐participate in institutional committees, and (3) those perceived as influential. We empirically test these opportunity structures using unique survey data gathered from 10 anti‐corruption multi‐stakeholder partnerships within the public infrastructure domain in countries of Latin America, Africa, and Eurasia. Results from Exponential Random Graph Models suggest that shared participatory motivations do not significantly impact information exchange within our context, whereas the perceived influence of a partner emerges as a critical predictor. In addition, co‐participation in institutional committees significantly facilitates information dissemination, particularly when those committees involve discussions on deliberating about strategies to communicate findings on public‐sector infrastructure discrepancies and formulating recommendations to governments on transparency and accountability. These findings prompt discussions on four network management strategies aimed at restructuring networks and fostering stakeholder involvement and inclusivity. [ABSTRACT FROM AUTHOR]

In this paper, we study the mean Li-Yorke chaotic phenomenon along any infinite positive integer sequence for infinite-dimensional random dynamical systems. To be precise, we prove that if an injective continuous infinite-dimensional random dynamical system (X , ϕ) over an invertible ergodic Polish system (Ω , F , P , θ) admits a ϕ -invariant random compact set K with positive topological entropy, then given a positive integer sequence a = { a i } i ∈ N with lim i → + ∞ ⁡ a i = + ∞ , for P -a.s. ω ∈ Ω there exists an uncountable subset S (ω) ⊂ K (ω) and ϵ (ω) > 0 such that for any two distinct points x 1 , x 2 ∈ S (ω) , one has lim inf N → + ∞ 1 N ∑ i = 1 N d (ϕ (a i , ω) x 1 , ϕ (a i , ω) x 2) = 0 , lim sup N → + ∞ 1 N ∑ i = 1 N d (ϕ (a i , ω) x 1 , ϕ (a i , ω) x 2) > ϵ (ω) , where d is a compatible complete metric on X. To overcome the difficulties arising in the infinite-dimensional random dynamical systems, we use the regularity of measure to construct the expected measurable partitions and to decompose the distance function. [ABSTRACT FROM AUTHOR]

Given a graph G = (V , E) with n = | V | vertices, the graph coloring problem is defined as Find a color vector C = (c (v)) , where c (v) ∈ { 1 , 2 , ... , n } denotes the color of vertex v ∈ V , such that no monochromatic edge exists in G and the span , the total number of distinct colors in C , is minimized. Since the problem is NP-complete, a greedy coloring is commonly used for solving it. Greedy coloring visits the vertices of G following an order S , and while visiting a vertex v , it puts the minimum color absent in all neighbors of v. We show that the orders producing span ≤ k , where k ≤ n is a positive integer, can be partitioned into disjoint subsets of equivalent orders. Next, we propose a selective search (SS) algorithm, which takes ρ as an input parameter, selects ≥ ρ orders each from a different set of equivalent orders with high probability, applies greedy coloring on them, and returns the color vector with minimum span. We analytically show that SS performs better than greedy coloring with high probability by evaluating the same number of orders. We propose an incremental search heuristic (ISH), which ρ 1 times execute SS with parameter ρ 2 and returns the color vector with minimum span. A parallel version of ISH called PISH is also proposed, executing ρ 1 SS calls in parallel. We show that ISH hits an optimum coloring for a graph G = (V , E) with χ (G) (Δ (G) + 1) ≤ n e in expected O (| V | + | E |) time and space complexities. We have evaluated ISH and PISH on 136 challenging benchmarks and shown that they significantly outperform 10 existing state-of-the-art algorithms. Finally, we validated our theoretical findings by evaluating ISH and greedy coloring on random graphs. [ABSTRACT FROM AUTHOR]

Western Muslim youth engage less in romantic relationships than their non-Muslim peers, an observation usually attributed to chastity norms that oppose Muslim youths’ premarital sexual activity. In this study, I ask whether chastity norms also shape cross-gender interaction beyond romantic relationships and lead to fewer cross-gender friendships among Muslim than non-Muslim youth. To isolate the consequences of chastity norms from institutionalized practices of gender segregation in Muslim religious communities, I study friendship-making in German coeducational schools, which provide ample opportunities for cross-gender friendships. I apply multilevel exponential random graph models to large-scale data on adolescents’ school-based friendship networks, finding cross-gender friendships to be generally infrequent but notably rarer among Muslim than non-Muslim youth. However, this lack of cross-gender friendships is limited to Muslim youth who hold strong chastity norms, while more liberal Muslim youth have as many cross-gender friends as non-Muslims. Among non-Muslims, chastity norms are unrelated to cross-gender friendships. [ABSTRACT FROM AUTHOR]

Neuro‐imaging data can often be represented as statistical networks, especially for functional magnetic resonance imaging (fMRI) data, where brain regions are defined as nodes and the functional interactions between those regions are taken as edges. Such networks are commonly divided into classes depending on the type of edges, namely binary or weighted. A binary network means edges can either be present or absent. Whereas the edges of a weighted network are associated with weight values, and fMRI networks belong to weighted networks. Statistical methods are often adopted to analyse such networks, among which, the exponential random graph model (ERGM) is an important network analysis approach. Typically ERGMs are applied to binary networks, and weighted networks often need to be binarised by arbitrarily selecting a threshold value to define the presence of the edges, which can lead to non‐robustness and loss of valuable edge weight information representing the strength of fMRI interaction in fMRI networks. While it is therefore important to gain deeper insight in adopting ERGM on weighted networks, there only exists a few different ERGM frameworks for weighted networks; some of these are not directly implementable on fMRI networks based on their original proposal. We systematically review, implement, analyse and compare five such frameworks via a simulation study and provide guidelines on each modelling framework as well as conclude the suitability of them on fMRI networks based on a range of criteria. We concluded that Multi‐Layered ERGM is currently the most suitable framework. [ABSTRACT FROM AUTHOR]

The prevalent approach to motif analysis seeks to describe the local connectivity structure of networks by identifying subgraph patterns that appear significantly more often in a network then expected under a null model that conserves certain features of the original network. In this article we advocate for an alternative approach based on statistical inference of generative models where nodes are connected not only by edges but also copies of higher order subgraphs. These models naturally lead to the consideration of latent states that correspond to decompositions of networks into higher order interactions in the form of subgraphs that can have the topology of any simply connected motif. Being based on principles of parsimony the method can infer concise sets of motifs from within thousands of candidates allowing for consistent detection of larger motifs. The inferential approach yields not only a set of statistically significant higher order motifs but also an explicit decomposition of the network into these motifs, which opens new possibilities for the systematic study of the topological and dynamical implications of higher order connectivity structures in networks. After briefly reviewing core concepts and methods, we provide example applications to empirical data sets and discuss how the inferential approach addresses current problems in motif analysis and explore how concepts and methods common to motif analysis translate to the inferential framework. [ABSTRACT FROM AUTHOR]

Ecological interactions among benthic communities are crucial for shaping marine ecosystems. Understanding these interactions is essential for predicting how ecosystems will respond to environmental changes, invasive species, and conservation management. However, determining the prevalence of species interactions at the community scale is challenging. To overcome this challenge, we employ tools from social network analysis, specifically exponential random graph modelling (ERGM). Our approach explores the relationships among animal and plant organisms within their neighbourhoods. Inspired by companion planting in agriculture, we use spatiotemporal co-occurrence as a measure of mixed species interaction. In other words, the variety of community interactions based on co-occurrence defines what we call 'co-occurrence social diversity'. Our objective is to use ERGM to quantify the proportion of interactions at both the simple paired level and the more complex triangle level, enabling us to measure and compare co-occurrence social diversity. Applying our approach to the Spanish coastal zone across eight sites, five depths, and sunlit/shaded aspects, we discover that 80% of sessile communities, consisting of over a hundred species, exhibit co-occurrence social diversity, with 5% of species consistently forming associations with other species. These organism-level interactions probably have a significant impact on the overall character of the site. This article is part of the theme issue 'Connected interactions: enriching food web research by spatial and social interactions'. [ABSTRACT FROM AUTHOR]

This paper explores the structure of organised crime movement across local communities and the drivers underpinning such movement. Firstly, it builds on network analysis to offer a novel methodological approach to empirically and quantitatively study the movement of organised crime offenders across geographical areas. The paper then applies this approach to evidence from Cambridgeshire in the United Kingdom. It reconstructs the movement of organised crime members across local areas based on a large-scale police dataset that includes 41 months of recorded crime events. It identifies organised crime "turf" and "target" areas and then explores the drivers of movement from the former to the latter using Exponential Random Graph Models. Findings confirm that geographical distance matters; however, socio-demographic, urban, economic and crime-related characteristics of communities play a key role. Organised crime group members target urban communities with higher than average illegal market opportunities (proxied by drug-related activity). The work also finds the effect of socio-demographic homophily between turf and target communities, suggesting that organised crime group members might target territories that are similar to their own. While a high level of deprivation makes a community more likely to send organised crime members, its impact on a community's probability of being a receiver is less clear. Finally, the paper offers a way to identify communities (local areas) at risk of being targeted by criminal organisations, thus providing practitioners with a tool for early interventions. [ABSTRACT FROM AUTHOR]

This paper concerns the analysis of large quantum states. It is a notoriously difficult problem to quantify separability of quantum states, and for large quantum states, it is unfeasible. Here we posit that when quantum states are large, we can deduce reasonable expectations for the complex structure of non-classical multipartite correlations with surprisingly little information about the state. We show, with pegagogical examples, how known results from combinatorics can be used to reveal the expected structure of various correlations hidden in the ensemble described by a state. [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) have been highly successful in graph representation learning. The goal of GNNs is to enrich node representations by aggregating information from neighboring nodes. Much work has attempted to improve the quality of aggregation by introducing a variety of graph information with representational capabilities. The class of GNNs that improves the quality of aggregation by encoding graph information with representational capabilities into the weights of neighboring nodes through different learnable transformation structures (LTSs) are referred to as implicit GNNs. However, we argue that LTSs only transform graph information into the weights of neighboring nodes in the direction that minimizes the loss function during the learning process and does not actually utilize the effective properties of graph information, a phenomenon that we refer to as graph information vanishing (GIV). To validate this point, we perform thousands of experiments on seven node classification benchmark datasets. We first replace the graph information utilized by five implicit GNNs with random values and surprisingly observe that the variation range of accuracies is less than ± 0.3%. Then, we quantitatively characterize the similarity of the weights generated from graph information and random values by cosine similarity, and the cosine similarities are greater than 0.99. The empirical experiments show that graph information is equivalent to initializing the input of LTSs. We believe that graph information as an additional supervised signal to constrain the training of GNNs can effectively solve GIV. Here, we propose GinfoNN, which utilizes both labels and discrete graph curvature as supervised signals to jointly constrain the training of the model. The experimental results show that the classification accuracies of GinfoNN improve by two percentage points over baselines on large and dense datasets. [ABSTRACT FROM AUTHOR]

The convergence of heterogeneous wireless sensor networks provides many benefits, including increased coverage, flexible load balancing capabilities, more efficient use of network resources, and the provision of additional data by different types of sensors, thus leading to improved customer service based on more complete information. However, despite these advances, the challenge of ensuring reliability and survivability remains due to low-cost sensor requirements and the inherent unreliability of the wireless environment. Integrating different sensor networks and unifying protocols naturally leads to the creation of a network with multiple sinks, necessitating the exploration of new approaches to rational reliability assurance. The failure of some sensors does not necessarily lead to a shutdown of the network, since other sensors can duplicate information and deliver data to sinks via an increased number of alternative routes. In this paper, the reliability indicator is defined as the probability that sinks can collect data from a given number of sensors. In this context, a dedicated reliability metric is introduced and examined for its effectiveness. This metric is computed using an algorithm rooted in the modified factoring method. Furthermore, we introduce a heuristic algorithm designed for optimal sink placement in wireless sensor networks to achieve the highest level of network reliability. [ABSTRACT FROM AUTHOR]

Subgraph counts, in particular the number of occurrences of small shapes such as triangles, characterize properties of random networks. As a result, they have seen wide use as network summary statistics. Subgraphs are typically counted globally, making existing approaches unable to describe vertex-specific characteristics. In contrast, rooted subgraphs focus on vertex neighbourhoods, and are fundamental descriptors of local network properties. We derive the asymptotic joint distribution of rooted subgraph counts in inhomogeneous random graphs, a model that generalizes most statistical network models. This result enables a shift in the statistical analysis of graphs, from estimating network summaries to estimating models linking local network structure and vertex-specific covariates. As an example, we consider a school friendship network and show that gender and race are significant predictors of local friendship patterns. [ABSTRACT FROM AUTHOR]

Cloud-based computing networks have taken over the digital landscape. From small non-profits to large multinational corporations, more and more entities have been offloading computing effort to the cloud in order to take advantage of the increased cost-efficiency and scalability of cloud computing. One of the new types of cloud that have emerged is P2P cloud, which disengages from a traditional datacenter setup by allowing users to instead share their own computing hardware into a cloud to reap the benefits of cloud computing's advantages at an even lower cost. However, this new paradigm comes with a slew of challenges: (i) security, when operating with the devices of strangers and (ii) fairness when not operating in a market-based system. This paper aims to address these two issues by proposing an algorithm based on social credits for a P2P cloud system that uses a social network to establish its security measures. We implement our new Social Credit algorithm along with two other task-migration-based load-balancing algorithms adapted for a P2P social cloud in "Cloudsim Plus", and the relative gains are shown in terms of fairness and other related metrics. [ABSTRACT FROM AUTHOR]

A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph G(n,r,d) ${\mathscr{G}}(n,r,d)$. In particular, we find the sharp threshold for balanced binary trees. More generally, we show that all sequences of balanced trees with uniformly bounded degrees and height tending to infinity appear above a sharp threshold, and none of these appears below the same value. Our results hold more generally for geometric graphs satisfying a mild condition on the distribution of their vertex set, and we provide a polynomial time algorithm to find such trees. [ABSTRACT FROM AUTHOR]

We offer an alternative proof, using the Stein-Chen method, of Bollobás' theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices. [ABSTRACT FROM AUTHOR]

We study in a general graph-theoretic formulation a long-range percolation model introduced by Lamperti [27]. For various underlying digraphs, we discuss connections between this model and random exchange processes. We clarify, for all $n \in \mathbb{N}$ , under which conditions the lattices $\mathbb{N}_0^n$ and $\mathbb{Z}^n$ are essentially covered in this model. Moreover, for all $n \geq 2$ , we establish that it is impossible to cover the directed n -ary tree in our model. [ABSTRACT FROM AUTHOR]

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for 57 % of 459 random Erdos–Rényi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing. [ABSTRACT FROM AUTHOR]

We consider random graph models in which the events describing the inclusion of potential edges have to be independent of each other if the corresponding edges are non‐adjacent and ask: what is the minimum probability ρ(n)$$ \rho (n) $$, such that for any distribution 풢 (in this model) on graphs with n$$ n $$ vertices in which each potential edge has a marginal probability of being present at least ρ(n)$$ \rho (n) $$, a graph drawn from 풢 is connected with non‐zero probability? The answer to this question is sensitive to the formalization of the independence condition. We introduce a strict hierarchy of five conditions, which give rise to at least three different functions ρ(n)$$ \rho (n) $$. For each condition, we provide upper and lower bounds for ρ(n)$$ \rho (n) $$. For the strongest condition, the coloring model, we show that ρ(n)→2−ϕ≈0.38$$ \rho (n)\to 2-\phi \approx 0.38 $$ for n→∞$$ n\to \infty $$. In contrast, for the weakest condition, pairwise independence, we show that ρ(n)$$ \rho (n) $$ lies within O(1/n2)$$ O\left(1/{n}^2\right) $$ of the threshold 1−2/n$$ 1-2/n $$ for completely arbitrary distributions. [ABSTRACT FROM AUTHOR]

In [Trans. Am. Math. Soc. 375 (2022), no. 1, 627–668], Kahn gave the strongest possible, affirmative, answer to Shamir's problem, which had been open since the late 1970s: Let r⩾3$$ r\geqslant 3 $$ and let n$$ n $$ be divisible by r$$ r $$. Then, in the random r$$ r $$‐uniform hypergraph process on n$$ n $$ vertices, as soon as the last isolated vertex disappears, a perfect matching emerges. In the present work, we prove the analogue of this result for clique factors in the random graph process: at the time that the last vertex joins a copy of the complete graph Kr$$ {K}_r $$, the random graph process contains a Kr$$ {K}_r $$‐factor. Our proof draws on a novel sequence of couplings which embeds the random hypergraph process into the cliques of the random graph process. An analogous result is proved for clique factors in the s$$ s $$‐uniform hypergraph process (s⩾3$$ s\geqslant 3 $$). [ABSTRACT FROM AUTHOR]

We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given α∈(0,1)$$ \alpha \in \left(0,1\right) $$, the union of any n$$ n $$‐vertex graph with minimum degree αn$$ \alpha n $$ and the binomial random graph G(n,p)$$ G\left(n,p\right) $$. This is known when α>1/2$$ \alpha >1/2 $$ and we determine the exact perturbed threshold probability in all the remaining cases, that is, for each α≤1/2$$ \alpha \le 1/2 $$. We demonstrate that, as α$$ \alpha $$ ranges over the interval (0,1)$$ \left(0,1\right) $$, the threshold performs a countably infinite number of 'jumps'. Our result has implications on the perturbed threshold for two‐universality, where we also fully address all open cases. [ABSTRACT FROM AUTHOR]

This study examines the information diffusion of "Airbnb discrimination" and related digital activism on Twitter. The model-based inferential network analysis shows a hub-and-spoke network that is loosely connected, indicating that the diffusion network of Airbnb discrimination includes various issues (e.g., antisemitism). The retweet network mirrors the existing offline relationship of users (e.g., those who support opinion leaders of antisemitism), demonstrating a core–periphery structure during the information diffusion process. This study not only empirically tested the retweet relationships but also provided theoretical explanations on how these relationships form through the notion of curative logic and two step information flow theory. The findings of this research challenge the widely accepted assumption about social media that "the more users share, the more people will see." [ABSTRACT FROM AUTHOR]

Online travel communities (OTCs) enable users to interact and share travel information voluntarily. Extant research has primarily focused on the content generated through user interactions but neglected how user interactions are structured. This study employed exponential random graph models to examine the formation of user interactions and the outcomes of homophily in terms of network structure across levels (actor, dyad, triad, and network). A dataset of 2,926 posts and 25,854 replies involving 9,712 users in an OTC was used. Results reveal that users' question initiating and replying ties in OTCs exhibit significant positive structural dependencies in terms of reciprocity, activity spread, generalized transitive closure, and multiple connectivity. Homophily serves as the basis of dyadic interactions and homophilous ties evolve after formation. The study advances hospitality and tourism network research and methodology by going beyond traditional dyadic user interactions, and provides insights into user interactions in OTCs from the social network perspective. [ABSTRACT FROM AUTHOR]

We study the asymptotic growth rate of the labels of high-degree vertices in weighted recursive graphs (WRGs) when the weights are independent, identically distributed, almost surely bounded random variables, and as a result confirm a conjecture by Lodewijks and Ortgiese ('The maximal degree in random recursive graphs with random weights', preprint, 2020). WRGs are a generalisation of the random recursive tree and directed acyclic graph models, in which vertices are assigned vertex-weights and where new vertices attach to $m\in\mathbb{N}$ predecessors, each selected independently with a probability proportional to the vertex-weight of the predecessor. Prior work established the asymptotic growth rate of the maximum degree of the WRG model, and here we show that there exists a critical exponent $\mu_m$ such that the typical label size of the maximum-degree vertex equals $n^{\mu_m(1+o(1))}$ almost surely as n , the size of the graph, tends to infinity. These results extend results on the asymptotic behaviour of the location of the maximum degree, formerly only known for the random recursive tree model, to the more general weighted multigraph case of the WRG model. Moreover, for the weighted recursive tree model, that is, the WRG model with $m=1$ , we prove the joint convergence of the rescaled degree and label of high-degree vertices under additional assumptions on the vertex-weight distribution, and also extend results on the growth rate of the maximum degree obtained by Eslava, Lodewijks, and Ortgiese (Stoch. Process. Appl. 158 , 2023). [ABSTRACT FROM AUTHOR]

Online social networks (OSNs) are an indispensable part of social communication where people connect and share information. Spammers and other malicious actors use the OSN's power to propagate spam content. In an OSN with mutual relations between nodes, two kinds of spammer detection methods can be employed: feature based and propagation based. However, both of these are incomplete in themselves. The feature-based methods cannot exploit mutual connections between nodes, and propagation-based methods cannot utilize the rich discriminating node features. We propose a hybrid model—Markov enhanced graph attention network (MEGAT)—using graph attention networks (GAT) and pairwise Markov random fields (pMRF) for the spammer detection task. It efficiently utilizes node features as well as propagation information. We experiment our GAT model with a smoother Swish activation function having non-monotonic derivatives, instead of the leakyReLU function. The experiments performed on a real-world Twitter Social Honeypot (TwitterSH) benchmark dataset and subsequent comparative analysis reveal that our proposed MEGAT model outperforms the state-of-the-art models in accuracy, precision–recall area under curve (PRAUC), and F1-score performance measures. [ABSTRACT FROM AUTHOR]