Abstract We welcome our new editors and provide background on an unusual duo of articles in this issue.
摘要我们欢迎我们的新编辑，并提供本期两篇不同寻常的文章的背景。
{"title":"Editors’ Note","authors":"Stanley Wasserman, Ulrik Brandes","doi":"10.1017/nws.2022.8","DOIUrl":"https://doi.org/10.1017/nws.2022.8","url":null,"abstract":"Abstract We welcome our new editors and provide background on an unusual duo of articles in this issue.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"1 - 2"},"PeriodicalIF":1.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43648656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
a set of theoretical differences between the models and a proposed for model comparison based on out-of-sample prediction. the theoretical comparison or simulation framework. be using the processes, the of the to the and the impossibility of model comparison using dyadic prediction is by evidence, the discussion: Does the contain theory, and how can its inherent be
{"title":"The stochastic actor-oriented model is a theory as much as it is a method and must be subject to theory tests","authors":"Philip Leifeld, S. Cranmer","doi":"10.1017/nws.2022.7","DOIUrl":"https://doi.org/10.1017/nws.2022.7","url":null,"abstract":"a set of theoretical differences between the models and a proposed for model comparison based on out-of-sample prediction. the theoretical comparison or simulation framework. be using the processes, the of the to the and the impossibility of model comparison using dyadic prediction is by evidence, the discussion: Does the contain theory, and how can its inherent be","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"15 - 19"},"PeriodicalIF":1.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43466587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Block, P., Hollway, J., Stadtfeld, C., Koskinen, J., & Snijders, T. (2022). Circular specifications and “predicting” with information from the future: Errors in the empirical SAOM–TERGM comparison of Leifeld & Cranmer. Network Science, 10(1). https://doi.org/10.1017/nws.2022.6 Leifeld, P., & Cranmer, S. (2019a). A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model. Network Science, 7(1), 20–51. https://doi.org/10.1017/nws.2018.26 Leifeld, P., & Cranmer, S. (2019b). Replication Data for: A Theoretical and Empirical Comparison of the Temporal Exponential Random Graph Model and the Stochastic Actor-Oriented Model, https://doi.org/10.7910/DVN/NEM2XU, Harvard Dataverse, V1. Leifeld, P., & Cranmer, S. (2022). The stochastic actor-oriented model is a theory as much as it is a method and must be subject to theory tests. Network Science, 10(1). https://doi.org/10.1017/nws.2022.7 Wasserman, S., & Brandes, U. (2022) Editors’ Note. Network Science, 10(1). https://doi.org/10.1017/nws.2022.8
{"title":"A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model – Corrigendum","authors":"Philip Leifeld, S. Cranmer","doi":"10.1017/nws.2022.11","DOIUrl":"https://doi.org/10.1017/nws.2022.11","url":null,"abstract":"Block, P., Hollway, J., Stadtfeld, C., Koskinen, J., & Snijders, T. (2022). Circular specifications and “predicting” with information from the future: Errors in the empirical SAOM–TERGM comparison of Leifeld & Cranmer. Network Science, 10(1). https://doi.org/10.1017/nws.2022.6 Leifeld, P., & Cranmer, S. (2019a). A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model. Network Science, 7(1), 20–51. https://doi.org/10.1017/nws.2018.26 Leifeld, P., & Cranmer, S. (2019b). Replication Data for: A Theoretical and Empirical Comparison of the Temporal Exponential Random Graph Model and the Stochastic Actor-Oriented Model, https://doi.org/10.7910/DVN/NEM2XU, Harvard Dataverse, V1. Leifeld, P., & Cranmer, S. (2022). The stochastic actor-oriented model is a theory as much as it is a method and must be subject to theory tests. Network Science, 10(1). https://doi.org/10.1017/nws.2022.7 Wasserman, S., & Brandes, U. (2022) Editors’ Note. Network Science, 10(1). https://doi.org/10.1017/nws.2022.8","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"111 - 111"},"PeriodicalIF":1.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44610212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the detection and the reconstruction of a large very dense subgraph in a social graph with n nodes and m edges given as a stream of edges, when the graph follows a power law degree distribution, in the regime when $m=O(n. log n)$ . A subgraph S is very dense if it has $Omega(|S|^2)$ edges. We uniformly sample the edges with a Reservoir of size $k=O(sqrt{n}.log n)$ . Our detection algorithm checks whether the Reservoir has a giant component. We show that if the graph contains a very dense subgraph of size $Omega(sqrt{n})$ , then the detection algorithm is almost surely correct. On the other hand, a random graph that follows a power law degree distribution almost surely has no large very dense subgraph, and the detection algorithm is almost surely correct. We define a new model of random graphs which follow a power law degree distribution and have large very dense subgraphs. We then show that on this class of random graphs we can reconstruct a good approximation of the very dense subgraph with high probability. We generalize these results to dynamic graphs defined by sliding windows in a stream of edges.
{"title":"Large very dense subgraphs in a stream of edges","authors":"Claire Mathieu, Michel de Rougemont","doi":"10.1017/nws.2021.17","DOIUrl":"https://doi.org/10.1017/nws.2021.17","url":null,"abstract":"<p>We study the detection and the reconstruction of a large very dense subgraph in a social graph with <span>n</span> nodes and <span>m</span> edges given as a stream of edges, when the graph follows a power law degree distribution, in the regime when <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220125124825863-0283:S2050124221000175:S2050124221000175_inline1.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$m=O(n. log n)$\u0000</span></span>\u0000</span>\u0000</span>. A subgraph <span>S</span> is very dense if it has <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220125124825863-0283:S2050124221000175:S2050124221000175_inline2.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$Omega(|S|^2)$\u0000</span></span>\u0000</span>\u0000</span> edges. We uniformly sample the edges with a Reservoir of size <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220125124825863-0283:S2050124221000175:S2050124221000175_inline3.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$k=O(sqrt{n}.log n)$\u0000</span></span>\u0000</span>\u0000</span>. Our detection algorithm checks whether the Reservoir has a giant component. We show that if the graph contains a very dense subgraph of size <span>\u0000<span>\u0000<img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220125124825863-0283:S2050124221000175:S2050124221000175_inline4.png\"/>\u0000<span data-mathjax-type=\"texmath\"><span>\u0000$Omega(sqrt{n})$\u0000</span></span>\u0000</span>\u0000</span>, then the detection algorithm is almost surely correct. On the other hand, a random graph that follows a power law degree distribution almost surely has no large very dense subgraph, and the detection algorithm is almost surely correct. We define a new model of random graphs which follow a power law degree distribution and have large very dense subgraphs. We then show that on this class of random graphs we can reconstruct a good approximation of the very dense subgraph with high probability. We generalize these results to dynamic graphs defined by sliding windows in a stream of edges.</p>","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"40 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Many real-world networks, including social networks and computer networks for example, are temporal networks. This means that the vertices and edges change over time. However, most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of discrete time for modeling temporal networks. Our approach also allows for considering nondeterministic time and incomplete data, two issues that are often found when analyzing datasets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks. In addition, we implemented an R-package that provides programming support for all concepts discussed in this paper. The R-package is publicly available for download.
{"title":"Toward a generalized notion of discrete time for modeling temporal networks","authors":"Konstantin Kueffner, Mark Strembeck","doi":"10.1017/nws.2021.20","DOIUrl":"https://doi.org/10.1017/nws.2021.20","url":null,"abstract":"Abstract Many real-world networks, including social networks and computer networks for example, are temporal networks. This means that the vertices and edges change over time. However, most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of discrete time for modeling temporal networks. Our approach also allows for considering nondeterministic time and incomplete data, two issues that are often found when analyzing datasets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks. In addition, we implemented an R-package that provides programming support for all concepts discussed in this paper. The R-package is publicly available for download.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"443 - 477"},"PeriodicalIF":1.7,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43885061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bogumil Kami'nski, Ł. Kraiński, P. Prałat, F. Théberge
Abstract Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced in [15]. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible and scalable and can deal with undirected/directed and weighted/unweighted graphs.
{"title":"A multi-purposed unsupervised framework for comparing embeddings of undirected and directed graphs","authors":"Bogumil Kami'nski, Ł. Kraiński, P. Prałat, F. Théberge","doi":"10.1017/nws.2022.27","DOIUrl":"https://doi.org/10.1017/nws.2022.27","url":null,"abstract":"Abstract Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its subgraphs, and nodes themselves. If these objectives are achieved, an embedding is a meaningful, understandable, and often compressed representation of a network. Unfortunately, selecting the best embedding is a challenging task and very often requires domain experts. In this paper, we extend the framework for evaluating graph embeddings that was recently introduced in [15]. Now, the framework assigns two scores, local and global, to each embedding that measure the quality of an evaluated embedding for tasks that require good representation of local and, respectively, global properties of the network. The best embedding, if needed, can be selected in an unsupervised way, or the framework can identify a few embeddings that are worth further investigation. The framework is flexible and scalable and can deal with undirected/directed and weighted/unweighted graphs.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"323 - 346"},"PeriodicalIF":1.7,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45004872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
$m=O(n. log n)$ . A subgraph S is very dense if it has 
$Omega(|S|^2)$ edges. We uniformly sample the edges with a Reservoir of size 
$k=O(sqrt{n}.log n)$ . Our detection algorithm checks whether the Reservoir has a giant component. We show that if the graph contains a very dense subgraph of size 
$Omega(sqrt{n})$ , then the detection algorithm is almost surely correct. On the other hand, a random graph that follows a power law degree distribution almost surely has no large very dense subgraph, and the detection algorithm is almost surely correct. We define a new model of random graphs which follow a power law degree distribution and have large very dense subgraphs. We then show that on this class of random graphs we can reconstruct a good approximation of the very dense subgraph with high probability. We generalize these results to dynamic graphs defined by sliding windows in a stream of edges.
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