Random Graph Models Research Articles

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.

Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labels

Two-sample network hypothesis testing is an important inference task with applications across diverse fields such as medicine, neuroscience, and sociology. Many of these testing methodologies operate under the implicit assumption that the vertex correspondence across networks is a priori known. This assumption is often untrue, and the power of the subsequent test can degrade when there are misaligned/label-shuffled vertices across networks. This power loss due to shuffling is theoretically explored in the context of random dot product and stochastic block model networks for a pair of hypothesis tests based on Frobenius norm differences between estimated edge probability matrices or between adjacency matrices. The loss in testing power is further reinforced by numerous simulations and experiments, both in the stochastic block model and in the random dot product graph model, where the power loss across multiple recently proposed tests in the literature is considered. Lastly, the impact that shuffling can have in real-data testing is demonstrated in a pair of examples from neuroscience and from social network analysis.

The scaling limit of random cubic planar graphs

AbstractWe study the random cubic planar graph with an even number of vertices. We show that the Brownian map arises as Gromov–Hausdorff–Prokhorov scaling limit of as tends to infinity, after rescaling distances by for a specific constant . This is the first time a model of random graphs that are not embedded into the plane is shown to converge to the Brownian map. Our approach features a new method that allows us to relate distances on random graphs to first‐passage percolation distances on their 3‐connected core.

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.

Asymptotic Analysis of k-Hop Connectivity in the 1D Unit Disk Random Graph Model

Asymptotic Analysis of k-Hop Connectivity in the 1D Unit Disk Random Graph Model

Improved MRF rail surface defect segmentation method based on clustering features

Aiming at the characteristics of small number and many types of rail surface defect samples, as well as the problems of unstable transfer learning effect and threshold segmentation being easily affected by environmental factors in real scenes, an improved Markov defect segmentation method with zero samples is proposed. Firstly, the collected data is processed by Gabor function to highlight the defect features and reduce the data dimension to obtain the reduced dimension feature map; Kmeans clustering is performed on the processed feature map to reduce the distribution of data and reduce the influence of reflection and shadow, and the clustering result is used as the pre-classification matrix; an improved Markov random field two-layer graph model is constructed and inferred through the reduced dimension feature map and the pre-classification matrix; the local geometric structure of the defect part is analyzed according to the eigenvalues of the classification matrix inferred by the model; finally, the defect area is marked and the defect segmentation is completed. The experimental part uses a self-sampling data set, and the final conclusion is drawn based on the comparative experiment and ablation experiment. The experimental results show that the pixel accuracy, average pixel accuracy, weighted intersection-over-union ratio, and average intersection-over-union ratio of this method on the self-sampling data set are respectively 93.6%、80.7%、89.4%、68.2% , which exceeds the accuracy of other comparative detection algorithms.

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.

Switchover phenomenon for general graphs

AbstractWe study SIR‐type epidemics (susceptible‐infected‐resistant) on graphs in two scenarios: (i) when the initial infections start from a well‐connected central region and (ii) when initial infections are distributed uniformly. Previously, Ódor et al. demonstrated on a few random graph models that the expectation of the total number of infections undergoes a switchover phenomenon; the central region is more dangerous for small infection rates, while for large rates, the uniform seeding is expected to infect more nodes. We rigorously prove this claim under mild, deterministic assumptions on the underlying graph. If we further assume that the central region has a large enough expansion, the second moment of the degree distribution is bounded and the number of initial infections is comparable to the number of vertices, the difference between the two scenarios is shown to be macroscopic.

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.

Epidemics on critical random graphs with heavy-tailed degree distribution

We study the susceptible-infected-recovered (SIR) epidemic on a random graph chosen uniformly over all graphs with certain critical, heavy-tailed degree distributions. We prove process level scaling limits for the number of individuals infected on day h on the largest connected components of the graph. The scaling limits contain non-negative jumps corresponding to some vertices of large degree. These weak convergence techniques allow us to describe the height profile of the α-stable continuum random graph (Goldschmidt et al., 2022; Conchon–Kerjan and Goldschmidt, 2023), extending results known in the Brownian case (Miermont and Sen, 2022). We also prove model-independent results that can be used on other critical random graph models.

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.

Copula Approximate Bayesian Computation Using Distribution Random Forests

Ongoing modern computational advancements continue to make it easier to collect increasingly large and complex datasets, which can often only be realistically analyzed using models defined by intractable likelihood functions. This Stats invited feature article introduces and provides an extensive simulation study of a new approximate Bayesian computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, that unifies and extends previous ABC methods proposed separately. This framework, copulaABCdrf, aims to accurately estimate and describe the possibly skewed and high-dimensional posterior distribution by a novel multivariate copula-based meta-t distribution based on univariate marginal posterior distributions that can be accurately estimated by distribution random forests (drf), while performing automatic summary statistics (covariates) selection, based on robustly estimated copula dependence parameters. The copulaABCdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of the ABC framework is illustrated and compared with previous standard ABC methods through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. This paper also proposes and studies a new solution to the simulation cost problem in ABC involving the posterior estimation of parameters from datasets simulated from the given model that are smaller compared to the potentially large size of the dataset being analyzed. This proposal is motivated by the fact that, for many models defined by intractable likelihoods, such as the network models when they are applied to analyze massive networks, the repeated simulation of large datasets (networks) for posterior-based parameter estimation can be too computationally costly and vastly slow down or prohibit the use of standard ABC methods. The copulaABCdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks of sizes ranging between 28,000 and 65.6 million nodes (between 3 million and 1.8 billion edges), including a large multilayer network with weighted directed edges. The results of the simulation studies show that, in settings where the true posterior distribution is not highly multimodal, copulaABCdrf usually produced similar point estimates from the posterior distribution for low-dimensional parametric models as previous ABC methods, but the copula-based method can produce more accurate estimates from the posterior distribution for high-dimensional models, and, in both dimensionality cases, usually produced more accurate estimates of univariate marginal posterior distributions of parameters. Also, posterior estimation accuracy was usually improved when pre-selecting the important summary statistics using drf compared to ABC employing no pre-selection of the subset of important summaries. For all ABC methods studied, accurate estimation of a highly multimodal posterior distribution was challenging. In light of the results of all the simulation studies, this article concludes by discussing how the copulaABCdrf framework can be improved for future research.

Unraveling the dynamics of information exchange in governance networks: Opportunity structures in anti‐corruption multi‐stakeholder partnerships

AbstractInformation exchange is critical to the functionality of governance networks. Traditionally, it has been argued that actors within governance networks tend to engage in information exchange with others who share similar beliefs and motivations, as these are deemed catalysts for achieving collective objectives. An alternative viewpoint posits that actors may prioritize strategies aimed at minimizing transaction costs and maximizing returns when selecting their partners. This paper proposes that information exchange predominantly occurs with partners who are easily accessible (i.e., where transaction costs are low) and with partners who are perceived as influential (i.e., where benefits are high). To investigate these alternative propositions, we examine three distinct opportunity structures that actors may utilize, which are based on their preferences for (1) partners with similar participatory motivations, (2) partners who co‐participate in institutional committees, and (3) those perceived as influential. We empirically test these opportunity structures using unique survey data gathered from 10 anti‐corruption multi‐stakeholder partnerships within the public infrastructure domain in countries of Latin America, Africa, and Eurasia. Results from Exponential Random Graph Models suggest that shared participatory motivations do not significantly impact information exchange within our context, whereas the perceived influence of a partner emerges as a critical predictor. In addition, co‐participation in institutional committees significantly facilitates information dissemination, particularly when those committees involve discussions on deliberating about strategies to communicate findings on public‐sector infrastructure discrepancies and formulating recommendations to governments on transparency and accountability. These findings prompt discussions on four network management strategies aimed at restructuring networks and fostering stakeholder involvement and inclusivity.

Social network analysis of regional transport carbon emissions in China: Based on motif analysis and exponential random graph model

Given the significant impact of transportation-related carbon emissions on air quality and climate change, understanding the regional dynamics of these emissions is crucial. Despite numerous studies on carbon emissions, there is a lack of comprehensive analysis of China's interprovincial transport carbon emission correlation network. Based on China's provincial data from 2007 to 2021, we analyzed the network's basic structural characteristics and categorized it into four significant plates to investigate their interactions. Subsequently, motif analysis is employed to examine the micro-correlation patterns within the network, and the Exponential random graph model (ERGM) is utilized to analyze the network's formation mechanism. Findings reveal that: (1) Provinces with high correlation intensity are predominantly concentrated in the eastern region, such as Shanghai and Beijing. Additionally, provinces in the eastern region assume a central role in the transport carbon emission correlation network, mainly receiving carbon emissions from other provinces. In contrast, the western region primarily emits carbon emissions to other provinces, continuously converging towards the center. (2) The network is segmented into net beneficiary plate, net overflow plate, bidirectional spillover plate, and broker plate, with distinct roles and influences across different years. (3) Bidirectional correlation motif structures emerge as primary influencers within the network, although specific structures impede interregional communication and collaborative emission reduction. (4) Internal network's structural variables, such as mutuality, cyclic triple, and geometrically weighted edgewise shared partner, along with influencing factors including government intervention, urbanization rate, openness, fiscal expenditure on transport, and province adjacency significantly impact the formation of the transport carbon emission correlation network. The above transportation network research provides a theoretical basis for the country to promote low-carbon transportation and improve air quality, and also has important guiding significance for the cross-regional collaborative emission reduction work of provinces.

Gender segregation in the friendship networks of Muslim youth in Germany: the role of chastity norms

ABSTRACT Western Muslim youth engage less in romantic relationships than their non-Muslim peers, an observation usually attributed to chastity norms that oppose Muslim youths’ premarital sexual activity. In this study, I ask whether chastity norms also shape cross-gender interaction beyond romantic relationships and lead to fewer cross-gender friendships among Muslim than non-Muslim youth. To isolate the consequences of chastity norms from institutionalized practices of gender segregation in Muslim religious communities, I study friendship-making in German coeducational schools, which provide ample opportunities for cross-gender friendships. I apply multilevel exponential random graph models to large-scale data on adolescents’ school-based friendship networks, finding cross-gender friendships to be generally infrequent but notably rarer among Muslim than non-Muslim youth. However, this lack of cross-gender friendships is limited to Muslim youth who hold strong chastity norms, while more liberal Muslim youth have as many cross-gender friends as non-Muslims. Among non-Muslims, chastity norms are unrelated to cross-gender friendships.

Network Analysis of Two-Stage Customer Decisions with Preference-Guided Market Segmentation

Abstract Network-based analyses have shown their effectiveness in understanding customer preferences through interactions and relationships between customers and products, particularly for tailored product design. There is limited research on applying this analysis to diverse customers with varied preferences. This paper introduces a market-segmented network modeling approach, guided by customer preference, to explore heterogeneity in customers' two-stage decision-making process: consideration-then-choice. In heterogeneous markets, like household appliances, even customers with similar characteristics or purchasing similar products can exhibit different decision-making processes. Therefore, In this method, we segment customers into groups based on preferences rather than just characteristics, allowing for more accurate choice modeling. Using Joint Correspondence Analysis, we identify associations between customer attributes and preferred products, characterizing market segments through clustering. We then build individual bipartite customer-product networks and apply the Exponential Random Graph Model to compare the product features influencing customer considerations and choices in various market segments. Using a US household vacuum cleaner survey, our method detected different customer preferences for the same product attribute at different decision-making stages. The market-segmentation model outperforms the non-segmented benchmark in prediction, highlighting its accuracy in predicting varied customer behaviors. This study underscores the vital role of preference-guided segmentation in product design, illustrating how a deeper understanding of customer preferences at different decision stages can inform and refine design strategies, ensuring products are more closely aligned with the dynamic needs and tastes of diverse markets.

Variation in patient-sharing network characteristics of health care professionals treating different mental and substance use disorder patient sub-groups in primary care.

Providing efficient and targeted services for patients with mental health problems requires efficient collaboration and coordination within healthcare providers, but measuring collaboration using traditional methods is challenging. To explore the patient-sharing networks of professionals taking care of different groups of patients with mental or substance use disorders. We used data that covered adult patients' visits to the primary care service providers of seven municipalities in Finland during year 2021. Data included 8,217 patients (147,430 visits) with mental or substance use disorders who were treated by 1,566 health care professionals. We calculated descriptive network metrics to examine the connectivity of professionals in three different patient groups (patients with substance use disorders, psychotic disorders, and depressive disorders) and compared these characteristics to a network based on all patients. We also analyzed whether patient sharing was associated with the health care professionals' attributes (occupational group, municipality) using Exponential Random Graph Models (ERGM). Diagnosis-specific networks were denser and more connected compared to the all-patients network. Nurses were the most central occupation in all the diagnosis-specific networks and especially in the substance use disorder patients network. When examining all patients, two professionals were more likely to share patients when they belonged to the same occupational group. However, in the network with depressive disorder patients we found the opposite: professionals were more likely to share patients if they were of different occupational groups. Patient-sharing networks within patients with a specific mental or substance use disorders are denser and more connected than networks based on all patients with mental or substance use disorders. In the substance use disorder patients network particularly, nurses were the most central occupation. Multi-professional connections were more likely in depressive disorder networks than in the all-patients network.