Abstract This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.
{"title":"Sampling methods and estimation of triangle count distributions in large networks","authors":"Nelson Antunes, Tianjian Guo, V. Pipiras","doi":"10.1017/nws.2021.2","DOIUrl":"https://doi.org/10.1017/nws.2021.2","url":null,"abstract":"Abstract This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"S134 - S156"},"PeriodicalIF":1.7,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2021.2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44995788","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 Collaborative production networks among unequal actors manuel muñoz-herrera, jacob dijkstra, andreas flache and rafael wittek 1 Social network change after moving into permanent supportive housing: Who stays and who goes? harmony rhoades, hsun-ta hsu, eric rice, taylor harris, wichada la motte-kerr, hailey winetrobe, benjamin henwood and suzanne wenzel 18 Social cohesion emerging from a community-based physical activity program: A temporal network analysis ana maría jaramillo, felipe montes, olga l. sarmiento, ana paola ríos, lisa g. rosas, ruth f. hunter, ana lucía rodríguez and abby c. king 35 Superbubbles as an empirical characteristic of directed networks fabian gärtner, felix kühnl, carsten r. seemann, the students of the graphs and networks computer lab 2018/19, christian höner zu siederdissen and peter f. stadler 49 Single-seed cascades on clustered networks john k. mcsweeney 59 Sensitivity analysis for network observations with applications to inferences of social influence effects ran xu and kenneth a. frank 73 Analysis of population functional connectivity data via multilayer network embeddings james d.wilson, melanie baybay, rishi sankar, paul stillman and abbie m. popa 99 Imitation, network size, and efficiency carlos alós-ferrer, johannes buckenmaier and federica farolfi 123 network science editorial team
{"title":"NWS volume 9 issue 1 Cover and Back matter","authors":"manuel muñoz-herrera, rafael wittek","doi":"10.1017/nws.2020.47","DOIUrl":"https://doi.org/10.1017/nws.2020.47","url":null,"abstract":"original Articles Collaborative production networks among unequal actors manuel muñoz-herrera, jacob dijkstra, andreas flache and rafael wittek 1 Social network change after moving into permanent supportive housing: Who stays and who goes? harmony rhoades, hsun-ta hsu, eric rice, taylor harris, wichada la motte-kerr, hailey winetrobe, benjamin henwood and suzanne wenzel 18 Social cohesion emerging from a community-based physical activity program: A temporal network analysis ana maría jaramillo, felipe montes, olga l. sarmiento, ana paola ríos, lisa g. rosas, ruth f. hunter, ana lucía rodríguez and abby c. king 35 Superbubbles as an empirical characteristic of directed networks fabian gärtner, felix kühnl, carsten r. seemann, the students of the graphs and networks computer lab 2018/19, christian höner zu siederdissen and peter f. stadler 49 Single-seed cascades on clustered networks john k. mcsweeney 59 Sensitivity analysis for network observations with applications to inferences of social influence effects ran xu and kenneth a. frank 73 Analysis of population functional connectivity data via multilayer network embeddings james d.wilson, melanie baybay, rishi sankar, paul stillman and abbie m. popa 99 Imitation, network size, and efficiency carlos alós-ferrer, johannes buckenmaier and federica farolfi 123 network science editorial team","PeriodicalId":51827,"journal":{"name":"Network Science","volume":" ","pages":"b1 - b2"},"PeriodicalIF":1.7,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.47","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184434","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 State preferences play an important role in international politics. Unfortunately, actually observing and measuring these preferences are impossible. In general, scholars have tried to infer preferences using either UN voting or alliance behavior. The two most notable measures of state preferences that have flowed from this research area are ideal points (Bailey et al., 2017) and S-scores (Signorino & Ritter, 1999). The basis of both these models is a spatial weighting scheme that has proven useful but discounts higher-order effects that might be present in relational data structures such as UN voting and alliances. We begin by arguing that both alliances and UN voting are simply examples of the multiple layers upon which states interact with one another. To estimate a measure of state preferences, we utilize a tensor decomposition model that provides a reduced-rank approximation of the main patterns across the layers. Our new measure of preferences plausibly describes important state relations and yields important insights on the relationship between preferences, democracy, and international conflict. Additionally, we show that a model of conflict using this measure of state preferences decisively outperforms models using extant measures when it comes to predicting conflict in an out-of-sample context.
摘要国家偏好在国际政治中发挥着重要作用。不幸的是，实际观察和测量这些偏好是不可能的。一般来说，学者们试图通过联合国投票或联盟行为来推断偏好。这一研究领域产生的两个最显著的州偏好衡量标准是理想分数（Bailey et al.，2017）和S分数（Signorino&Ritter，1999）。这两个模型的基础都是一个空间加权方案，该方案已被证明是有用的，但不考虑联合国投票和联盟等关系数据结构中可能存在的高阶效应。我们首先认为，联盟和联合国投票只是国家相互作用的多个层面的例子。为了估计状态偏好的度量，我们使用张量分解模型，该模型提供了跨层的主要模式的降阶近似。我们对偏好的新衡量似乎合理地描述了重要的国家关系，并对偏好、民主和国际冲突之间的关系产生了重要的见解。此外，我们还表明，在样本外环境中预测冲突时，使用这种国家偏好衡量标准的冲突模型明显优于使用现有衡量标准的模型。
{"title":"A network approach to measuring state preferences","authors":"Max Gallop, Shahryar Minhas","doi":"10.1017/nws.2020.44","DOIUrl":"https://doi.org/10.1017/nws.2020.44","url":null,"abstract":"Abstract State preferences play an important role in international politics. Unfortunately, actually observing and measuring these preferences are impossible. In general, scholars have tried to infer preferences using either UN voting or alliance behavior. The two most notable measures of state preferences that have flowed from this research area are ideal points (Bailey et al., 2017) and S-scores (Signorino & Ritter, 1999). The basis of both these models is a spatial weighting scheme that has proven useful but discounts higher-order effects that might be present in relational data structures such as UN voting and alliances. We begin by arguing that both alliances and UN voting are simply examples of the multiple layers upon which states interact with one another. To estimate a measure of state preferences, we utilize a tensor decomposition model that provides a reduced-rank approximation of the main patterns across the layers. Our new measure of preferences plausibly describes important state relations and yields important insights on the relationship between preferences, democracy, and international conflict. Additionally, we show that a model of conflict using this measure of state preferences decisively outperforms models using extant measures when it comes to predicting conflict in an out-of-sample context.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"135 - 152"},"PeriodicalIF":1.7,"publicationDate":"2021-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.44","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48686916","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 study considers a network formation model in which each dyad of agents strategically determines the link status. Our model allows the agents to have unobserved group heterogeneity in the propensity of link formation. For the model estimation, we propose a three-step maximum likelihood method, in which the latent group structure is estimated using the binary segmentation algorithm in the second step. As an empirical illustration, we focus on the network data of international visa-free travels. The results indicate the presence of significant strategic complementarity and a certain level of degree heterogeneity in the network formation behavior.
{"title":"A pairwise strategic network formation model with group heterogeneity: With an application to international travel","authors":"Tadao Hoshino","doi":"10.1017/nws.2022.16","DOIUrl":"https://doi.org/10.1017/nws.2022.16","url":null,"abstract":"Abstract This study considers a network formation model in which each dyad of agents strategically determines the link status. Our model allows the agents to have unobserved group heterogeneity in the propensity of link formation. For the model estimation, we propose a three-step maximum likelihood method, in which the latent group structure is estimated using the binary segmentation algorithm in the second step. As an empirical illustration, we focus on the network data of international visa-free travels. The results indicate the presence of significant strategic complementarity and a certain level of degree heterogeneity in the network formation behavior.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"10 1","pages":"170 - 189"},"PeriodicalIF":1.7,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47906994","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 A number of theoretical results have provided sufficient conditions for the selection of payoff-efficient equilibria in games played on networks when agents imitate successful neighbors and make occasional mistakes (stochastic stability). However, those results only guarantee full convergence in the long-run, which might be too restrictive in reality. Here, we employ a more gradual approach relying on agent-based simulations avoiding the double limit underlying these analytical results. We focus on the circular-city model, for which a sufficient condition on the population size relative to the neighborhood size was identified by Alós-Ferrer & Weidenholzer [(2006) Economics Letters, 93, 163–168]. Using more than 100,000 agent-based simulations, we find that selection of the efficient equilibrium prevails also for a large set of parameters violating the previously identified condition. Interestingly, the extent to which efficiency obtains decreases gradually as one moves away from the boundary of this condition.
{"title":"Imitation, network size, and efficiency","authors":"Carlos Alós-Ferrer, J. Buckenmaier, F. Farolfi","doi":"10.1017/nws.2020.43","DOIUrl":"https://doi.org/10.1017/nws.2020.43","url":null,"abstract":"Abstract A number of theoretical results have provided sufficient conditions for the selection of payoff-efficient equilibria in games played on networks when agents imitate successful neighbors and make occasional mistakes (stochastic stability). However, those results only guarantee full convergence in the long-run, which might be too restrictive in reality. Here, we employ a more gradual approach relying on agent-based simulations avoiding the double limit underlying these analytical results. We focus on the circular-city model, for which a sufficient condition on the population size relative to the neighborhood size was identified by Alós-Ferrer & Weidenholzer [(2006) Economics Letters, 93, 163–168]. Using more than 100,000 agent-based simulations, we find that selection of the efficient equilibrium prevails also for a large set of parameters violating the previously identified condition. Interestingly, the extent to which efficiency obtains decreases gradually as one moves away from the boundary of this condition.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"123 - 133"},"PeriodicalIF":1.7,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.43","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48332943","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 Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.
{"title":"On the impact of network size and average degree on the robustness of centrality measures","authors":"Christoph Martin, Peter Niemeyer","doi":"10.1017/nws.2020.37","DOIUrl":"https://doi.org/10.1017/nws.2020.37","url":null,"abstract":"Abstract Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"S61 - S82"},"PeriodicalIF":1.7,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.37","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47438776","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 validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.
{"title":"Sensitivity analysis for network observations with applications to inferences of social influence effects","authors":"Ran Xu, K. Frank","doi":"10.1017/nws.2020.36","DOIUrl":"https://doi.org/10.1017/nws.2020.36","url":null,"abstract":"Abstract The validity of network observations is sometimes of concern in empirical studies, since observed networks are prone to error and may not represent the population of interest. This lack of validity is not just a result of random measurement error, but often due to systematic bias that can lead to the misinterpretation of actors’ preferences of network selections. These issues in network observations could bias the estimation of common network models (such as those pertaining to influence and selection) and lead to erroneous statistical inferences. In this study, we proposed a simulation-based sensitivity analysis method that can evaluate the robustness of inferences made in social network analysis to six forms of selection mechanisms that can cause biases in network observations—random, homophily, anti-homophily, transitivity, reciprocity, and preferential attachment. We then applied this sensitivity analysis to test the robustness of inferences for social influence effects, and we derived two sets of analytical solutions that can account for biases in network observations due to random, homophily, and anti-homophily selection.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"73 - 98"},"PeriodicalIF":1.7,"publicationDate":"2020-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.36","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41844677","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 Isolation is a concept originally conceived in the context of clique enumeration in static networks, mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.
{"title":"Isolation concepts applied to temporal clique enumeration","authors":"Hendrik Molter, R. Niedermeier, Malte Renken","doi":"10.1017/nws.2020.38","DOIUrl":"https://doi.org/10.1017/nws.2020.38","url":null,"abstract":"Abstract Isolation is a concept originally conceived in the context of clique enumeration in static networks, mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we transform the isolation concept to the temporal setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of parameterized enumeration algorithms for five of these six isolation types for clique enumeration, employing the parameter “degree of isolation.” In a nutshell, this means that the more isolated these cliques are, the faster we can find them. On the empirical side, we implemented and tested these algorithms on (temporal) social network data, obtaining encouraging results.","PeriodicalId":51827,"journal":{"name":"Network Science","volume":"9 1","pages":"S83 - S105"},"PeriodicalIF":1.7,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/nws.2020.38","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42263009","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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