{"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":"11 2","pages":"1-1"},"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":"11 2","pages":"52508-52524"},"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":"30 1","pages":""},"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":"4 1","pages":""},"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":"73 1","pages":""},"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":"17 1","pages":"101768"},"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":"14 1","pages":""},"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}
Pub Date : 2022-12-01DOI: 10.48550/arXiv.2212.00445
Thomas Jahn, T. Ullrich, Felix Voigtländer
Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in $L^2$. In particular, we show that in relevant cases such as mixed and isotropic weighted Wiener classes or Sobolev spaces with mixed smoothness, sampling numbers in $L^2$ can be upper bounded by best $n$-term trigonometric widths in $L^infty$. We describe a recovery procedure from $m$ function values based on $ell^1$-minimization (basis pursuit denoising). With this method, a significant gain in the rate of convergence compared to recently developed linear recovery methods is achieved. In this deterministic worst-case setting we see an additional speed-up of $m^{-1/2}$ (up to log factors) compared to linear methods in case of weighted Wiener spaces. For their quasi-Banach counterparts even arbitrary polynomial speed-up is possible. Surprisingly, our approach allows to recover mixed smoothness Sobolev functions belonging to $S^r_pW(mathbb{T}^d)$ on the $d$-torus with a logarithmically better rate of convergence than any linear method can achieve when $1
利用压缩感知领域最新发展的技术，我们证明了$L^2$中(拟-)Banach平滑空间的一般(非线性)采样数的新上界。特别地，我们证明了在相关的情况下，如混合和各向同性加权Wiener类或具有混合平滑性的Sobolev空间中，$L^2$中的采样数可以被$L^ inty $中的最佳$n$项三角宽度的上界。我们描述了基于$ well ^1$最小化(基追求去噪)的$m$函数值的恢复过程。与最近开发的线性恢复方法相比，这种方法的收敛速度有了显著的提高。在这种确定的最坏情况设置中，我们看到与加权Wiener空间的线性方法相比，$m^{-1/2}$(高达对数因子)的额外加速。对于它们的拟巴拿赫对应物，甚至任意多项式加速是可能的。令人惊讶的是，我们的方法允许在$d$-环面上恢复属于$S^r_pW(mathbb{T}^d)$的混合平滑Sobolev函数，其收敛速度比任何线性方法在$1时都要高
{"title":"Sampling numbers of smoothness classes via 𝓁1-minimization","authors":"Thomas Jahn, T. Ullrich, Felix Voigtländer","doi":"10.48550/arXiv.2212.00445","DOIUrl":"https://doi.org/10.48550/arXiv.2212.00445","url":null,"abstract":"Using techniques developed recently in the field of compressed sensing we prove new upper bounds for general (nonlinear) sampling numbers of (quasi-)Banach smoothness spaces in $L^2$. In particular, we show that in relevant cases such as mixed and isotropic weighted Wiener classes or Sobolev spaces with mixed smoothness, sampling numbers in $L^2$ can be upper bounded by best $n$-term trigonometric widths in $L^infty$. We describe a recovery procedure from $m$ function values based on $ell^1$-minimization (basis pursuit denoising). With this method, a significant gain in the rate of convergence compared to recently developed linear recovery methods is achieved. In this deterministic worst-case setting we see an additional speed-up of $m^{-1/2}$ (up to log factors) compared to linear methods in case of weighted Wiener spaces. For their quasi-Banach counterparts even arbitrary polynomial speed-up is possible. Surprisingly, our approach allows to recover mixed smoothness Sobolev functions belonging to $S^r_pW(mathbb{T}^d)$ on the $d$-torus with a logarithmically better rate of convergence than any linear method can achieve when $1","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"21 1","pages":"101786"},"PeriodicalIF":2.1,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80386334","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 : 2022-11-04DOI: 10.48550/arXiv.2211.02346
Chris Jones, K. Wiesner
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the tree-likeness of each node's local neighbourhood. We show that our new model outperforms all other generating function models in prediction accuracy when testing their estimates on a wide range of real-world network data. We compare the new model's performance against the recently introduced message passing models and provide evidence that the standard version is also outperformed, while the `loopy' version is only outperformed on a targeted attack strategy. As we show, however, the computational complexity of our model implementation is much lower than that of message passing algorithms. We provide evidence that all discussed models are poor in predicting networks with highly modular structure with dispersed modules, which are also characterised by high mixing times, identifying this as a general limitation of percolation prediction models.
{"title":"Improving mean-field network percolation models with neighbourhood information and their limitations on highly modular, highly dispersed networks","authors":"Chris Jones, K. Wiesner","doi":"10.48550/arXiv.2211.02346","DOIUrl":"https://doi.org/10.48550/arXiv.2211.02346","url":null,"abstract":"Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the tree-likeness of each node's local neighbourhood. We show that our new model outperforms all other generating function models in prediction accuracy when testing their estimates on a wide range of real-world network data. We compare the new model's performance against the recently introduced message passing models and provide evidence that the standard version is also outperformed, while the `loopy' version is only outperformed on a targeted attack strategy. As we show, however, the computational complexity of our model implementation is much lower than that of message passing algorithms. We provide evidence that all discussed models are poor in predicting networks with highly modular structure with dispersed modules, which are also characterised by high mixing times, identifying this as a general limitation of percolation prediction models.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"559 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75813974","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 : 2022-10-26DOI: 10.48550/arXiv.2210.15009
Bogumil Kami'nski, P. Prałat, F. Théberge
The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known Lancichinetti, Fortunato, Radicchi (LFR) one, and its main parameter ξ can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. In this article, we introduce hypergraph counterpart of the ABCD model, h–ABCD, which also produces random hypergraph with distributions of ground-truth community sizes and degrees following power-law. As in the original ABCD, the new model h–ABCD can produce hypergraphs with various levels of noise. More importantly, the model is flexible and can mimic any desired level of homogeneity of hyperedges that fall into one community. As a result, it can be used as a suitable, synthetic playground for analyzing and tuning hypergraph community detection algorithms. [Received on 22 October 2022; editorial decision on 18 July 2023; accepted on 19 July 2023]
ABCD (Artificial Benchmark for Community Detection)图是近年来提出的一种随机图模型，它具有社团结构和社团大小的幂律分布。该模型生成的图与著名的Lancichinetti, Fortunato, Radicchi (LFR)模型具有相似的性质，并且其主要参数ξ可以被调整以模拟LFR模型中的对应参数，即混合参数μ。在本文中，我们引入了ABCD模型的对应超图h-ABCD, h-ABCD也产生了基于真值社区大小和度服从幂律分布的随机超图。与原来的ABCD一样，新模型h-ABCD可以产生具有不同程度噪声的超图。更重要的是，该模型是灵活的，可以模拟属于一个社区的任何期望级别的超边缘同质性。因此，它可以作为一个合适的综合平台，用于分析和调优超图社区检测算法。[2022年10月22日收到;2023年7月18日的编辑决定;于2023年7月19日接受]
{"title":"Hypergraph Artificial Benchmark for Community Detection (h-ABCD)","authors":"Bogumil Kami'nski, P. Prałat, F. Théberge","doi":"10.48550/arXiv.2210.15009","DOIUrl":"https://doi.org/10.48550/arXiv.2210.15009","url":null,"abstract":"\u0000 The Artificial Benchmark for Community Detection (ABCD) graph is a recently introduced random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known Lancichinetti, Fortunato, Radicchi (LFR) one, and its main parameter ξ can be tuned to mimic its counterpart in the LFR model, the mixing parameter μ. In this article, we introduce hypergraph counterpart of the ABCD model, h–ABCD, which also produces random hypergraph with distributions of ground-truth community sizes and degrees following power-law. As in the original ABCD, the new model h–ABCD can produce hypergraphs with various levels of noise. More importantly, the model is flexible and can mimic any desired level of homogeneity of hyperedges that fall into one community. As a result, it can be used as a suitable, synthetic playground for analyzing and tuning hypergraph community detection algorithms.\u0000 [Received on 22 October 2022; editorial decision on 18 July 2023; accepted on 19 July 2023]","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":"54 81 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80601680","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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