{"title":"Correction to: Configuration models of random hypergraphs","authors":"","doi":"10.1093/comnet/cnad014","DOIUrl":"https://doi.org/10.1093/comnet/cnad014","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84959280","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 : 2023-03-29DOI: 10.48550/arXiv.2303.16328
L. Plaskota, Pawe l Siedlecki
We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.
{"title":"Worst case tractability of linear problems in the presence of noise: linear information","authors":"L. Plaskota, Pawe l Siedlecki","doi":"10.48550/arXiv.2303.16328","DOIUrl":"https://doi.org/10.48550/arXiv.2303.16328","url":null,"abstract":"We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77472549","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}
Q. F. Lotito, Martina Contisciani, C. D. Bacco, Leonardo Di Gaetano, L. Gallo, A. Montresor, F. Musciotto, Nicolò Ruggeri, F. Battiston
From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of units. Here, we present an open-source python library, hypergraphx (HGX), providing a comprehensive collection of algorithms and functions for the analysis of higher-order networks. These include different ways to convert data across distinct higher-order representations, a large variety of measures of higher-order organization at the local and the mesoscale, statistical filters to sparsify higher-order data, a wide array of static and dynamic generative models, and an implementation of different dynamical processes with higher-order interactions. Our computational framework is general, and allows to analyse hypergraphs with weighted, directed, signed, temporal and multiplex group interactions. We provide visual insights on higher-order data through a variety of different visualization tools. We accompany our code with an extended higher-order data repository and demonstrate the ability of HGX to analyse real-world systems through a systematic analysis of a social network with higher-order interactions. The library is conceived as an evolving, community-based effort, which will further extend its functionalities over the years. Our software is available at https://github.com/HGX-Team/hypergraphx.
{"title":"Hypergraphx: a library for higher-order network analysis","authors":"Q. F. Lotito, Martina Contisciani, C. D. Bacco, Leonardo Di Gaetano, L. Gallo, A. Montresor, F. Musciotto, Nicolò Ruggeri, F. Battiston","doi":"10.1093/comnet/cnad019","DOIUrl":"https://doi.org/10.1093/comnet/cnad019","url":null,"abstract":"\u0000 From social to biological systems, many real-world systems are characterized by higher-order, non-dyadic interactions. Such systems are conveniently described by hypergraphs, where hyperedges encode interactions among an arbitrary number of units. Here, we present an open-source python library, hypergraphx (HGX), providing a comprehensive collection of algorithms and functions for the analysis of higher-order networks. These include different ways to convert data across distinct higher-order representations, a large variety of measures of higher-order organization at the local and the mesoscale, statistical filters to sparsify higher-order data, a wide array of static and dynamic generative models, and an implementation of different dynamical processes with higher-order interactions. Our computational framework is general, and allows to analyse hypergraphs with weighted, directed, signed, temporal and multiplex group interactions. We provide visual insights on higher-order data through a variety of different visualization tools. We accompany our code with an extended higher-order data repository and demonstrate the ability of HGX to analyse real-world systems through a systematic analysis of a social network with higher-order interactions. The library is conceived as an evolving, community-based effort, which will further extend its functionalities over the years. Our software is available at https://github.com/HGX-Team/hypergraphx.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83427853","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 centrality measures of the nodes and edges of the street networks are related to various urban phenomena. In particular, betweenness centrality correlates with the spatial distribution of economic activities, the levels of congestion, and the structural changes in cities. In this work, we study how betweenness tends to concentrate in a small set of edges and develop a model to analyse this concentration throughout the growth of graphs. We show that random planar graphs tend to betweenness concentration as the number of nodes increases. The evolution of Paris and Tijuana street networks shows the same behaviour but at a higher rate. A set of 300 street networks worldwide follows a similar relationship between the number of nodes and the betweenness concentration. We find a significant correlation between congestion ranks and betweenness concentration.
{"title":"The concentration of edge betweenness in the evolution of planar graphs and street networks","authors":"J A Pichardo-Corpus","doi":"10.1093/comnet/cnad004","DOIUrl":"https://doi.org/10.1093/comnet/cnad004","url":null,"abstract":"The centrality measures of the nodes and edges of the street networks are related to various urban phenomena. In particular, betweenness centrality correlates with the spatial distribution of economic activities, the levels of congestion, and the structural changes in cities. In this work, we study how betweenness tends to concentrate in a small set of edges and develop a model to analyse this concentration throughout the growth of graphs. We show that random planar graphs tend to betweenness concentration as the number of nodes increases. The evolution of Paris and Tijuana street networks shows the same behaviour but at a higher rate. A set of 300 street networks worldwide follows a similar relationship between the number of nodes and the betweenness concentration. We find a significant correlation between congestion ranks and betweenness concentration.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49937035","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}
F. Bauza, G. Ruiz-Manzanares, J. Gómez-Gardeñes, A. Tarancón, D. Iñiguez
Community detection theory is vital for the structural analysis of many types of complex networks, especially for human-like collaboration networks. In this work, we present a new community detection algorithm, the Targeted Community Merging algorithm, based on the well-known Girvan–Newman algorithm, which allows obtaining community partitions with high values of modularity and a small number of communities. We then perform an analysis and comparison between the departmental and community structure of scientific collaboration networks within the University of Zaragoza. Thus, we draw valuable conclusions from the inter- and intra-departmental collaboration structure that could be useful to take decisions on an eventual departmental restructuring.
{"title":"Targeted Community Merging provides an efficient comparison between collaboration clusters and departmental partitions","authors":"F. Bauza, G. Ruiz-Manzanares, J. Gómez-Gardeñes, A. Tarancón, D. Iñiguez","doi":"10.1093/comnet/cnad012","DOIUrl":"https://doi.org/10.1093/comnet/cnad012","url":null,"abstract":"\u0000 Community detection theory is vital for the structural analysis of many types of complex networks, especially for human-like collaboration networks. In this work, we present a new community detection algorithm, the Targeted Community Merging algorithm, based on the well-known Girvan–Newman algorithm, which allows obtaining community partitions with high values of modularity and a small number of communities. We then perform an analysis and comparison between the departmental and community structure of scientific collaboration networks within the University of Zaragoza. Thus, we draw valuable conclusions from the inter- and intra-departmental collaboration structure that could be useful to take decisions on an eventual departmental restructuring.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74318322","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}
Complex network is a versatile tool for exploring the internal structures and dynamical properties of complex system. The Earth's climate is a typical complex system, and the climate variability is mainly controlled by Sun–Earth interactions on planetary scales. The Earth's rotation could induce Rossby waves, and the oceanic Rossby waves significantly affect the Earth's climate in turn. In this study, climate network, a kind of complex network for climate sciences, has been applied to detect Rossby waves in extratropics of global oceans. The nodes of the climate networks are the regular grid points zonally distributed in four regions of global oceans (North Pacific, South Pacific, North Atlantic and South Atlantic-Indian), and the links represent the statistically significant cross-correlations of sea level anomalies. The results show that the westward propagation of oceanic Rossby waves in the extratropics could be detected by the climate network. Also, the climate network has the potential to detect the more oceanic dynamics.
{"title":"Detection of oceanic Rossby waves in the extratropics by complex networks","authors":"Meng Gao;Aidi Zhang;Han Zhang;Yueqi Wang","doi":"10.1093/comnet/cnad003","DOIUrl":"https://doi.org/10.1093/comnet/cnad003","url":null,"abstract":"Complex network is a versatile tool for exploring the internal structures and dynamical properties of complex system. The Earth's climate is a typical complex system, and the climate variability is mainly controlled by Sun–Earth interactions on planetary scales. The Earth's rotation could induce Rossby waves, and the oceanic Rossby waves significantly affect the Earth's climate in turn. In this study, climate network, a kind of complex network for climate sciences, has been applied to detect Rossby waves in extratropics of global oceans. The nodes of the climate networks are the regular grid points zonally distributed in four regions of global oceans (North Pacific, South Pacific, North Atlantic and South Atlantic-Indian), and the links represent the statistically significant cross-correlations of sea level anomalies. The results show that the westward propagation of oceanic Rossby waves in the extratropics could be detected by the climate network. Also, the climate network has the potential to detect the more oceanic dynamics.","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":"49961484","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}
Liquid water, besides being fundamental for life on Earth, has long fascinated scientists due to several anomalies. Different hypotheses have been put forward to explain these peculiarities. The most accredited one foresees the presence in the supercooled region of two phases at different densities: the low-density liquid phase and the high-density liquid phase. In our previous work [Faccio et al. (2022), J. Mol. Liq., 355, 118922], we showed that it is possible to identify these two forms in water networks through a computational approach based on molecular dynamics simulation and on the calculation of the total communicability of the associated graph, in which the nodes correspond to water molecules and the edges represent the connections (interactions) between molecules. In this article, we present a more in-depth investigation of the application of graph-theory based approaches to the analysis of the structure of water networks. In particular, we investigate different connectivity and centrality measures and we report on the use of a variety of global metrics aimed at giving a topological and geometrical characterization of liquid water.
液态水除了是地球生命的基础外，还因其一些异常现象而长期吸引着科学家。人们提出了不同的假设来解释这些特性。最可信的一种预测在过冷区存在两种不同密度的相:低密度液相和高密度液相。在我们之前的工作[Faccio et al. (2022)， J. Mol. Liq.， 355, 118922]中，我们表明，可以通过基于分子动力学模拟和关联图的总可通通性计算的计算方法来识别水网络中的这两种形式，其中节点对应于水分子，边缘代表分子之间的连接(相互作用)。在本文中，我们对基于图论的方法在水网络结构分析中的应用进行了更深入的研究。特别是，我们研究了不同的连通性和中心性度量，并报告了各种旨在给出液态水的拓扑和几何特征的全局度量的使用。
{"title":"Structural analysis of water networks","authors":"Michele Benzi;Isabella Daidone;Chiara Faccio;Laura Zanetti-Polzi","doi":"10.1093/comnet/cnad001","DOIUrl":"https://doi.org/10.1093/comnet/cnad001","url":null,"abstract":"Liquid water, besides being fundamental for life on Earth, has long fascinated scientists due to several anomalies. Different hypotheses have been put forward to explain these peculiarities. The most accredited one foresees the presence in the supercooled region of two phases at different densities: the low-density liquid phase and the high-density liquid phase. In our previous work [Faccio et al. (2022), J. Mol. Liq., 355, 118922], we showed that it is possible to identify these two forms in water networks through a computational approach based on molecular dynamics simulation and on the calculation of the total communicability of the associated graph, in which the nodes correspond to water molecules and the edges represent the connections (interactions) between molecules. In this article, we present a more in-depth investigation of the application of graph-theory based approaches to the analysis of the structure of water networks. In particular, we investigate different connectivity and centrality measures and we report on the use of a variety of global metrics aimed at giving a topological and geometrical characterization of liquid water.","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":"49961485","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}
Miguel E P Silva;Robert E Gaunt;Luis Ospina-Forero;Caroline Jay;Thomas House
Network comparison is a widely used tool for analysing complex systems, with applications in varied domains including comparison of protein interactions or highlighting changes in structure of trade networks. In recent years, a number of network comparison methodologies based on the distribution of graphlets (small connected network subgraphs) have been introduced. In particular, NetEmd has recently achieved state of the art performance in undirected networks. In this work, we propose an extension of NetEmd to directed networks and deal with the significant increase in complexity of graphlet structure in the directed case by denoising through linear projections. Simulation results show that our framework is able to improve on the performance of a simple translation of the undirected NetEmd algorithm to the directed case, especially when networks differ in size and density.
{"title":"Comparing directed networks via denoising graphlet distributions","authors":"Miguel E P Silva;Robert E Gaunt;Luis Ospina-Forero;Caroline Jay;Thomas House","doi":"10.1093/comnet/cnad006","DOIUrl":"https://doi.org/10.1093/comnet/cnad006","url":null,"abstract":"Network comparison is a widely used tool for analysing complex systems, with applications in varied domains including comparison of protein interactions or highlighting changes in structure of trade networks. In recent years, a number of network comparison methodologies based on the distribution of graphlets (small connected network subgraphs) have been introduced. In particular, NetEmd has recently achieved state of the art performance in undirected networks. In this work, we propose an extension of NetEmd to directed networks and deal with the significant increase in complexity of graphlet structure in the directed case by denoising through linear projections. Simulation results show that our framework is able to improve on the performance of a simple translation of the undirected NetEmd algorithm to the directed case, especially when networks differ in size and density.","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":"49937037","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}
Complex networks encoding the topological architecture of real-world complex systems have recently been undergoing a fundamental transition beyond pairwise interactions described by dyadic connections among nodes. Higher-order structures such as hypergraphs and simplicial complexes have been utilized to model group interactions for varied networked systems from brain, society, to biological and physical systems. In this article, we investigate the consensus dynamics over temporal hypergraphs featuring non-linear modulating functions, time-dependent topology and random perturbations. Based upon analytical tools in matrix, hypergraph, stochastic process and real analysis, we establish the sufficient conditions for all nodes in the network to reach consensus in the sense of almost sure convergence and $mathscr{L}^2$ convergence. The rate of consensus and the moments of the equilibrium have been determined. Our results offer a theoretical foundation for the recent series of numerical studies and physical observations in the multi-body non-linear dynamical systems.
{"title":"Non-linear consensus dynamics on temporal hypergraphs with random noisy higher-order interactions","authors":"Yilun Shang","doi":"10.1093/comnet/cnad009","DOIUrl":"https://doi.org/10.1093/comnet/cnad009","url":null,"abstract":"Complex networks encoding the topological architecture of real-world complex systems have recently been undergoing a fundamental transition beyond pairwise interactions described by dyadic connections among nodes. Higher-order structures such as hypergraphs and simplicial complexes have been utilized to model group interactions for varied networked systems from brain, society, to biological and physical systems. In this article, we investigate the consensus dynamics over temporal hypergraphs featuring non-linear modulating functions, time-dependent topology and random perturbations. Based upon analytical tools in matrix, hypergraph, stochastic process and real analysis, we establish the sufficient conditions for all nodes in the network to reach consensus in the sense of almost sure convergence and \u0000<tex>$mathscr{L}^2$</tex>\u0000 convergence. The rate of consensus and the moments of the equilibrium have been determined. Our results offer a theoretical foundation for the recent series of numerical studies and physical observations in the multi-body non-linear dynamical systems.","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/iel7/8016804/10056757/10091815.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49937039","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}
We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only the distance measurements to a few ‘landmark nodes’. This landmark heuristic makes L-hydra applicable to large-scale graphs and improves upon previously introduced methods. As a mathematical justification, we show that a point configuration in $d$ -dimensional hyperbolic space can be perfectly recovered (up to isometry) from distance measurements to just $d+1$ landmarks. We also show that L-hydra solves a two-stage strain-minimization problem, similar to our previous (unlandmarked) method ‘hydra’. Testing on real network data, we show that L-hydra is an order of magnitude faster than the existing hyperbolic embedding methods and scales linearly in the number of nodes. While the embedding error of L-hydra is higher than the error of the existing methods, we introduce an extension, L-hydra+, which outperforms the existing methods in both runtime and embedding quality.
{"title":"Strain-minimizing hyperbolic network embeddings with landmarks","authors":"Martin Keller-Ressel;Stephanie Nargang","doi":"10.1093/comnet/cnad002","DOIUrl":"https://doi.org/10.1093/comnet/cnad002","url":null,"abstract":"We introduce L-hydra (landmarked hyperbolic distance recovery and approximation), a method for embedding network- or distance-based data into hyperbolic space, which requires only the distance measurements to a few ‘landmark nodes’. This landmark heuristic makes L-hydra applicable to large-scale graphs and improves upon previously introduced methods. As a mathematical justification, we show that a point configuration in \u0000<tex>$d$</tex>\u0000-dimensional hyperbolic space can be perfectly recovered (up to isometry) from distance measurements to just \u0000<tex>$d+1$</tex>\u0000 landmarks. We also show that L-hydra solves a two-stage strain-minimization problem, similar to our previous (unlandmarked) method ‘hydra’. Testing on real network data, we show that L-hydra is an order of magnitude faster than the existing hyperbolic embedding methods and scales linearly in the number of nodes. While the embedding error of L-hydra is higher than the error of the existing methods, we introduce an extension, L-hydra+, which outperforms the existing methods in both runtime and embedding quality.","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":"49961487","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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