Temporal Exponential Random Graph Models Research Articles

New insight into social relationships in dairy cows and how time of birth, parity, and relatedness affect spatial interactions later in life

Social interactions between cows play a fundamental role in the daily activities of dairy cattle. Real-time location systems provide on a continuous and automated basis information about the position of individual cows inside barns, offering a valuable opportunity to monitor dyadic social contacts. Understanding dyadic social interactions could be applied to enhance the stability of the social structure promoting animal welfare and to model disease transmission in dairy cattle. This study aimed to identify the impact of different cow characteristics on the likelihood of the formation and persistence of social contacts in dairy cattle. The individual position of the lactating cows was automatically collected once per second for 2 weeks, using an ultra-wideband system on a Swedish commercial farm consisting of nearly 200 dairy cows inside a free-stall barn. Social networks were constructed using the position data of 149 cows with available information on all characteristics during the study period. Social contacts were considered as a binary variable indicating whether a cow pair was within 2.5 m of each other for at least 10 min per day. The role of cow characteristics in social networks was studied by applying separable temporal exponential random graph models. Our results revealed that cows of the same parity interacted more consistently, as well as those born within 7 d of each other or are closely related by pedigree. The repeatability of the topological parameters indicated a consistent short-term stability of the individual animal roles within the social network structure. Additional research is required to elucidate the underlying mechanisms governing the long-term evolution of social contacts among dairy cattle and to investigate the relationship between these networks and the transmission of diseases in the dairy cattle population.

Dynamic change and evolutionary mechanism of city land leasing network—Taking the Yangtze River Delta region in China as an example

Mapping city networks has attracted scholarly attention in urban studies, while the relevant studies focusing on land elements are lacking. This study aims to address and fill this research gap by analyzing across-city land leasing relationships. Using Yangtze River Delta region (YRDR) in China as a case, we explore the dynamic change and evolutionary mechanism of city land leasing network based on urban land leasing data and temporal exponential random graph model (TERGM). The findings reveal that: 1) At the macro level, as the interconnections between cities in the YRDR grow stronger, the inter-city flow of land elements has become growingly convenient and accessible, there is a corresponding increase in the frequency of land use rights transfer between cities. This has led to the emergence of a more intricate and interconnected city land leasing network in the YRDR. 2) At the medium level, city land leasing network in the YRDR fosters land leasing communities within province boundary. Shanghai community is identified as the strongest community, which establish a compact relationship with a large number of cities in Zhejiang, Jiangsu, and Anhui provinces. The province of Zhejiang, Jiangsu, and Anhui have also foster communities with provincial capitals as the core, respectively. 3) At the individual level, Shanghai is the primary recipient city in terms of cross-city land leasing relationships, followed by provincial capital cities of Hangzhou, Nanjing, and Hefei. 4) Significant effects, including endogenous structural effects, actor-relation effects, exogenous network effects, and time effects, could be found in the city land leasing network of the YRDR. The city land leasing network in the YRDR is influenced by endogenous structural factors such as popularity, transitivity, and connectivity. Cities with low economic development levels, strong land leasing intervention, high real estate development investment levels, and high land leasing prices are more likely to lease land to other cities. Cities with higher levels of economic development, higher levels of industrial structure upgrading, higher levels of real estate development investment, and higher land prices are more likely to lease land from other cities. Furthermore, cities within the same province or within Yangtze River Delta Urban Agglomerations (YRDUR) are more likely to foster inter-city land leasing relationships, while the distance between cities negatively affects the establishment of inter-city land leasing relationships.

Democratic governance and global science: A longitudinal analysis of the international research collaboration network.

The democracy-science relationship has traditionally been examined through philosophical conjecture and country case studies. There remains limited global-scale empirical research on the topic. This study explores country-level factors related to the dynamics of the global research collaboration network, focusing on structural associations between democratic governance and the strength of international research collaboration ties. This study combines longitudinal data on 170 countries between 2008 and 2017 from the Varieties of Democracy Institute, World Bank Indicators, Scopus, and Web of Science bibliometric data. Methods include descriptive network analysis, temporal exponential random graph models (TERGM), and valued exponential random graph models (VERGM). The results suggest significant positive effects of democratic governance on the formation and strength of international research collaboration ties and homophily between countries with similar levels of democratic governance. The results also show the importance of exogenous factors, such as GDP, population size, and geographical distance, as well as endogenous network factors, including preferential attachment and transitivity.

Complex network analysis on provincial innovation development in China

From the perspective of innovation output, the innovation output networks of 30 provinces (excluding Tibert, Hong Kong, Macao and Taiwan) are constructed based on the modified gravity model in the past 20 years (2001–2020). Combined with the method of principal component analysis and TOPSIS, the innovation development level of each province and seven regions is evaluated by integrating some node statistical indicators. Finally, we employ the temporal exponential random graph model to study the main characteristics that affect the evolution of China’s innovation capability in the past 20 years. The conclusions are as follows: (1) There are reciprocity effect, hierarchy effect and time dependence effect in China’s innovation linkages. There is a positive correlation between innovation output and innovation absorption. (2) In the past 20 years China’s innovation output has shown a pattern of strong in the south and weak in the north, strong in the east and weak in the west. The innovation development of each province and region has changed greatly, and the gap is obvious. At present, the national innovation pattern has formed a big cycle in the eastern, central and western regions. East China and south central regions are the regional centers of innovation output in China; Southwest China is a region with rapid innovation and development; Northwest China has been isolated. (3) Provinces in the same region are likely to have innovation linkages with provinces with coexisting economic output effects. (4) The introduction of foreign capital technology promotes China’s independent innovation capability. (5) The intensity of government investment in scientific and technological research and development has ensured the orderly progress of innovation and stabilized innovation capacity. (6) Talents and education level determine the upper limit of China’s innovation ability. (7) Economic level and innovation ability complement each other.

Continuous time graph processes with known ERGM equilibria: contextual review, extensions, and synthesis

ABSTRACT Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions for such convergence, and provide examples of novel and/or known processes that do so. These include subfamilies of the well-known stochastic actor-oriented models, as well as continuum extensions of temporal and separable temporal exponential family random graph models. We also comment on some related threads in the broader work on network dynamics, which provide additional context for the continuous time case.

To make and keep friends: The role of health status in adolescent network tie formation and persistence

Health status may shape network structure through network dynamics (tie formation and persistence) and direction (sent and received ties), net of typical network processes. We apply Separable Temporal Exponential Random Graph Models (STERGMs) to National Longitudinal Study of Adolescent to Adult Health survey data (n = 1779) to differentiate how health status shapes network sent and received tie formation and persistence. Results indicate that networks are shaped by withdrawal of adolescents experiencing poor health, highlighting the importance of separating distinct and directed processes of friendship formation and persistence when considering how health relates to adolescent social life.

Dynamic change of international arms trade network structure and its influence mechanism

PurposeThe purpose of this study is to analyze the dynamic changes of the arms trade network not only from the network structure but also the influence mechanism from the aspects of the economy, politics, security, strategy and transaction costs.Design/methodology/approachThe study employs the Temporal Exponential Random Graph Model and the Separable Temporal Exponential Random Graph Model to analyze the endogenous network structure effect, the attribute effect and the exogenous network effect of 47 major arms trading countries from 2015 to 2020.FindingsThe results show that the international arms trade market is unevenly distributed, and there are great differences in military technology. There is a fixed hierarchical structure in the arms trade, but the rise of emerging countries is expected to break this situation. In international arms trade relations, economic forces dominate, followed by political, security and strategic factors.Practical implicationsEconomic and political factors play an important role in the arms trade. Therefore, countries should strive to improve their economic strength and military technology. Also, countries should increase political mutual trust and gain a foothold in the industrial chain of arms production to enhance their military power.Originality/valueThe contribution of this paper is to analyze the special trade area of arms trade from a dynamic network perspective by incorporating economic, political, security, strategic and transaction cost factors together into the TERGM and STERGM models.

Modelling the large and dynamically growing bipartite network of German patents and inventors

Abstract To explore the driving forces behind innovation, we analyse the dynamic bipartite network of all inventors and patents registered within the field of electrical engineering in Germany in the past two decades. To deal with the sheer size of the data, we decompose the network by exploiting the fact that most inventors tend to only stay active for a relatively short period. We thus propose a Temporal Exponential Random Graph Model with time-varying actor set and sufficient statistics mirroring substantial expectations for our analysis. Our results corroborate that inventor characteristics and team formation are essential to the dynamics of invention.

Impact of the tariff concessions of the RCEP agreement on the structure and evolution mechanism of manufacturing trade networks

In the world’s largest free trade area, the Regional Comprehensive Economic Partnership (RCEP) agreement will gradually eliminate tariffs on over 90% of member countries’ goods over the next 36 years. We construct a tariff policy effects evaluation framework based on the complex network theory. In this framework, the standard Global Trade Analysis Project (GTAP) model is recursively extended to generate forecasted data of bilateral trade. Based on this, we model the RCEP manufacturing trade networks and analyze the response of its core–periphery structure to the tariff concessions. Then, we evaluate policy effects on the evolution of trade patterns based on motif analysis. Finally, we construct separable temporal exponential family random graph models (STERGM) to explore the influence path and degree of the new tariff agreement on the evolutionary mechanisms of trade networks.

Longitudinal network models and permutation‐uniform Markov chains

AbstractConsider longitudinal networks whose edges turn on and off according to a discrete‐time Markov chain with exponential‐family transition probabilities. We characterize when their joint distributions are also exponential families with the same parameter, improving data reduction. Further we show that the permutation‐uniform subclass of these chains permit interpretation as an independent, identically distributed sequence on the same state space. We then apply these ideas to temporal exponential random graph models, for which permutation uniformity is well suited, and discuss mean‐parameter convergence, dyadic independence, and exchangeability. Our framework facilitates our introducing a new network model; simplifies analysis of some network and autoregressive models from the literature, including by permitting closed‐form expressions for maximum likelihood estimates for some models; and facilitates applying standard tools to longitudinal‐network Markov chains from either asymptotics or single‐observation exponential random graph models.

Can the Social Network Hinder the Impact of COVID-19 on Economic Uncertainty? New Evidence from China

ABSTRACT This study investigates the impact of the COVID-19 pandemic on economic uncertainty and its spillover network based on social network analysis. The study constructs the inter-provincial Chinese economic uncertainty spillover network using a mixed frequency dataset and the provincial social network using microblog user data. Furthermore, the temporal exponential random graph model is used to analyze the impact of COVID-19 and social network during three periods. The results show that the COVID-19 pandemic significantly affects China’s provincial economic uncertainty and social network significantly hinders economic uncertainty spillover networks. The inhibitory effect of social networks on uncertainty spillover network has regional heterogeneity, which is more significant in provinces severely affected by the pandemic and strictly controlled.

Effects of temporal resolution adjustments on dynamic sexual contact models

Simulation and inferential modeling of sexual contact dynamics can be used to help predict the propagation of sexually transmitted infections (STI) such as HIV, by providing information on both cross-sectional network structure and how that structure changes over time. Researchers’ choices regarding the temporal resolution of such network models is often driven by the resolution of the data collected to support model fitting and evaluation. These inherited temporal resolutions can become problematic if they differ from the resolution of other processes to which the network must be related. In such cases, a model “correction” is necessary: specifically, we would like to have a systematic method for adjusting a fitted model to allow it to make predictions at a different timescale than the one on which it was initially based. Here, we introduce a basic set of desiderata for such adjustments, and assess three very simple approaches to timescale adjustments for models of sexual contact networks (SCNs), with focus on models parameterized within the separable temporal exponential family random graph model (STERGM) framework. We also examine the impact of time-scale changes on SCN characteristics themselves, and outline a set of desiderata for what an adjustment strategy may be expected to achieve. Our findings have implications both for timescale correction of dynamic network models, and for dynamic network data collection.

New friends and cohesive classrooms: A research practice partnership to promote inclusion

This longitudinal unusual case study explored the efficacy of a Research Practice Partnership (RPP) between researchers and educators aiming to promote inclusion of students identified as having Special Educational Needs and Disabilities (SEND) in an urban, highly diverse, high-need elementary school in Southern California. In the context of this study, an RPP is defined as an approach where researchers and educators work collaboratively over time to solve pressing pedagogical problems of mutual concern. Lessons have been constructed and implemented by educators as part of the RPP, spanning one school year. A total of 116 students across four classrooms participated in a social network survey to examine their friendship ties before (T1) and after (T2) the RPP. The pre-RPP data collection (T1) occurred three months into the school year and the post-RPP data collection (T2) took place at the end of the school year. To explore our hypotheses, we conducted bootstrapped paired sample t tests and Separable Temporal Exponential Random Graph Models (STERGMs). Results showed that the number of friendship ties increased significantly from T1 to T2 for all students and students identified as having SEND were significantly more likely to send new friendship ties. Implications for practice are being discussed.

Migration in Libya: A spatial network analysis

Libya is the African country with the highest proportion of migrants and it is the major migration gateway to Europe. Since the fall of Gaddafi’s regime in 2011, Libya has been experiencing a prolonged period of instability and conflict which has also affected migration flows. This paper provides the first analytical study of the networks of irregular migrants toward, within, and from Libya since the beginning of the Second Civil War in 2014. We use longitudinal-geolocalised data on migrants’ movements and combine tools taken from spatial statistics and network analysis to reconstruct the network of migrants’ international movements towards and from Libya, and the network of migrants’ internal movements within Libya. Employing the information obtained from these networks, we map the different migrant routes within the country, we provide evidence that migrants sort into routes according to their nationality, and we show how these routes have evolved over time. Moreover, using a Separable Temporal Exponential Random Graph (STERG) model, we document that migrants are more likely to move towards areas with higher economic opportunities, lower level of conflict intensity, more same country-of-origin migrants, and connecting to multiple routes. Our analysis shows how to combine migration data with insights from spatial statistics and network analysis in order to reconstruct migrants’ movements.

The impact of the Belt and Road Initiative on the natural gas trade: A network structure dependence perspective

Given the increasing complexity of multilateral relations in the natural gas trade along the Belt and Road (B&R), it is necessary to quantify the impact of the Belt and Road Initiative (BRI) on natural gas trade from the perspective of structure dependence. First, the multilateral trade of natural gas along B&R is abstracted as the liquefied natural gas and pipeline natural gas trade networks (BR-LNGTN and BR-PNGTN, respectively). Second, we analyze the evolution of the network structure and the status change of countries before and after the implementation of the BRI. Finally, based on the temporal exponential random graph models (TERGMs), the evolutionary mechanism of the natural gas trade network and impact of the BRI on the evolutionary mechanism are comprehensively studied. The results show that the implementation of the BRI promotes the network size, but the advantages of trade cooperation have not been fully realized. China and India are the authoritative trading countries, while Russia and Qatar are the primary intermediary countries. Structure dependence, time dependence and trade facilitation significantly impact the generation of the network, but the explanatory power of the exogenous attributes decrease, which indicates that the trade conditions along B&R have been significantly improved.

The structural change and influencing factors of carbon transfer network in global value chains.

Based on the gross trade accounting method and WIOD data, this paper quantifies the global carbon transfer from 2000 to 2014. The social network analysis and temporal exponential random graph model (TERGM) are employed to investigate the structural change and influencing factors of global carbon transfer network from a global value chains (GVCs) perspective. Results show that the deepening of the GVC division connection has enhanced the relations in global carbon transfer network, and the low reciprocity and high disassortativity lie in the difference in GVC division positions among economies. Block model analysis manifests that Plate Ⅱ acts as the engine plate in the network which consists of China and the other four economies. The GVC division connection and relative GVC division position significantly facilitate the formation of carbon emission transfer relations. Moreover, economies' attribute effects and endogenous network structure effects are non-negligible important determinants of network formation.

A hostile reputation: A social network approach to interstate hostility

State-level decisions to initiate militarized conflicts are the result of various factors, ranging from geographic proximity to the previous actions of potential foes. However, we know little about how the reputations of hostile actions shape future conflict and whether they vary for different types of country pairs. Through the adoption of a social network perspective, this research examines the role of post-Cold War hostility on the likelihood of future conflicts using the Militarized Interstate Dispute data from the Correlates of War project. We apply temporal exponential random graph models to evaluate whether the previous hostility levels of a country can determine future patterns of interstate conflict. Additionally, we consider how this association varies based on whether a country’s experience with an adversary is direct (a result of previous conflict with the adversary) or indirect (based on extra-dyadic disputes). Consistent with previous research, results suggest that pairs of countries with a direct history of hostile actions are more likely to fight in the future. However, in absence of this shared history, states are less likely to initiate conflict with those that have a particularly hostile or peaceful history, and instead target adversaries with middling levels of previous hostility.

Preferential attachment, R&D expenditure and the evolution of international trade networks from the perspective of complex networks

From the perspective of complex networks, whether international trade networks (ITNs) can remain robust and connected in the face of random emergencies or intentional attacks is an important indicator of the security of international trade. Thus, we introduced the scale-free property to describe it. Using trade data from 1996–2018 for 126 economies, we constructed ITNs and investigated their scale-free property. Our results reveal that ITNs are not scale free in most years and that they become decentralized. In addition, our study explored the evolution of ITNs using the temporal exponential random graph model (TERGM) and verified the nonexistence of the preferential attachment mechanism that drives the formation of scale-free networks. Furthermore, we emphasized the impact of different R&D expenditure levels on the formation of trade relationships. Economies with medium (low) levels of R&D expenditures are less connected to those with the same level, while economies with high levels of R&D expenditures prefer to establish trade relationships with those with the same level. This finding indicates that the establishment of trade relationships could occur more often between economies with a high level of R&D expenditures and economies with a medium (low) level of R&D expenditures or among economies with a high level of R&D expenditures. Therefore, economies with a high level of R&D expenditures are more active and attractive when selecting trade partners. Overall, we extend the exploration in the field of ITN research and provide an innovative analysis framework to study real networks.

Evolutionary analysis of the global rare earth trade networks

This study used social network analysis, spatial measurement, and network statistical analysis to study the relationships among countries in the global rare earth trade. Using data on rare earth products from the UN Comtrade database, the global rare earth trade network and its evolving topological characteristics are analyzed for the period 1999–2020. Spatial correlation analysis using the global Moran index showed that countries tended to carry out rare earth trade with neighboring countries, and there were certain spatial aggregations in the trade patterns. A temporal exponential random graph model (TERGM) was used to analyze the influencing factors and evolution of the global rare earth trade, and network motif analysis was used to analyze the influence of network topology on the trading network structure. The results showed that the global rare earth trade model presented the following characteristics: trade from one core country to many other countries, reciprocity between trading countries, and trade around near neighboring rare earth-rich countries. Other factors, such as countries with the same GDP levels and World Trade Organization (WTO) member countries, influenced the global rare earth trade but not the formation of the rare earth trade network. In examining the temporal dependence of rare earth trade networks over a 22-year period, it was found that the linkages of rare earth trade networks among countries remained relatively stable, pointing to the long-term dependence of countries with scarce rare earth resources on resource-rich countries.

Be my (little) partner?!—Universities' role in regional innovation systems when large firms are rare

AbstractStructural differences regarding the presence of large firms are likely to influence the performance of Regional Innovation Systems. Regions lacking large firms to act as brokers of knowledge and coordinators of regional (R&D) collaboration may have to rely on other actors to form internal and external links. We investigate whether, in this case, universities can fulfill the needs of Small‐ and Medium‐sized Enterprises (SMEs) with regard to coordination and knowledge flows. Using a data set of subsidized R&D collaborations, we compare universities' network positions in four model regions in Germany. Applying a Temporal Exponential Random Graph Model approach, we examine link formation and network structure with a focus on university–SME ties and their development over time. Results indicate that SMEs profit from connections to the university in all regions. Nevertheless, universities take more central roles in regions where the economic surrounding does contain fewer large firms as sources for knowledge exchange.