Abstract Researchers have found that although external attacks, exogenous shocks, and node knockouts can disrupt networked systems, they rarely lead to the system’s collapse. Although these processes are widely understood, most studies of how exogenous shocks affect networks rely on simulated or observational data. Thus, little is known about how groups of real individuals respond to external attacks. In this article, we employ an experimental design in which exogenous shocks, in the form of the unexpected removal of a teammate, are imposed on small teams of people who know each other. This allows us to causally identify the removed individual’s contribution to the team structure, the effect that an individual had on those they were connected, and the effect of the node knockout on the team. At the team level, we find that node knockouts decrease overall internal team communication. At the individual level, we find that node knockouts cause the remaining influential players to become more influential, while the remaining peripheral players become more isolated within their team. In addition, we also find that node knockouts may have a nominal influence on team performance. These findings shed light on how teams respond and adapt to node knockouts.
{"title":"How teams adapt to exogenous shocks: Experimental evidence with node knockouts of central members","authors":"Jared F. Edgerton, S. Cranmer, V. Finomore","doi":"10.1017/nws.2022.26","DOIUrl":"https://doi.org/10.1017/nws.2022.26","url":null,"abstract":"Abstract Researchers have found that although external attacks, exogenous shocks, and node knockouts can disrupt networked systems, they rarely lead to the system’s collapse. Although these processes are widely understood, most studies of how exogenous shocks affect networks rely on simulated or observational data. Thus, little is known about how groups of real individuals respond to external attacks. In this article, we employ an experimental design in which exogenous shocks, in the form of the unexpected removal of a teammate, are imposed on small teams of people who know each other. This allows us to causally identify the removed individual’s contribution to the team structure, the effect that an individual had on those they were connected, and the effect of the node knockout on the team. At the team level, we find that node knockouts decrease overall internal team communication. At the individual level, we find that node knockouts cause the remaining influential players to become more influential, while the remaining peripheral players become more isolated within their team. In addition, we also find that node knockouts may have a nominal influence on team performance. These findings shed light on how teams respond and adapt to node knockouts.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"261 - 282"},"PeriodicalIF":1.7,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42460808","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 article considers the link removal problem in a strongly connected directed network with the goal of minimizing the dominant eigenvalue of the network’s adjacency matrix while maintaining its strong connectivity. Due to the complexity of the problem, this article focuses on computing a suboptimal solution. Furthermore, it is assumed that the knowledge of the overall network topology is not available. This calls for distributed algorithms which rely solely on the local information available to each individual node and information exchange between each node and its neighbors. Two different strategies based on matrix perturbation analysis are presented, namely simultaneous and iterative link removal strategies. Key ingredients in implementing both strategies include novel distributed algorithms for estimating the dominant eigenvectors of an adjacency matrix and for verifying strong connectivity of a directed network under link removal. It is shown via numerical simulations on different type of networks that in general the iterative link removal strategy yields a better suboptimal solution. However, it comes at a price of higher communication cost in comparison to the simultaneous link removal strategy.
{"title":"Connectivity-preserving distributed algorithms for removing links in directed networks","authors":"Azwirman Gusrialdi","doi":"10.1017/nws.2022.25","DOIUrl":"https://doi.org/10.1017/nws.2022.25","url":null,"abstract":"Abstract This article considers the link removal problem in a strongly connected directed network with the goal of minimizing the dominant eigenvalue of the network’s adjacency matrix while maintaining its strong connectivity. Due to the complexity of the problem, this article focuses on computing a suboptimal solution. Furthermore, it is assumed that the knowledge of the overall network topology is not available. This calls for distributed algorithms which rely solely on the local information available to each individual node and information exchange between each node and its neighbors. Two different strategies based on matrix perturbation analysis are presented, namely simultaneous and iterative link removal strategies. Key ingredients in implementing both strategies include novel distributed algorithms for estimating the dominant eigenvectors of an adjacency matrix and for verifying strong connectivity of a directed network under link removal. It is shown via numerical simulations on different type of networks that in general the iterative link removal strategy yields a better suboptimal solution. However, it comes at a price of higher communication cost in comparison to the simultaneous link removal strategy.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"215 - 233"},"PeriodicalIF":1.7,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48193587","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}
Henry L. Carscadden, C. Kuhlman, M. Marathe, Sujith Ravi, D. Rosenkrantz
Abstract We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm.
{"title":"Techniques for blocking the propagation of two simultaneous contagions over networks using a graph dynamical systems framework","authors":"Henry L. Carscadden, C. Kuhlman, M. Marathe, Sujith Ravi, D. Rosenkrantz","doi":"10.1017/nws.2022.18","DOIUrl":"https://doi.org/10.1017/nws.2022.18","url":null,"abstract":"Abstract We consider the simultaneous propagation of two contagions over a social network. We assume a threshold model for the propagation of the two contagions and use the formal framework of discrete dynamical systems. In particular, we study an optimization problem where the goal is to minimize the total number of new infections subject to a budget constraint on the total number of available vaccinations for the contagions. While this problem has been considered in the literature for a single contagion, our work considers the simultaneous propagation of two contagions. This optimization problem is NP-hard. We present two main solution approaches for the problem, namely an integer linear programming (ILP) formulation to obtain optimal solutions and a heuristic based on a generalization of the set cover problem. We carry out a comprehensive experimental evaluation of our solution approaches using many real-world networks. The experimental results show that our heuristic algorithm produces solutions that are close to the optimal solution and runs several orders of magnitude faster than the ILP-based approach for obtaining optimal solutions. We also carry out sensitivity studies of our heuristic algorithm.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"234 - 260"},"PeriodicalIF":1.7,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42880008","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 Machine learning applications on large-scale network-structured data commonly encode network information in the form of node embeddings. Network embedding algorithms map the nodes into a low-dimensional space such that the nodes that are “similar” with respect to network topology are also close to each other in the embedding space. Real-world networks often have multiple versions or can be “multiplex” with multiple types of edges with different semantics. For such networks, computation of Consensus Embeddings based on the node embeddings of individual versions can be useful for various reasons, including privacy, efficiency, and effectiveness of analyses. Here, we systematically investigate the performance of three dimensionality reduction methods in computing consensus embeddings on networks with multiple versions: singular value decomposition, variational auto-encoders, and canonical correlation analysis (CCA). Our results show that (i) CCA outperforms other dimensionality reduction methods in computing concensus embeddings, (ii) in the context of link prediction, consensus embeddings can be used to make predictions with accuracy close to that provided by embeddings of integrated networks, and (iii) consensus embeddings can be used to improve the efficiency of combinatorial link prediction queries on multiple networks by multiple orders of magnitude.
{"title":"Consensus embedding for multiple networks: Computation and applications","authors":"Mengzhen Li, Mustafa Coşkun, Mehmet Koyutürk","doi":"10.1017/nws.2022.17","DOIUrl":"https://doi.org/10.1017/nws.2022.17","url":null,"abstract":"Abstract Machine learning applications on large-scale network-structured data commonly encode network information in the form of node embeddings. Network embedding algorithms map the nodes into a low-dimensional space such that the nodes that are “similar” with respect to network topology are also close to each other in the embedding space. Real-world networks often have multiple versions or can be “multiplex” with multiple types of edges with different semantics. For such networks, computation of Consensus Embeddings based on the node embeddings of individual versions can be useful for various reasons, including privacy, efficiency, and effectiveness of analyses. Here, we systematically investigate the performance of three dimensionality reduction methods in computing consensus embeddings on networks with multiple versions: singular value decomposition, variational auto-encoders, and canonical correlation analysis (CCA). Our results show that (i) CCA outperforms other dimensionality reduction methods in computing concensus embeddings, (ii) in the context of link prediction, consensus embeddings can be used to make predictions with accuracy close to that provided by embeddings of integrated networks, and (iii) consensus embeddings can be used to improve the efficiency of combinatorial link prediction queries on multiple networks by multiple orders of magnitude.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"190 - 206"},"PeriodicalIF":1.7,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42375078","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 For interventions that affect how individuals interact, social network data may aid in understanding the mechanisms through which an intervention is effective. Social networks may even be an intermediate outcome observed prior to end of the study. In fact, social networks may also mediate the effects of the intervention on the outcome of interest, and Sweet (2019) introduced a statistical model for social networks as mediators in network-level interventions. We build on their approach and introduce a new model in which the network is a mediator using a latent space approach. We investigate our model through a simulation study and a real-world analysis of teacher advice-seeking networks.
{"title":"A hierarchical latent space network model for mediation","authors":"T. Sweet, S. Adhikari","doi":"10.1017/nws.2022.12","DOIUrl":"https://doi.org/10.1017/nws.2022.12","url":null,"abstract":"Abstract For interventions that affect how individuals interact, social network data may aid in understanding the mechanisms through which an intervention is effective. Social networks may even be an intermediate outcome observed prior to end of the study. In fact, social networks may also mediate the effects of the intervention on the outcome of interest, and Sweet (2019) introduced a statistical model for social networks as mediators in network-level interventions. We build on their approach and introduce a new model in which the network is a mediator using a latent space approach. We investigate our model through a simulation study and a real-world analysis of teacher advice-seeking networks.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"113 - 130"},"PeriodicalIF":1.7,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49241172","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 Several papers have highlighted the potential of network science to appeal to a younger audience of high school children and provided lesson material on network science for high school children. However, network science also provides a great topic for outreach activities for primary school children. Therefore, this article gives a short summary of an outreach activity on network science for primary school children aged 8–12 years. The material provided in this article contains presentation material for a lesson of approximately 1 hour, including experiments, exercises, and quizzes, which can be used by other scientists interested in popularizing network science. We then discuss the lessons learned from this material.
{"title":"Bringing network science to primary school","authors":"C. Stegehuis","doi":"10.1017/nws.2022.15","DOIUrl":"https://doi.org/10.1017/nws.2022.15","url":null,"abstract":"Abstract Several papers have highlighted the potential of network science to appeal to a younger audience of high school children and provided lesson material on network science for high school children. However, network science also provides a great topic for outreach activities for primary school children. Therefore, this article gives a short summary of an outreach activity on network science for primary school children aged 8–12 years. The material provided in this article contains presentation material for a lesson of approximately 1 hour, including experiments, exercises, and quizzes, which can be used by other scientists interested in popularizing network science. We then discuss the lessons learned from this material.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"207 - 213"},"PeriodicalIF":1.7,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42657281","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}
Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.
{"title":"The duality of networks and groups: Models to generate two-mode networks from one-mode networks","authors":"Z. Neal","doi":"10.1017/nws.2023.3","DOIUrl":"https://doi.org/10.1017/nws.2023.3","url":null,"abstract":"\u0000 Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"11 1","pages":"397-410"},"PeriodicalIF":1.7,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57044220","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}
Per Block, James Hollway, Christoph Stadtfeld, J. Koskinen, T. Snijders
Abstract We review the empirical comparison of Stochastic Actor-oriented Models (SAOMs) and Temporal Exponential Random Graph Models (TERGMs) by Leifeld & Cranmer in this journal [Network Science 7(1):20–51, 2019]. When specifying their TERGM, they use exogenous nodal attributes calculated from the outcome networks’ observed degrees instead of endogenous ERGM equivalents of structural effects as used in the SAOM. This turns the modeled endogeneity into circularity and obtained results are tautological. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. Thus, their analysis rests on erroneous model specifications that invalidate the article’s conclusions. Finally, beyond these specific points, we argue that their evaluation metric—tie-level predictive accuracy—is unsuited for the task of comparing model performance.
{"title":"Circular specifications and “predicting” with information from the future: Errors in the empirical SAOM–TERGM comparison of Leifeld & Cranmer","authors":"Per Block, James Hollway, Christoph Stadtfeld, J. Koskinen, T. Snijders","doi":"10.1017/nws.2022.6","DOIUrl":"https://doi.org/10.1017/nws.2022.6","url":null,"abstract":"Abstract We review the empirical comparison of Stochastic Actor-oriented Models (SAOMs) and Temporal Exponential Random Graph Models (TERGMs) by Leifeld & Cranmer in this journal [Network Science 7(1):20–51, 2019]. When specifying their TERGM, they use exogenous nodal attributes calculated from the outcome networks’ observed degrees instead of endogenous ERGM equivalents of structural effects as used in the SAOM. This turns the modeled endogeneity into circularity and obtained results are tautological. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. Thus, their analysis rests on erroneous model specifications that invalidate the article’s conclusions. Finally, beyond these specific points, we argue that their evaluation metric—tie-level predictive accuracy—is unsuited for the task of comparing model performance.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"60 1","pages":"3 - 14"},"PeriodicalIF":1.7,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85850193","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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