Dynamic Exponential Random Graph Model
Dynamic Exponential Random Graph Model (Temporal ERGM) · Also known as: TERGM, Temporal ERGM, Dynamic ERGM, STERGM
The Dynamic Exponential Random Graph Model (TERGM / STERGM) extends the classic ERGM framework to panel network data, modeling how a network's ties form and dissolve over time as a function of structural tendencies, nodal attributes, and the network's own past state. It provides statistically principled inference about longitudinal network change.
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When to use it
Use a dynamic ERGM when you have two or more observed snapshots of the same network over time and want to model the endogenous and exogenous drivers of tie formation and dissolution simultaneously. It is appropriate for relatively small to medium networks (up to a few thousand nodes) with binary ties and panel structure. Do not use it when the network has continuous edge weights (weighted networks require different frameworks), when only a single cross-sectional snapshot is available (use static ERGM instead), when the network has tens of thousands of nodes (computational cost becomes prohibitive), or when the temporal lag structure is unknown and theoretically undefined.
Strengths & limitations
- Jointly models tie formation and dissolution, separating the forces that create new ties from those that maintain existing ones.
- Conditions on the observed past network, enabling causal-style inference about longitudinal network change.
- Handles endogenous network statistics (reciprocity, triangles) that violate independence assumptions of standard regression.
- Goodness-of-fit diagnostics via simulation reveal whether the model reproduces the observed network distribution.
- Interpretable coefficients on structural and covariate terms support theory-driven network analysis.
- Computationally intensive: MCMLE can be slow or fail to converge on networks larger than a few thousand nodes.
- Model degeneracy is a persistent risk — certain combinations of triangle and two-star terms can produce near-complete or near-empty networks.
- Requires at least two network observations; more time points improve estimation but increase cost.
- The choice of temporal lag (t to t-1) is theoretically driven; misspecifying the lag can bias all estimates.
Frequently asked
How is TERGM different from a static ERGM?
A static ERGM models one network snapshot as a function of structural statistics. A TERGM additionally conditions on the prior time point's network, allowing the model to capture how past ties influence future ones and to separately estimate formation versus dissolution processes.
What is STERGM and how does it relate to TERGM?
STERGM (Separable Temporal ERGM) is a variant developed by Krivitsky and Handcock (2014) that models tie formation and tie dissolution with separate parameter vectors, recognizing that the same structural forces need not drive both processes equally. It is the most widely used dynamic ERGM implementation, available in the R tergm package.
How many time points do I need?
A minimum of two observations is required. In practice, three or more time points improve parameter stability and allow cross-validation. Very short panels (two points) should be interpreted cautiously, especially for dissolution parameters.
What should I do if my model shows signs of degeneracy?
Degeneracy appears when simulated networks from the fitted model are mostly empty or mostly complete. Reduce the number of triangle or two-star terms, consider geometrically-weighted alternating statistics (GWESP, GWDEGREE) which are less prone to degeneracy, and re-run goodness-of-fit diagnostics after each revision.
Can I use TERGM on weighted or valued networks?
Standard TERGM implementations assume binary ties. Valued (weighted) dynamic networks require separate frameworks such as valued ERGMs or latent space models. Dichotomizing edge weights before fitting TERGM is an option but loses information and should be theoretically justified.
Sources
- Hanneke, S., Fu, W., & Xing, E. P. (2010). Discrete temporal models of social networks. Electronic Journal of Statistics, 4, 585–605. DOI: 10.1214/09-EJS548 ↗
- Krivitsky, P. N., & Handcock, M. S. (2014). A separable model for dynamic networks. Journal of the Royal Statistical Society: Series B, 76(1), 29–46. DOI: 10.1111/rssb.12014 ↗
How to cite this page
ScholarGate. (2026, June 3). Dynamic Exponential Random Graph Model (Temporal ERGM). ScholarGate. https://scholargate.app/en/network-analysis/dynamic-exponential-random-graph-model
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