Exponential Random Graph Models Research Articles

Power of Persuasion: How Planners Shape Decisions Through Communication

Problem, research strategy, and findings Because most planning decisions are ultimately made by politicians, effective communication with elected officials is essential for shaping their decisions. In this study, we empirically examined whether email communications initiated by urban planners affect planning-related decisions made by politicians and what communication tactics work. We leveraged a unique data set of all email communications between planners and politicians and voter records of politicians on planning-related decisions in the city of Tallahassee (FL). We built a dynamic network model as a temporal exponential random graph model and adopted text-mining methods to examine email communication dynamics. We found that a more positive sentiment conveyed from email content was statistically significantly associated with a politician’s tendency to vote consistently with a planner’s recommendation. Moreover, corroborating communications from various planners were more persuasive than repeated communication from a single planner, suggesting that an organic, decentralized approach to communication is more effective than a hierarchical, top-down one. Takeaway for practice Urban planners should take the initiative to reach out to politicians to establish positive communication channels. In addition, strengthening collaboration within the planning department by presenting unified information from various planners to a politician can enhance the politician’s confidence in the message and lead to more effective shaping of their decisions.

Evolution of the collaborative innovation network in China’s integrated circuit industry: a hypernetwork analysis

ABSTRACT The integrated circuit industry is a cornerstone of modern information technology. The collaborative innovation network represents an effective path for industries to achieve technological innovation. Therefore, this paper constructs a multi-level collaborative innovation network for the integrated circuit industry and analyzes its evolutionary characteristics and formation mechanisms. The results show that: the cooperation network demonstrates an overall characteristic of ‘small clusters and large dispersions’, with prominent central nodes and a relatively high average path length, which is not conducive to information transmission. The knowledge network nodes exhibit high transmission efficiency, and the overall technological field is gradually transitioning towards focusing on technology-intensive design and innovation. The edges between heterogeneous nodes in the two-level network continue to intensify, exhibiting an overall spatial correlation characteristic of ‘multi-centers to multi-centers’. Analyzing the network formation mechanism using the Exponential Random Graph model (ERGM) reveals that nodes within the collaborative innovation network primarily establish connections through direct relationships. There is a significant interaction between cross-level connections in the two-level network. Degree centrality has a relatively prominent role in promoting network evolution. Findings here provide theoretical support and reference for the government to formulate innovation policies and optimise the industrial environment for the integrated circuit industry.

Stochastic step-wise feature selection for Exponential Random Graph Models (ERGMs).

This study introduces a novel methodology for endogenous variable selection in Exponential Random Graph Models (ERGMs) to enhance the analysis of social networks across various scientific disciplines. Addressing critical challenges such as ERGM degeneracy and computational complexity, our method integrates a systematic step-wise feature selection process. This approach effectively manages the intractable normalizing constants characteristic of ERGMs, ensuring the generation of accurate and non-degenerate network models. An empirical application to nine real-life binary networks demonstrates the method's effectiveness in accommodating network dependencies and providing meaningful insights into complex network interactions. Particularly notable is the adaptability of this methodology to both directed and undirected networks, overcoming the limitations of traditional ERGMs in capturing realistic network structures. The findings contribute to network analysis, offering a robust framework for modeling and interpreting social networks and laying a foundation for future advancements in statistical network analysis techniques.

Structures Indicating a Shift Toward a Culture of Collaboration in National Park Service Urban Networks

Park and protected area agencies are increasingly enacting a “culture of collaboration” – or viewing relationships (with agencies, nonprofits, educational institutions, etc.) as the routine approach to meeting immediate needs and longer-term goals (e.g., relevance, stewardship). Trust is fundamental to developing a culture of collaboration. We examine potential components of trust in a culture of collaboration in National Park Service (NPS)-identified urban relationships promoting relevance with stakeholders. Specifically, we detail three-actor relationships and network-wide structures using a quantitative Exponential Random Graph Model analysis. Networks in Detroit, Tucson, and Boston exhibit potential transitions toward a culture of collaboration, perhaps spurred by the NPS’ Urban Agenda efforts. These relate to the development of trust, the NPS positionality as supportive rather than core in the networks, and the large potential for increasing reciprocity (which decreases network hierarchy). These structures highlight where Urban Agenda relationship-building processes may aid in developing collaborative cultures across settings.

Statistical Network Analysis of Macroeconomic Variables in Ghana

In the rapidly evolving economic landscape of Ghana, understanding the intricate interdependencies between macroeconomic variables is pivotal for informed policymaking and strategic economic planning. The study employed network analysis to enhance our comprehension of Ghana's macroeconomic dynamics. Data was sourced from the world development indicators. Initially, a statistical network was constructed to represent the interconnections between Ghana's principal macroeconomic variables using partial correlation matrix, offering a visual and analytical perspective of their relationships. Subsequently, centrality measures and other network analysis tools were utilized to identify and quantify the influence of key economic indicators within this network. Results showed that Exports, Inflation, Exchange rate, Gross Domestic Saving, Manufacturing and Gross National Expenditure played a significant role in the network. However, Agriculture and Imports were identified as most influential variables with high centrality scores across all centrality measures. Finally, Exponential Random Graph Model was employed to provide a comparative baseline, shedding light on the uniqueness or randomness of the observed interrelationships. The significant parameters in the model include the presence of edges between nodes and the presence of generalized geodesic triads (gwesp), which capture the tendency for nodes to form connections based on common neighbors. The findings also revealed that there is a probability of 16.19% for a relationship to exist between two macroeconomic variables if they are both connected to the same third variable.

Research on Interprovincial Embodied Carbon Transfer Network in China and Its Endogenous Dynamic Evolutionary Mechanism

This paper uses the multi-regional input–output model to measure China’s interprovincial embodied carbon transfer and constructs an interprovincial network; then, the temporal exponential random graph model is applied to analyze the spatial correlation characteristics and endogenous evolutionary mechanism of the network. The results show that interprovincial embodied carbon transfer relationships are increasingly close in China, but the weak symmetric accessibility between the eastern and central regions leads to less reciprocity in the embodied carbon network, and carbon emission inequality still exists. Based on the identification of networks, it is shown that the global network structures are stable, with obvious small-world characteristics and a core–periphery structure. And a structure-dependent effect and time-dependent effect also exist in the formation and evolution of the interprovincial embodied carbon transfer network in China. The popularity, multi-connectivity, and path-dependent effects among the provinces are significant, but the imperfection of interprovincial communication and the cooperation mechanism leads to the failure to form stable structures of ternary closed loops. Interprovincial embodied carbon transfer relationships tend to occur between provinces, with large differences in energy consumption structures, while geographical distance can hinder the formation of embodied carbon transfer relationships. Consequently, considering the spatial network correlation and its endogenous dynamic evolutionary mechanism, it is important to implement policies to guide coordinated carbon reduction among the provinces and to improve the fairness in embodied carbon transferring, in order to promote the fine governance of all links in the transferring process of embodied carbon.

Strong ties, strong homophily? Variation in homophily on sociodemographic characteristics by relationship strength

Abstract Social networks are segregated by sociodemographic characteristics such as gender, ethnicity, religion, and socioeconomic status. A key reason for this segregation is homophily, or people's preferences to associate with similar others. Homophily is documented for relationships of different strengths, ranging from marriage and close friendship to weaker acquaintanceships. But does sociodemographic homophily vary by relationship strength? While most researchers assume more pronounced sociodemographic homophily for strong than for weak relationships, theoretical expectations and empirical evidence are inconclusive. For instance, shared sociodemographic characteristics can come with joint experiences and identities that could facilitate the development of strong relationships. At the same time, however, matching personalities and attitudes may be necessary for forming strong relationships, so the superficial similarity that accompanies shared sociodemographic traits may only suffice for weak relationships. Based on these considerations, we test whether and how gender, ethnic, religious, and socioeconomic status homophily vary by relationship strength in over 600 school-based networks of more than 20,000 adolescents from Israel, England, Germany, the Netherlands, and Sweden. Using valued exponential random graph models, we find consistent evidence that strong tie homophily exceeds weak tie homophily. While adolescents are more likely to report strong ties with those who share their gender, ethnicity, religion, and socioeconomic status, homophily is less pronounced for weaker ties. Our finding suggests that it is crucial to consider the link between homophily and tie strength to understand the flow of information, resources, social support, and opportunities in social networks.

Study on the pattern and driving factors of water scarcity risk transfer networks in China from the perspective of transfer value—Based on complex network methods

The transfer value of risk, measured by the asymmetric impact of virtual water flows, is vital for regions addressing the global water crisis, achieving Sustainable Development Goal 6 (SDG6), and implementing sustainable water management. This study uses multi-regional input-output models, complex network analysis, and the Exponential Random Graph Model (ERGM) to construct and analyze China's water scarcity risk transfer network. Findings show frequent but weakly connected risk transfers between provinces, with significant spatial clustering. The network displays both random and hierarchical features, with clustered development being prominent. Reciprocal cooperation and extensive connections are crucial to avoiding the “prisoner's dilemma” in water conservation. High levels of “dual circulation” and water resource utilization enhance risk transfer value, while lower industrialization and digitization levels facilitate value reception. The efficiency of water resource use is key in shaping high-risk value pathways, underscoring the need for risk management at both source and sink ends. This study offers a scientific basis for improving water resource management, ensuring national water security, and redefining risk flow patterns.

Unveiling the dynamics and determinants of world city network: Insights from global airline data

Existing research on world city networks (WCNs) has predominantly focused on macro-structure analysis, leaving a gap in understanding the dynamic changes from a multi-scale perspective and underlying factors shaping WCNs. Therefore, this study utilizes airline data to explore WCN dynamics at both macroscale and mesoscale, and employ a weighted exponential random graph model to investigate determinants of WCN formation. The research findings reveal that WCN displays hierarchical and regional tendencies. At the macroscale, the evolution of urban hierarchy demonstrates both stability and change, and at the mesoscale, WCN morphology follows a core-periphery spatial arrangement with strong regional patterns. ERGM results highlight the influence of both endogenous network structures and exogenous city characteristics on WCN formation. Preferential attachment emerges as a crucial driving force, with disassortativity facilitating connectivity between peripheral and core cities. Additionally, GDP, language, institutional proximity and path dependence positively contribute to WCN formation, while population and distance have negative effects.

Structural characteristics and mechanism of collaborative environmental governance network of urban agglomerations: perspective of multilevel network

Collaborative environmental governance (CEG) is increasingly advocated to address the environmental risk issues in the integrated development of urban agglomerations. Constructing an effective CEG network from the perspective of interdependent multilevel network plays a vital role in promoting the environmental governance of urban agglomerations. To investigate the structure characteristics and formation mechanism of CEG network, this paper takes the Yangtze River Delta urban agglomeration as the research area, and employes the social network analysis and Exponential Random Graph Model (ERGM) methods to analyze the CEG network, which consists of the collaborative network of cities, relationship network of topics, and affiliation network connecting cities to topics. Research results show that the CEG level in the Yangtze River Delta urban agglomeration continues to improve, while the CEG network is still not in a tightly connected state. For the collaborative network of cities, it presents the small world characteristics and forms a cooperative trend of “central-subcentral-peripheral city.“For the relationship network of topics, the evolution of environmental governance topics is characterized by “from aspect to point.” For the affiliation network connecting cities to topics, as the diversity of environmental governance topics increases among cities, cities within the Yangtze River Delta urban agglomeration tend to share the similar topics. In addition, the interactive triangular structures, star structures, open triangular structures and closed triangular structures in the network can promote the formation of new cooperative relationships in CEG network.

Characterizing the spatial correlation network structure and impact mechanism of carbon emission efficiency: Evidence from China's transportation sector

Numerous countries and regions are actively seeking to reduce carbon emissions through policy guidance and technological innovation. In this process, balancing economic development with environmental protection and achieving synergistic carbon reduction between regions pose challenges for policymakers and the academic community alike. This study analyzes data from 30 provinces in China over the period from 2005 to 2020, employing the SBM-DEA, block model, and the Exponential Random Graph Models (ERGM) to explore the spatial association network structure characteristics of carbon emission efficiency and its driving factors. The findings indicate that: the carbon emission efficiency of the transportation industry is generally on an upward trend, with the eastern region having the highest carbon emission efficiency; the spatial association network exhibits a “dense in the east, sparse in the west” pattern; the block model demonstrates clear inter-regional carbon emission transfer behaviors; the result of ERGM shows that factors such as the level of economic development and population density significantly affect the network structure. The macro-micro individual analysis framework for the carbon emission efficiency network fills the theoretical gap in the context of the digital economy, providing a scientific basis and decision-making reference for policymakers when formulating and optimizing carbon reduction policies, which holds significant theoretical and practical value.

Evolutionary characteristics and structural dependence determinants of global lithium trade network: An industry chain perspective

As a globally emerging critical mineral, lithium is increasingly prominent in international trade, emphasizing the importance for energy transition and industrial structure upgrading to understand the evolution and formation of the global lithium trade networks (GLTN). From the perspective of industry chain, this paper uses complex network theory to construct GLTN for 2000–2021, investigates the determinants of network structure dependence through an exponential random graph model (ERGM), for analyzing the evolutionary characteristics and formation mechanisms of trade networks in both the holistic and local dimensions. The results show that, firstly, GLTN exhibits the overall characteristics of a "sparse upstream and tight midstream and downstream" network. The downstream exhibits a distinctive small-world network feature. China, the United States and Europe are the most active countries and regions in GLTN, covering the whole industry chains. Second, endogenous structure, node attributes and exogenous network effects all exert an influence on network structure. Regarding the impact of network structural dependence, lithium trade has transitivity effect, connectivity effect, and popularity effect. Third, the shocks of COVID-19 cut off the transitivity effect formed by indirect dependencies to the downstream industry chain first, resulting in a high network volatility. There is a strong heterogeneity in the network structural dependency for the industry chain.

On the edge: a multilevel perspective on innovation complexities and dynamic attractors in the supply network

PurposeIn innovation management, the complexity inherited in the supply network may be necessary for success. This study aims to holistically examine innovation complexities and system attractors within a hierarchically nested supply network and explore how they dynamically interact and influence adaptive innovation processes.Design/methodology/approachTaking a complexity theory perspective, we employed a methodological bricolage approach using a single case study with multiple embedded units of analysis – namely, a supply network encompassing 36 firms. We drew upon primary data obtained from 42 interviewees and rich secondary data, and we employed a temporal exponential random graph model to examine the micro-foundations of the evolution of the sampled supply network over a decade.FindingsThis study presents a comprehensive overview of the innovation complexities—relational, temporal, dynamic, operational and structural – and how they manifest within a supply network. It also identifies three systemic attractors – point, periodic and strange – and elucidates their relationships with the complexities and their impact on innovative supply network dynamics. The resulting conceptual framework and working propositions provide a detailed perspective on the complex interplay between balanced order and chaos and the potentially unbalanced innovation states within a supply network.Originality/valueThis research offers an in-depth perspective on the innovation complexities and dynamic attractors within a supply network from a holistic, multilevel perspective. It advances complexity theory and deepens the understanding of supply networks as complex adaptive systems.

Score-driven exponential random graphs: A new class of time-varying parameter models for temporal networks.

Motivated by the increasing abundance of data describing real-world networks that exhibit dynamical features, we propose an extension of the exponential random graph models (ERGMs) that accommodates the time variation of its parameters. Inspired by the fast-growing literature on dynamic conditional score models, each parameter evolves according to an updating rule driven by the score of the ERGM distribution. We demonstrate the flexibility of score-driven ERGMs (SD-ERGMs) as data-generating processes and filters and show the advantages of the dynamic version over the static one. We discuss two applications to temporal networks from financial and political systems. First, we consider the prediction of future links in the Italian interbank credit network. Second, we show that the SD-ERGM allows discriminating between static or time-varying parameters when used to model the U.S. Congress co-voting network dynamics.

Crisis management from a relational perspective: an analysis of interorganizational transboundary crisis networks

Abstract Although transboundary crises have gained relevance in an increasingly interdependent world, our understanding of the relational dynamics governing these phenomena remains limited. This paper addresses this knowledge gap by identifying common characteristics across interorganizational transboundary crisis networks and drivers of tie formation in successful structures. For this purpose, it applies descriptive Social Network Analysis and Exponential Random Graph Models to an original dataset of three networks. Results show that these structures combine elements of issue networks and policy communities. Common features include moderately high centralization, reciprocated ties, core-periphery structures, and the popularity of international organizations. Additionally, successful networks display smooth communication between NGOs and international organizations, whereas unsuccessful networks have fewer heterophilous interactions. Transitivity seems to play a role in network success too. These findings suggest that crisis networks are robust structures that reconcile bridging and bonding dynamics, thereby highlighting how evidence from relational studies could guide transboundary crisis management.

Exponential Random Graph Model Perspective: Formation and Evolution of a Collaborative Innovation Network in China’s New Energy Vehicle Industry

In light of the crucial role of collaborative R&D in advancing technology within the new energy vehicle industry, this study seeks to explore ways to overcome the barriers to technological innovation by establishing an effective collaborative innovation network. Utilizing joint patent-authorized data from China’s new energy vehicles between 2005 and 2019, the collaborative innovation network was developed, and the Exponential Random Graph Model (ERGM) was employed to analyze its formation and evolution mechanisms. The results indicate that the network has undergone significant expansion, closely linked to strong national policy support and the active involvement of innovation participants. The network exhibits effects of expansion, transfer, and closure. External attribute analysis revealed the Matthew effect and geographical compatibility effect and found that organizational compatibility tends to foster complementary cooperation. The findings offer insights into optimizing collaborative innovation networks in the NEVs industry and suggest strategies for policymakers and industry players to promote collaborative innovation.

From Protectionist to Regulator: Policy-Driven Transformation of Digital Urban Networks in China’s Online Gaming Industry

In the digital era, data-driven production organizes digital urban networks. This study explores the critical role of government policies in shaping these networks, focusing on China’s evolving policy contexts. While existing research has mainly emphasized qualitative analyses, this paper quantitatively assesses the impact of policy changes on digital urban networks, specifically through the lens of China’s online gaming industry. The study aimed to elucidate the relationship between the policy environment and digital urban networks. By examining China’s transition from protectionist to regulatory policies, this research employed a social network analysis and valued exponential random graph models (ERGMs) across two key phases: the competitive protection phase (2014–2017) and the systematic regulatory phase (2018–2022). The findings revealed a significant transformation in urban network structure, shifting from a centralized model dominated by a few core cities to a decentralized, multi-centered network. The key factors influencing this evolution include the institutional proximity and cross-regional collaborations. This study offers valuable insights into how policy shifts affect urban networks in the digital economy, contributing both theoretically and practically to future policy design.

Estimating the impact of physician risky-prescribing on the network structure underlying physician shared-patient relationships

Social network analysis and shared-patient physician networks have become effective ways of studying physician collaborations. Assortative mixing or “homophily” is the network phenomenon whereby the propensity for similar individuals to form ties is greater than for dissimilar individuals. Motivated by the public health concern of risky-prescribing among older patients in the United States, we develop network models and tests involving novel network measures to study whether there is evidence of homophily in prescribing and deprescribing in the specific shared-patient network of physicians linked to the US state of Ohio in 2014. Evidence of homophily in risky-prescribing would imply that prescribing behaviors help shape physician networks and would suggest strategies for interventions seeking to reduce risky-prescribing (e.g., strategies to directly reduce risky prescribing might be most effective if applied as group interventions to risky prescribing physicians connected through the network and the connections between these physicians could be targeted by tie dissolution interventions as an indirect way of reducing risky prescribing). Furthermore, if such effects varied depending on the structural features of a physician’s position in the network (e.g., by whether or not they are involved in cliques—groups of actors that are fully connected to each other—such as closed triangles in the case of three actors), this would further strengthen the case for targeting groups of physicians involved in risky prescribing and the network connections between them for interventions. Using accompanying Medicare Part D data, we converted patient longitudinal prescription receipts into novel measures of the intensity of each physician’s risky-prescribing. Exponential random graph models were used to simultaneously estimate the importance of homophily in prescribing and deprescribing in the network beyond the characteristics of physician specialty (or other metadata) and network-derived features. In addition, novel network measures were introduced to allow homophily to be characterized in relation to specific triadic (three-actor) structural configurations in the network with associated non-parametric randomization tests to evaluate their statistical significance in the network against the null hypothesis of no such phenomena. We found physician homophily in prescribing and deprescribing. We also found that physicians exhibited within-triad homophily in risky-prescribing, with the prevalence of homophilic triads significantly higher than expected by chance absent homophily. These results may explain why communities of prescribers emerge and evolve, helping to justify group-level prescriber interventions. The methodology may be applied, adapted or generalized to study homophily and its generalizations on other network and attribute combinations involving analogous shared-patient networks and more generally using other kinds of network data underlying other kinds of social phenomena.

Examining peer review network dynamics in higher education visual communication courses using ERGM

Peer review plays a pivotal role in shaping collaborative learning environments and evaluating student engagement, but there is a lack of research on the relational dynamics that underlie the interactions between students during the peer review process, which is critical for understanding the effectiveness of peer review for students’ learning outcomes. Using explanatory sequential study design, this study’s objectives are to explore the dynamics of peer review as a feedback mechanism in higher education within a social network context, focusing on student interactions during the feedback process. Specifically, we applied dyadic-independent Exponential Random Graph Modeling (ERGM), along with mixed-methods design to analyze peer review interactions within a visual communication course at a large state university. We collected and analyzed two samples: a quantitative sample of 167 students for network analysis, drawn from 3082 peer reviews and rubric scores, and a qualitative sample of 136 students from post-course surveys that provided feedback on the peer review process and course methodologies. Our investigation revealed the inherently social network nature of peer review, shedding light on its significance in engaging students and assessing student engagement. Specifically, we examined the role of students’ performance levels, edge-based attributes derived from the visual peer review rubric, and language used in the feedback on the likelihood of forming peer review connections in the network. Our findings indicate that attributes derived from the visual peer review rubric significantly influence the likelihood of peer connections. On the other hand, students’ performance levels do not have any impact on the formation of peer connections. The findings highlight the importance of visual peer review activities in shaping peer connections in the classroom. Future studies will incorporate higher-order structures, such as transitivity and triadic closure, into our ERGM model to further enhance our understanding of peer review dynamics in educational settings.

Product Design Incorporating Competition Relations: A Network-Based Design Framework Considering Local Dependencies

Abstract System design has been facing the challenges of incorporating complex dependencies between individual entities into design formulations. For example, while the decision-based design framework successfully integrated customer preference modeling into optimal design, the problem was formulated from a single entity’s perspective, and the competition between multiple enterprises was not considered in the formulation. Network science has offered several solutions for studying interdependencies in various system contexts. However, efforts have primarily focused on analysis (i.e., the forward problem). The inverse problem still remains: How can we achieve the desired system-level performance by promoting the formation of targeted relations among local entities? In this study, we answer this question by developing a network-based design framework. This framework uses network representations to characterize and capture dependencies and relations between individual entities in complex systems and integrate these representations into design formulations to find optimal decisions for the desired performance of a system. To demonstrate its utility, we applied this framework to the design for market systems with a case study on vacuum cleaners. The objective is to increase the sales of a vacuum cleaner or its market share by optimizing its design attributes, such as suction power and weight, with the consideration of market competition relations, such as inter-brand triadic competition involving three products from different brands. We solve this problem by integrating an exponential random graph model (ERGM) with a genetic algorithm. The results indicate that the new designs, which consider market competition, can effectively increase the purchase frequency of specific vacuum cleaner models and the proposed network-based design method outperforms traditional design optimization.