{"title":"Distance Measures for Unweighted Undirected Networks: A Comparison Study","authors":"Anna Simonetto, Matteo Ventura","doi":"10.1111/anzs.70015","DOIUrl":null,"url":null,"abstract":"<p>Networks are mathematical structures that allow the representation of complex systems by jointly modelling the elements of the system and the relationships that exist among them. To analyse different contexts or systems, methodological tools are necessary to allow for the quantitative estimation of the differences existing between two or more networks. For this purpose, various tools have been proposed in the literature. This study is an exploratory analysis of the impacts that different methods (distances and spectral methods) have on the comparative evaluation of two networks. The analyses were conducted through a simulation study that considered three different perturbation schemes to investigate the behaviour of each method with increasing randomness in the perturbation scheme (i.e., edge removal). Results show that the distances between adjacency matrices are sensitive only to changes in the network density, while spectral methods are sensitive to changes in both the network density and the degree of the nodes.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":"67 3","pages":"373-384"},"PeriodicalIF":0.8000,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.70015","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Australian & New Zealand Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.70015","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Networks are mathematical structures that allow the representation of complex systems by jointly modelling the elements of the system and the relationships that exist among them. To analyse different contexts or systems, methodological tools are necessary to allow for the quantitative estimation of the differences existing between two or more networks. For this purpose, various tools have been proposed in the literature. This study is an exploratory analysis of the impacts that different methods (distances and spectral methods) have on the comparative evaluation of two networks. The analyses were conducted through a simulation study that considered three different perturbation schemes to investigate the behaviour of each method with increasing randomness in the perturbation scheme (i.e., edge removal). Results show that the distances between adjacency matrices are sensitive only to changes in the network density, while spectral methods are sensitive to changes in both the network density and the degree of the nodes.
期刊介绍：
The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association.
The main body of the journal is divided into three sections.
The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data.
The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context.
The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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