In this article, we studied the role of the topological structure of semantic networking in creating verbal aggression. It is shown that centralities such as degree, betweenness and closeness play an important role in the activation of verbal aggression in the network. We have also shown that aggressive labelled nodes with spectral clustering in different spectra are often divided into two groups, with the larger group activating more aggressive labelled nodes. In addition, the parameter of eccentric distribution from the origin is introduced to study the dispersion of aggressive nodes around the specific nodes. Hence, studying two networks with different contexts shows that the dispersion of nodes with aggressive labelling around the network's hub, as the centre of the network with political context, is much more than artistic context. In addition, different clusters of verbal aggression in the political and artistic context have the same pattern of frequency. In addition, we investigated semantic features in creating verbal aggression, showing that non-aggressive words are prone to create verbal aggression as much as aggressive words.
{"title":"The role of network topological structure and semantic features in creating verbal aggression","authors":"Meghdad Abarghouei Nejad;Salman Abarghouei Nejad;Azizollah Memariani;Masoud Asadpour;Javad Hatami;Mohammad Mahdi Kashani","doi":"10.1093/comnet/cnac056","DOIUrl":"https://doi.org/10.1093/comnet/cnac056","url":null,"abstract":"In this article, we studied the role of the topological structure of semantic networking in creating verbal aggression. It is shown that centralities such as degree, betweenness and closeness play an important role in the activation of verbal aggression in the network. We have also shown that aggressive labelled nodes with spectral clustering in different spectra are often divided into two groups, with the larger group activating more aggressive labelled nodes. In addition, the parameter of eccentric distribution from the origin is introduced to study the dispersion of aggressive nodes around the specific nodes. Hence, studying two networks with different contexts shows that the dispersion of nodes with aggressive labelling around the network's hub, as the centre of the network with political context, is much more than artistic context. In addition, different clusters of verbal aggression in the political and artistic context have the same pattern of frequency. In addition, we investigated semantic features in creating verbal aggression, showing that non-aggressive words are prone to create verbal aggression as much as aggressive words.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49961483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other nodes’ opinions when they lie within some confidence bound of their own opinion. In this article, we extend the Deffuant–Weisbuch (DW) model, which is a well-known BCM, by examining the spread of opinions that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinions when they interact with neighbouring nodes and (2) break connections with neighbours based on an opinion tolerance threshold and then form new connections following the principle of homophily. This opinion tolerance threshold determines whether or not the opinions of adjacent nodes are sufficiently different to be viewed as ‘discordant’. Using numerical simulations, we find that our adaptive DW model requires a larger confidence bound than a baseline DW model for the nodes of a network to achieve a consensus opinion. In one region of parameter space, we observe ‘pseudo-consensus’ steady states, in which there exist multiple subclusters of an opinion cluster with opinions that differ from each other by a small amount. In our simulations, we also examine the roles of early-time dynamics and nodes with initially moderate opinions for achieving consensus. Additionally, we explore the effects of coevolution on the convergence time of our BCM.
{"title":"An adaptive bounded-confidence model of opinion dynamics on networks","authors":"Unchitta Kan;Michelle Feng;Mason A Porter","doi":"10.1093/comnet/cnac055","DOIUrl":"https://doi.org/10.1093/comnet/cnac055","url":null,"abstract":"Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which the nodes of a network have continuous-valued states that encode their opinions and are receptive to other nodes’ opinions when they lie within some confidence bound of their own opinion. In this article, we extend the Deffuant–Weisbuch (DW) model, which is a well-known BCM, by examining the spread of opinions that coevolve with network structure. We propose an adaptive variant of the DW model in which the nodes of a network can (1) alter their opinions when they interact with neighbouring nodes and (2) break connections with neighbours based on an opinion tolerance threshold and then form new connections following the principle of homophily. This opinion tolerance threshold determines whether or not the opinions of adjacent nodes are sufficiently different to be viewed as ‘discordant’. Using numerical simulations, we find that our adaptive DW model requires a larger confidence bound than a baseline DW model for the nodes of a network to achieve a consensus opinion. In one region of parameter space, we observe ‘pseudo-consensus’ steady states, in which there exist multiple subclusters of an opinion cluster with opinions that differ from each other by a small amount. In our simulations, we also examine the roles of early-time dynamics and nodes with initially moderate opinions for achieving consensus. Additionally, we explore the effects of coevolution on the convergence time of our BCM.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016804/10068397/10068398.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49961486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graphs have become crucial for representing and examining biological, social and technological interactions. In this context, the graph spectrum is an exciting feature to be studied because it encodes the structural and dynamic characteristics of the graph. Hence, it becomes essential to efficiently compute the graph's spectral distribution (eigenvalue's density function). Recently, some authors proposed degree-based methods to obtain the spectral density of locally tree-like networks in linear time. The bottleneck of their approach is that they assumed that the graph's assortativity is zero. However, most real-world networks, such as social and biological networks, present assortativity. Consequently, their spectral density approximations may be inaccurate. Here, we propose a method that considers assortativity. Our algorithm's time and space complexities are $mathscr{O}(d_{max}^{2})$ , where $d_{max}$ is the largest degree of the graph. Finally, we show our method's efficacy in simulated and empirical networks.
{"title":"A fast algorithm to approximate the spectral density of locally tree-like networks with assortativity","authors":"Grover E C Guzman;André Fujita","doi":"10.1093/comnet/cnad005","DOIUrl":"https://doi.org/10.1093/comnet/cnad005","url":null,"abstract":"Graphs have become crucial for representing and examining biological, social and technological interactions. In this context, the graph spectrum is an exciting feature to be studied because it encodes the structural and dynamic characteristics of the graph. Hence, it becomes essential to efficiently compute the graph's spectral distribution (eigenvalue's density function). Recently, some authors proposed degree-based methods to obtain the spectral density of locally tree-like networks in linear time. The bottleneck of their approach is that they assumed that the graph's assortativity is zero. However, most real-world networks, such as social and biological networks, present assortativity. Consequently, their spectral density approximations may be inaccurate. Here, we propose a method that considers assortativity. Our algorithm's time and space complexities are \u0000<tex>$mathscr{O}(d_{max}^{2})$</tex>\u0000, where \u0000<tex>$d_{max}$</tex>\u0000 is the largest degree of the graph. Finally, we show our method's efficacy in simulated and empirical networks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49937038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Structural analysis of water networks","authors":"","doi":"10.1093/comnet/cnad008","DOIUrl":"https://doi.org/10.1093/comnet/cnad008","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49937036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Identifying a group of key nodes with enormous capability for spreading information to other network nodes is one of the favourable research topics in complex networks. In most existing methods, only the current status of the network is used for identifying and selecting the member of these groups. The main weakness of these methods is a lack of attention to the highly dynamic nature of complex networks and continuous changes in them in terms of creating and eliminating nodes and links. This matter makes the selected group have no proper performance in spreading information relative to other nodes. Therefore, this article presents a novel method for identifying spreader nodes and selecting a superior set from them. In the proposed method, the diffusion power of network nodes is calculated in the first step, and some are selected as influential nodes. In the following steps, it is tried to modify the list of selected nodes by predicting the network variation. Six datasets gathered from real-world networks are utilized for evaluation. The proposed method and other methods are tested to evaluate their spread of influence and time complexity. Results show that using the link prediction in the proposed method can enhance the spread of influence by the selected set compared to other methods so that the spread of influence in some datasets is more than 30 $%$ . On the other hand, the time complexity of the proposed method confirms its utility in very large networks.
{"title":"A method based on link prediction for identifying set of super-spreaders in complex networks","authors":"Bayan Hosseini;Farshid Veisi;Amir Sheikhahmdi","doi":"10.1093/comnet/cnad007","DOIUrl":"https://doi.org/10.1093/comnet/cnad007","url":null,"abstract":"Identifying a group of key nodes with enormous capability for spreading information to other network nodes is one of the favourable research topics in complex networks. In most existing methods, only the current status of the network is used for identifying and selecting the member of these groups. The main weakness of these methods is a lack of attention to the highly dynamic nature of complex networks and continuous changes in them in terms of creating and eliminating nodes and links. This matter makes the selected group have no proper performance in spreading information relative to other nodes. Therefore, this article presents a novel method for identifying spreader nodes and selecting a superior set from them. In the proposed method, the diffusion power of network nodes is calculated in the first step, and some are selected as influential nodes. In the following steps, it is tried to modify the list of selected nodes by predicting the network variation. Six datasets gathered from real-world networks are utilized for evaluation. The proposed method and other methods are tested to evaluate their spread of influence and time complexity. Results show that using the link prediction in the proposed method can enhance the spread of influence by the selected set compared to other methods so that the spread of influence in some datasets is more than 30\u0000<tex>$%$</tex>\u0000. On the other hand, the time complexity of the proposed method confirms its utility in very large networks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49918047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The goal of this note is to assess whether simple machine learning algorithms can be used to determine whether and how a given network has been attacked. The procedure is based on the $k$-Nearest Neighbor and the Random Forest classification schemes, using both intact and attacked ErdH{o}s-R'enyi, Barabasi-Albert and Watts-Strogatz networks to train the algorithm. The types of attacks we consider here are random failures and maximum-degree or maximum-betweenness node deletion. Each network is characterized by a list of 4 metrics, namely the normalized reciprocal maximum degree, the global clustering coefficient, the normalized average path length and the assortativity: a statistical analysis shows that this list of graph metrics is indeed significantly different in intact or damaged networks. We test the procedure by choosing both artificial and real networks, performing the attacks and applying the classification algorithms to the resulting graphs: the procedure discussed here turns out to be able to distinguish between intact networks and those attacked by the maximum-degree of maximum-betweenness deletions, but cannot detect random failures. Our results suggest that this approach may provide a basis for the analysis and detection of network attacks.
本文的目的是评估是否可以使用简单的机器学习算法来确定给定网络是否受到攻击以及如何受到攻击。该过程基于$k$-最近邻和随机森林分类方案，使用完整和攻击的ErdH{o} - r enyi, barabsi - albert和Watts-Strogatz网络来训练算法。我们在这里考虑的攻击类型是随机故障和最大程度或最大间隔节点删除。每个网络都有一个包含4个指标的列表来表征，即归一化倒最大度、全局聚类系数、归一化平均路径长度和分类度:统计分析表明，这一列表的图指标在完整或损坏的网络中确实有显著差异。我们通过选择人工网络和真实网络，执行攻击并将分类算法应用于结果图来测试该过程:这里讨论的过程能够区分完整网络和被最大间数删除的最大程度攻击的网络，但不能检测随机故障。我们的研究结果表明，这种方法可以为分析和检测网络攻击提供基础。
{"title":"A machine-learning procedure to detect network attacks","authors":"Davide Coppes, P. Cermelli","doi":"10.1093/comnet/cnad017","DOIUrl":"https://doi.org/10.1093/comnet/cnad017","url":null,"abstract":"The goal of this note is to assess whether simple machine learning algorithms can be used to determine whether and how a given network has been attacked. The procedure is based on the $k$-Nearest Neighbor and the Random Forest classification schemes, using both intact and attacked ErdH{o}s-R'enyi, Barabasi-Albert and Watts-Strogatz networks to train the algorithm. The types of attacks we consider here are random failures and maximum-degree or maximum-betweenness node deletion. Each network is characterized by a list of 4 metrics, namely the normalized reciprocal maximum degree, the global clustering coefficient, the normalized average path length and the assortativity: a statistical analysis shows that this list of graph metrics is indeed significantly different in intact or damaged networks. We test the procedure by choosing both artificial and real networks, performing the attacks and applying the classification algorithms to the resulting graphs: the procedure discussed here turns out to be able to distinguish between intact networks and those attacked by the maximum-degree of maximum-betweenness deletions, but cannot detect random failures. Our results suggest that this approach may provide a basis for the analysis and detection of network attacks.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82823521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity. We compare these results to real networks. Social networks in particular tend to be assortatively mixed by degree in contrast to many other types of complex networks. However, we show here that these positive correlations diminish after one step and in most of the empirical networks analysed. Properties besides degree support this, such as the number of papers in scientific coauthorship networks, with no correlations beyond nearest neighbours. Beyond next-nearest neighbours we also observe a diasassortative tendency for nodes three steps away indicating that nodes at that distance are more likely different than similar.
{"title":"Correlation distances in social networks","authors":"Pádraig MacCarron, Shane Mannion, T. Platini","doi":"10.1093/comnet/cnad016","DOIUrl":"https://doi.org/10.1093/comnet/cnad016","url":null,"abstract":"In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity. We compare these results to real networks. Social networks in particular tend to be assortatively mixed by degree in contrast to many other types of complex networks. However, we show here that these positive correlations diminish after one step and in most of the empirical networks analysed. Properties besides degree support this, such as the number of papers in scientific coauthorship networks, with no correlations beyond nearest neighbours. Beyond next-nearest neighbours we also observe a diasassortative tendency for nodes three steps away indicating that nodes at that distance are more likely different than similar.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86581104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution to which the model is fit. Current methods for fitting to degree distributions in the literature are inconsistent and often assume a priori what distribution the data are drawn from. Much focus is given to fitting to the tail of the distribution, while a large portion of the distribution below the tail is ignored. It is important to account for these low degree nodes, as they play crucial roles in processes such as percolation. Here we address these issues, using maximum likelihood estimators to fit to the entire dataset, or close to it. This methodology is applicable to any network dataset (or discrete empirical dataset), and we test it on over 25 network datasets from a wide range of sources, achieving good fits in all but a few cases. We also demonstrate that numerical maximization of the likelihood performs better than commonly used analytical approximations. In addition, we have made available a Python package which can be used to apply this methodology.
{"title":"A robust method for fitting degree distributions of complex networks","authors":"Shane Mannion, Pádraig MacCarron","doi":"10.1093/comnet/cnad023","DOIUrl":"https://doi.org/10.1093/comnet/cnad023","url":null,"abstract":"This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution to which the model is fit. Current methods for fitting to degree distributions in the literature are inconsistent and often assume a priori what distribution the data are drawn from. Much focus is given to fitting to the tail of the distribution, while a large portion of the distribution below the tail is ignored. It is important to account for these low degree nodes, as they play crucial roles in processes such as percolation. Here we address these issues, using maximum likelihood estimators to fit to the entire dataset, or close to it. This methodology is applicable to any network dataset (or discrete empirical dataset), and we test it on over 25 network datasets from a wide range of sources, achieving good fits in all but a few cases. We also demonstrate that numerical maximization of the likelihood performs better than commonly used analytical approximations. In addition, we have made available a Python package which can be used to apply this methodology.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87624292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-12DOI: 10.48550/arXiv.2212.05780
G. Leobacher, F. Pillichshammer, Adrian Ebert
In this paper we consider integration and $L_2$-approximation for functions over $RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature, which is interesting on its own. Then we study tractability of the integration and $L_2$-approximation problem for the introduced Hermite spaces, which describes the growth rate of the information complexity when the error threshold $varepsilon$ tends to 0 and the problem dimension $s$ grows to infinity. Our main results are characterizations of tractability in terms of the involved weights, which model the importance of the successive coordinate directions for functions from the weighted Hermite spaces.
{"title":"Tractability of L2-approximation and integration in weighted Hermite spaces of finite smoothness","authors":"G. Leobacher, F. Pillichshammer, Adrian Ebert","doi":"10.48550/arXiv.2212.05780","DOIUrl":"https://doi.org/10.48550/arXiv.2212.05780","url":null,"abstract":"In this paper we consider integration and $L_2$-approximation for functions over $RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of several weighted Hermite spaces that appear in literature, which is interesting on its own. Then we study tractability of the integration and $L_2$-approximation problem for the introduced Hermite spaces, which describes the growth rate of the information complexity when the error threshold $varepsilon$ tends to 0 and the problem dimension $s$ grows to infinity. Our main results are characterizations of tractability in terms of the involved weights, which model the importance of the successive coordinate directions for functions from the weighted Hermite spaces.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90648254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete spacetime in quantum gravity; inferring network geometry in network science; and manifold learning in data science. The key contribution of this paper is to introduce and validate a new estimator of discrete sectional curvature for random graphs with low metric-distortion. The latter are constructed via a specific graph sprinkling method on different manifolds with constant sectional curvature. We define a notion of metric distortion, which quantifies how well the graph metric approximates the metric of the underlying manifold. We show how graph sprinkling algorithms can be refined to produce hard annulus random geometric graphs with minimal metric distortion. We construct random geometric graphs for spheres, hyperbolic and euclidean planes; upon which we validate our curvature estimator. Numerical analysis reveals that the error of the estimated curvature diminishes as the mean metric distortion goes to zero, thus demonstrating convergence of the estimate. We also perform comparisons to other existing discrete curvature measures. Finally, we demonstrate two practical applications: (i) estimation of the earth's radius using geographical data; and (ii) sectional curvature distributions of self-similar fractals.
{"title":"A cosine rule-based discrete sectional curvature for graphs","authors":"J. D. Plessis, X. Arsiwalla","doi":"10.1093/comnet/cnad022","DOIUrl":"https://doi.org/10.1093/comnet/cnad022","url":null,"abstract":"How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete spacetime in quantum gravity; inferring network geometry in network science; and manifold learning in data science. The key contribution of this paper is to introduce and validate a new estimator of discrete sectional curvature for random graphs with low metric-distortion. The latter are constructed via a specific graph sprinkling method on different manifolds with constant sectional curvature. We define a notion of metric distortion, which quantifies how well the graph metric approximates the metric of the underlying manifold. We show how graph sprinkling algorithms can be refined to produce hard annulus random geometric graphs with minimal metric distortion. We construct random geometric graphs for spheres, hyperbolic and euclidean planes; upon which we validate our curvature estimator. Numerical analysis reveals that the error of the estimated curvature diminishes as the mean metric distortion goes to zero, thus demonstrating convergence of the estimate. We also perform comparisons to other existing discrete curvature measures. Finally, we demonstrate two practical applications: (i) estimation of the earth's radius using geographical data; and (ii) sectional curvature distributions of self-similar fractals.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89522668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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