Exponential Random Graph Models (ERGM)

Exponential random graph models (ERGMs) are statistical models for network data that explain the presence of ties through local structural features, such as reciprocity and triangles, and node or dyad attributes.

지수 무작위 그래프 모형(ERGM)은 상호성·삼각구조 같은 국지적 구조 특성과 노드·쌍 속성으로 연결의 존재를 설명하는 네트워크 자료의 통계모형이다.

How do I test which structural processes and attributes explain ties in a social network?

사회 연결망에서 어떤 구조적 과정과 속성이 연결을 설명하는지 어떻게 검정하나요?

Exponential random graph models estimate how network features such as reciprocity, transitivity and attribute similarity make ties more or less likely, while treating ties as interdependent. They fit a single observed network with node attributes, with goodness of fit checked by comparing simulated and observed network statistics.

When to use Exponential Random Graph Models (ERGM)

• One observed network with node attributes, such as friendship or collaboration ties
• Testing homophily, reciprocity or transitivity
• Ties that are interdependent rather than independent observations

When to use something else

• Networks observed over time; use stochastic actor-oriented models
• Prediction of links from node features in large graphs; use graph neural networks

Assumptions and requirements

• Model terms capture the main dependence structure
• Model is not degenerate
• Convergence of MCMC maximum likelihood estimation
• Complete network data

What the analysis reports

• Coefficients (log-odds) for each network term
• Standard errors and p-values
• AIC and BIC
• Goodness-of-fit plots for degree, edgewise shared partners and geodesic distance
• MCMC diagnostics

How to report it

The ERGM showed significant homophily on [attribute], b = [value], SE = [value], p = [value], controlling for reciprocity and transitivity.

Related methods

• Stochastic Actor-Oriented Model
• Quadratic Assignment Procedure
• Stochastic Block Model

Run Exponential Random Graph Models (ERGM) on Quorant