Temporal Exponential Random Graph Models Research Articles

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.

Understanding the structure and determinants of intercity carbon emissions association network in China

It is important to understand the structure of the intercity carbon emissions association network and its determinants in promoting urban carbon emissions reductions and even regional high-quality coordinated development. Using carbon emissions data to depict intercity association, the network is constructed, as we: (1) identify network structure through the indegree, outdegree, pagerank and community detection; (2) take a step further in exploring the determinants using temporal exponential random graph models (TERGM) for dynamic network modeling, compared with previous studies only focusing on network description. The results are as follows: (1) The topology of intercity carbon emissions association network is heterogeneous and hierarchical effect tends to increase gradually. (2) The network is highly spatially coupled, and the boundary of the indegree-outdegree partition is relatively clear. A certain spatial correlation as well as spatial coincidence is shown in the indegree-outdegree partition and the pagerank hierarchy. In addition, the spatial correlation shows the core node carbon emissions correlation, and the first rank is at the core of the network. (3) The motif analysis reveals that reciprocal edges play a significant role in promoting network formation. The network structure effects, actor-attribute effects, dyadic predictors, and time-dependent terms have substantial effects on China intercity carbon emissions association network.

The Dynamic Evolution of the Structure of an Urban Housing Investment Niche Network and Its Underlying Mechanisms: A Case Study of 35 Large and Medium-Sized Cities in China

With the growth of urban agglomerations, the spatial diffusion of housing investment is clear; however, little research has been carried out to address its network characteristics and underlying mechanisms of influence. Using data on 35 large and medium-sized cities, this paper applies niche theory to housing investment, constructing a housing investment niche index that includes resources, the housing market, the social economy, and policy. The purpose is to study the characteristics of the network structure and its mechanisms of influence based on an improved gravity model and a temporal exponential random graph model (TERGM). Supported by the analysis of the network structure, we find that the node degree within the network is low, the network density exhibits an inverted “V” shape, and the network level suggests the existence of a “rich cities club”. According to the local network clustering analysis, the cities are divided into three clusters: the Yangtze River Delta region, the Beijing–Tianjin–Hebei region, and the central and eastern regions. Furthermore, analysis of the endogeneity in the structure reveals that there is a hierarchy of cities with high economic development levels, which makes it difficult to establish an investment network with strong relationships. The effects of the attributes are consistent with the predictions of location theory and new economic geography theory. The external network effects conform to the law of the general gravity model. Our research provides insights into the ways in which the misplaced competition in housing investment between cities in a region and the flow of production factors can be reasonably guided.

A dynamic network perspective on the evolution of the use of multiple mobile instant messaging apps

ABSTRACT Mobile instant messaging (MIM) services have emerged as digital platforms for closed and private modes of communication. The present study adopts a dynamic network approach to understanding how MIM apps are used in combination with each other. The changing patterns of cross-platform MIM use are reflected in the structural dynamics of the audience overlap network among 58 MIM apps over March 2019 to March 2021 period. The results of the separable temporal exponential random graph model indicated that the formation and persistence of audience overlap was explained by network self-organization and app reach, but not by app engagement. These effects were observed when app-level confounding factors were held constant.

Circular specifications and “predicting” with information from the future: Errors in the empirical SAOM–TERGM comparison of Leifeld & Cranmer

AbstractWe 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.

Temporal exponential random graph models of longitudinal brain networks after stroke.

Plasticity after stroke is a complex phenomenon. Functional reorganization occurs not only in the perilesional tissue but throughout the brain. However, the local connection mechanisms generating such global network changes remain largely unknown. To address this question, time must be considered as a formal variable of the problem rather than a simple repeated observation. Here, we hypothesized that the presence of temporal connection motifs, such as the formation of temporal triangles (T) and edges (E) over time, would explain large-scale brain reorganization after stroke. To test our hypothesis, we adopted a statistical framework based on temporal exponential random graph models (tERGMs), where the aforementioned temporal motifs were implemented as parameters and adapted to capture global network changes after stroke. We first validated the performance on synthetic time-varying networks as compared to standard static approaches. Then, using real functional brain networks, we showed that estimates of tERGM parameters were sufficient to reproduce brain network changes from 2 weeks to 1 year after stroke. These temporal connection signatures, reflecting within-hemisphere segregation (T) and between hemisphere integration (E), were associated with patients' future behaviour. In particular, interhemispheric temporal edges significantly correlated with the chronic language and visual outcome in subcortical and cortical stroke, respectively. Our results indicate the importance of time-varying connection properties when modelling dynamic complex systems and provide fresh insights into modelling of brain network mechanisms after stroke.

A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model – Corrigendum

A theoretical and empirical comparison of the temporal exponential random graph model and the stochastic actor-oriented model – Corrigendum

Factors Affecting the Evolution of Technical Cooperation among “Belt and Road Initiative” Countries Based on TERGMs and ERGMs

The Belt and Road Initiative (B&R), was initiated by China in 2013, and it covers over 60% and 30% of the world’s population and GDP, respectively. The initiative has directed a great deal of investment in energy, transportation, and 5G. Whilst much attention has been focused on cooperation in international trade, technological cooperation in the form of patents has been largely ignored. This paper investigates the formation of technological cooperative relationships among B&R countries within a technical cooperation network. Comprehensive consideration of various factors between participating countries was undertaken, using statistical methods from social network analysis theory. The node attributes and relations between countries and the network structure were studied in a sequence of network analyses using temporal exponential random graph models (TERGMs) and static exponential random graph models (ERGMs). The main findings suggest that research ability, financial ability, technological innovation ability, technological spillover proximity, geographical proximity, and technical proximity have an impact on participation in technical cooperation between B&R countries. Research ability, technological spillover proximity, geographical proximity, and technical proximity have a positive influence on the development of cooperation. However, the financial and technological innovation ability of a country does not actively promote the development of cooperation. The entire cooperation network structure does not have a greater aggregation effect compared with a random network, and intermediary multi-path cooperation is not obvious. This paper analyzes the driving factors for technological cooperation through a systematic study of the characteristics and relationships of B&R countries, and also of the network characteristics among B&R countries. The results of our analysis show that the characteristics of technical cooperation in the B&R region provide a reference for the study of international technical cooperation.