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}
original Articles Gradient and Harnack-type estimates for PageRank paul horn and lauren m. nelsen S4 Learning to count: A deep learning framework for graphlet count estimation xutong liu, yu-zhen janice chen, john c. s. lui and konstantin avrachenkov S23 On the impact of network size and average degree on the robustness of centrality measures christoph martin and peter niemeyer S61 Isolation concepts applied to temporal clique enumeration hendrik molter, rolf niedermeier and malte renken S83 A simple differential geometry for complex networks emil saucan, areejit samal and jürgen jost S106 Sampling methods and estimation of triangle count distributions in large networks nelson antunes, tianjian guo and vladas pipiras S134 Logic and learning in network cascades galen j.wilkerson and sotiris moschoyiannis S157 network science editorial team
{"title":"NWS volume 9 issue S1 Cover and Back matter","authors":"xutong liu","doi":"10.1017/nws.2021.14","DOIUrl":"https://doi.org/10.1017/nws.2021.14","url":null,"abstract":"original Articles Gradient and Harnack-type estimates for PageRank paul horn and lauren m. nelsen S4 Learning to count: A deep learning framework for graphlet count estimation xutong liu, yu-zhen janice chen, john c. s. lui and konstantin avrachenkov S23 On the impact of network size and average degree on the robustness of centrality measures christoph martin and peter niemeyer S61 Isolation concepts applied to temporal clique enumeration hendrik molter, rolf niedermeier and malte renken S83 A simple differential geometry for complex networks emil saucan, areejit samal and jürgen jost S106 Sampling methods and estimation of triangle count distributions in large networks nelson antunes, tianjian guo and vladas pipiras S134 Logic and learning in network cascades galen j.wilkerson and sotiris moschoyiannis S157 network science editorial team","PeriodicalId":51827,"journal":{"name":"Network Science","volume":" ","pages":"b1 - b2"},"PeriodicalIF":1.7,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42426152","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}
original Articles Robust coordination in adversarial social networks: From human behavior to agent-based modeling chen hajaj, zlatko joveski, sixie yu and yevgeniy vorobeychik 255 Separable and semiparametric network-based counting processes applied to the international combat aircraft trades cornelius fritz, paul w. thurner and göran kauermann 291 Efficient Laplacian spectral density computations for networks with arbitrary degree distributions grover e. c. guzman, peter f. stadler and andré fujita 312 Diffusion profile embedding as a basis for graph vertex similarity scott payne, edgar fuller, george spirou and cun-quan zhang 328 Investigating scientific mobility in co-authorship networks using multilayer temporal motifs hanjo d. boekhout, vincent a. traag and frank w. takes 354 network science editorial team
{"title":"NWS volume 9 issue 3 Cover and Back matter","authors":"","doi":"10.1017/nws.2021.16","DOIUrl":"https://doi.org/10.1017/nws.2021.16","url":null,"abstract":"original Articles Robust coordination in adversarial social networks: From human behavior to agent-based modeling chen hajaj, zlatko joveski, sixie yu and yevgeniy vorobeychik 255 Separable and semiparametric network-based counting processes applied to the international combat aircraft trades cornelius fritz, paul w. thurner and göran kauermann 291 Efficient Laplacian spectral density computations for networks with arbitrary degree distributions grover e. c. guzman, peter f. stadler and andré fujita 312 Diffusion profile embedding as a basis for graph vertex similarity scott payne, edgar fuller, george spirou and cun-quan zhang 328 Investigating scientific mobility in co-authorship networks using multilayer temporal motifs hanjo d. boekhout, vincent a. traag and frank w. takes 354 network science editorial team","PeriodicalId":51827,"journal":{"name":"Network Science","volume":" ","pages":"b1 - b2"},"PeriodicalIF":1.7,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44899246","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 The network Laplacian spectral density calculation is critical in many fields, including physics, chemistry, statistics, and mathematics. It is highly computationally intensive, limiting the analysis to small networks. Therefore, we present two efficient alternatives: one based on the network’s edges and another on the degrees. The former gives the exact spectral density of locally tree-like networks but requires iterative edge-based message-passing equations. In contrast, the latter obtains an approximation of the spectral density using only the degree distribution. The computational complexities are 𝒪(|E|log(n)) and 𝒪(n), respectively, in contrast to 𝒪(n3) of the diagonalization method, where n is the number of vertices and |E| is the number of edges.
{"title":"Efficient Laplacian spectral density computations for networks with arbitrary degree distributions","authors":"Grover E. C. Guzman, P. Stadler, André Fujita","doi":"10.1017/nws.2021.10","DOIUrl":"https://doi.org/10.1017/nws.2021.10","url":null,"abstract":"Abstract The network Laplacian spectral density calculation is critical in many fields, including physics, chemistry, statistics, and mathematics. It is highly computationally intensive, limiting the analysis to small networks. Therefore, we present two efficient alternatives: one based on the network’s edges and another on the degrees. The former gives the exact spectral density of locally tree-like networks but requires iterative edge-based message-passing equations. In contrast, the latter obtains an approximation of the spectral density using only the degree distribution. The computational complexities are 𝒪(|E|log(n)) and 𝒪(n), respectively, in contrast to 𝒪(n3) of the diagonalization method, where n is the number of vertices and |E| is the number of edges.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"312 - 327"},"PeriodicalIF":1.7,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45288613","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 This paper introduces a framework for understanding complex temporal interaction patterns in large-scale scientific collaboration networks. In particular, we investigate how two key concepts in science studies, scientific collaboration and scientific mobility, are related and possibly differ between fields. We do so by analyzing multilayer temporal motifs: small recurring configurations of nodes and edges. Driven by the problem that many papers share the same publication year, we first provide a methodological contribution: an efficient counting algorithm for multilayer temporal motifs with concurrent edges. Next, we introduce a systematic categorization of the multilayer temporal motifs, such that each category reflects a pattern of behavior relevant to scientific collaboration and mobility. Here, a key question concerns the causal direction: does mobility lead to collaboration or vice versa? Applying this framework to scientific collaboration networks extracted from Web of Science (WoS) consisting of up to 7.7 million nodes (authors) and 94 million edges (collaborations), we find that international collaboration and international mobility reciprocally influence one another. Additionally, we find that Social sciences & Humanities (SSH) scholars co-author to a greater extent with authors at a distance, while Mathematics & Computer science (M&C) scholars tend to continue to collaborate within the established knowledge network and organization.
{"title":"Investigating scientific mobility in co-authorship networks using multilayer temporal motifs","authors":"Hanjo D. Boekhout, V. Traag, F. Takes","doi":"10.1017/nws.2021.12","DOIUrl":"https://doi.org/10.1017/nws.2021.12","url":null,"abstract":"Abstract This paper introduces a framework for understanding complex temporal interaction patterns in large-scale scientific collaboration networks. In particular, we investigate how two key concepts in science studies, scientific collaboration and scientific mobility, are related and possibly differ between fields. We do so by analyzing multilayer temporal motifs: small recurring configurations of nodes and edges. Driven by the problem that many papers share the same publication year, we first provide a methodological contribution: an efficient counting algorithm for multilayer temporal motifs with concurrent edges. Next, we introduce a systematic categorization of the multilayer temporal motifs, such that each category reflects a pattern of behavior relevant to scientific collaboration and mobility. Here, a key question concerns the causal direction: does mobility lead to collaboration or vice versa? Applying this framework to scientific collaboration networks extracted from Web of Science (WoS) consisting of up to 7.7 million nodes (authors) and 94 million edges (collaborations), we find that international collaboration and international mobility reciprocally influence one another. Additionally, we find that Social sciences & Humanities (SSH) scholars co-author to a greater extent with authors at a distance, while Mathematics & Computer science (M&C) scholars tend to continue to collaborate within the established knowledge network and organization.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"354 - 386"},"PeriodicalIF":1.7,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49362697","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}
Scott Payne, Edgar Fuller, G. Spirou, Cun-Quan Zhang
Abstract We describe here a notion of diffusion similarity, a method for defining similarity between vertices in a given graph using the properties of random walks on the graph to model the relationships between vertices. Using the approach of graph vertex embedding, we characterize a vertex vi by considering two types of diffusion patterns: the ways in which random walks emanate from the vertex vi to the remaining graph and how they converge to the vertex vi from the graph. We define the similarity of two vertices vi and vj as the average of the cosine similarity of the vectors characterizing vi and vj. We obtain these vectors by modifying the solution to a differential equation describing a type of continuous time random walk. This method can be applied to any dataset that can be assigned a graph structure that is weighted or unweighted, directed or undirected. It can be used to represent similarity of vertices within community structures of a network while at the same time representing similarity of vertices within layered substructures (e.g., bipartite subgraphs) of the network. To validate the performance of our method, we apply it to synthetic data as well as the neural connectome of the C. elegans worm and a connectome of neurons in the mouse retina. A tool developed to characterize the accuracy of the similarity values in detecting community structures, the uncertainty index, is introduced in this paper as a measure of the quality of similarity methods.
{"title":"Diffusion profile embedding as a basis for graph vertex similarity","authors":"Scott Payne, Edgar Fuller, G. Spirou, Cun-Quan Zhang","doi":"10.1017/nws.2021.11","DOIUrl":"https://doi.org/10.1017/nws.2021.11","url":null,"abstract":"Abstract We describe here a notion of diffusion similarity, a method for defining similarity between vertices in a given graph using the properties of random walks on the graph to model the relationships between vertices. Using the approach of graph vertex embedding, we characterize a vertex vi by considering two types of diffusion patterns: the ways in which random walks emanate from the vertex vi to the remaining graph and how they converge to the vertex vi from the graph. We define the similarity of two vertices vi and vj as the average of the cosine similarity of the vectors characterizing vi and vj. We obtain these vectors by modifying the solution to a differential equation describing a type of continuous time random walk. This method can be applied to any dataset that can be assigned a graph structure that is weighted or unweighted, directed or undirected. It can be used to represent similarity of vertices within community structures of a network while at the same time representing similarity of vertices within layered substructures (e.g., bipartite subgraphs) of the network. To validate the performance of our method, we apply it to synthetic data as well as the neural connectome of the C. elegans worm and a connectome of neurons in the mouse retina. A tool developed to characterize the accuracy of the similarity values in detecting community structures, the uncertainty index, is introduced in this paper as a measure of the quality of similarity methods.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"328 - 353"},"PeriodicalIF":1.7,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47920926","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}
This special issue of Network Science contains a collection of extended papers from the 8th International Conference on Complex Networks & their Applications (COMPLEX NETWORKS 2019) . This major international event in network science brings together every year researchers from around the globe. The great diversity of the participants’ scientific backgrounds ranges from Finance and Economics, Medicine and Neuroscience, Biology and Earth Sciences, Sociology and Political Science to Mathematics and Computer Science, Physics, and many others, making it a special opportunity to review the current state of the field and formulate new directions. This edition of the conference took place at the Calouste Gulbenkian Foundation in Lisbon (Portugal) from December 10 to December 12, 2019. It attracted 470 submissions with authors from 58 countries all over the world. After thorough review, 161 papers were selected to be included in the proceedings Cherifi et al. (2020a,b). The conference program also included keynote presentations from Lada Adamic (Facebook, Inc., USA), Reka Albert (Pennsylvania State University, USA), Ulrik Brandes (ETH Zurich, Switzerland), Stefan Thurner (Medical University of Vienna, Austria), Jari Saramki (Aalto University, Finland), and Michalis Vazirgiannis (LIX, cole Polytechnique, France). Papers invited for this special issue have been selected from the accepted contributions based on relevance to the journal and excellent reviews of the conference version of the papers. The authors were asked to submit an extended version of their conference submission for journal publication in accordance with the customary practice of adding 30% new material. These submissions went through the standard double-blind review process dictated by the journal guidelines. The seven papers accepted to this special issue provide a remarkable sample illustrating the diversity of issues studied in network science research.
{"title":"Introduction to the special issue on COMPLEX NETWORKS 2019","authors":"H. Cherifi, Luis M. Rocha","doi":"10.1017/nws.2021.8","DOIUrl":"https://doi.org/10.1017/nws.2021.8","url":null,"abstract":"This special issue of Network Science contains a collection of extended papers from the 8th International Conference on Complex Networks & their Applications (COMPLEX NETWORKS 2019) . This major international event in network science brings together every year researchers from around the globe. The great diversity of the participants’ scientific backgrounds ranges from Finance and Economics, Medicine and Neuroscience, Biology and Earth Sciences, Sociology and Political Science to Mathematics and Computer Science, Physics, and many others, making it a special opportunity to review the current state of the field and formulate new directions. This edition of the conference took place at the Calouste Gulbenkian Foundation in Lisbon (Portugal) from December 10 to December 12, 2019. It attracted 470 submissions with authors from 58 countries all over the world. After thorough review, 161 papers were selected to be included in the proceedings Cherifi et al. (2020a,b). The conference program also included keynote presentations from Lada Adamic (Facebook, Inc., USA), Reka Albert (Pennsylvania State University, USA), Ulrik Brandes (ETH Zurich, Switzerland), Stefan Thurner (Medical University of Vienna, Austria), Jari Saramki (Aalto University, Finland), and Michalis Vazirgiannis (LIX, cole Polytechnique, France). Papers invited for this special issue have been selected from the accepted contributions based on relevance to the journal and excellent reviews of the conference version of the papers. The authors were asked to submit an extended version of their conference submission for journal publication in accordance with the customary practice of adding 30% new material. These submissions went through the standard double-blind review process dictated by the journal guidelines. The seven papers accepted to this special issue provide a remarkable sample illustrating the diversity of issues studied in network science research.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"S1 - S3"},"PeriodicalIF":1.7,"publicationDate":"2021-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42485168","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}
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