New topics in network modeling

2nd Chilean Summer School about Social Network Research

George G. Vega Yon, Ph.D.

The University of Utah

2026-01-16

Overview

  • With more data and computing resources, the things that we can ask and do with networks are becoming increasingly (even more) exciting and complex.

  • In this section, I will introduce some of the latest advancements and forthcoming topics in network modeling.

Part I: New models and extensions

Multi-ERGMs

  • In Krivitsky, Coletti, and Hens (2023a), the authors present a start-to-finish pooled ERGM example featuring heterogeneous data sources.

  • They increase power and allow exploring heterogeneous effects across types/classes of networks.

Statistical power of SOAM

  • Stochatsic Actor Oriented Models [SOAM] (or SIENA models) are used for the co-evolution of behavior and network structure.

  • The discussion around statistical power in Social Network Studies is relatively new.

  • SOAM Stadtfeld et al. (2020) proposes ways to perform power analysis for Siena models. At the center of their six-step approach is simulation.

Bayesian ALAAM

Ever wondered how to model influence exclusively?

\mathrm{P}\left(\text{Sufficient Stats} | Features\right) \text{ vs } \mathrm{P}\left(Features | \text{Sufficient Stats}\right)

  • The Auto-Logistic Actor Attribute Model [ALAAM] is a model that allows us to do just that.

  • ALAAMs switch the focus from network structure to behavior influence by the network:

  • Koskinen and Daraganova (2022) extends the ALAAM model to a Bayesian framework.

  • It provides greater flexibility to accommodate more complicated models and add extensions such as hierarchical models. Figure 1 reproduced from A. D. Stivala et al. (2020)

Relational Event Models

  • REMs are great for modeling (timed) sequences of ties (instead of panel or cross-sectional).

  • Examples include: email exchanges, conflict events, and social interactions.

  • Butts et al. (2023) provides a general overview of Relational Event Models [REMs,] new methods, and future steps.

Figure 3 reproduced from Brandenberger (2020)

Big ERGMs

  • ERGMs In A. Stivala, Robins, and Lomi (2020), a new method is proposed to estimate large ERGMs (featuring millions of nodes).

Partial map of the Internet based on the January 15, 2005 data found on opte.org. – Wiki

Exponential Random Network Models

  • Wang, Fellows, and Handcock recently published a re-introduction of the ERNM framework (Wang, Fellows, and Handcock 2023).

  • ERNMs generalize ERGMs to incorporate behavior and are the cross-sectional cousin of SIENA models.

\begin{align*} \text{ER\textbf{G}M}: & P_{\mathcal{Y}, \bm{\theta}}(\bm{Y}=\bm{y} | \bm{X}=\bm{x}) \\ \text{ER\textbf{N}M}: & P_{\mathcal{Y}, \bm{\theta}}(\bm{Y}=\bm{y}, \bm{X}=\bm{x}) \end{align*}

Other new (and not so new) models and extensions

Part II: Shameless self-promotion

ERGMitos: Small ERGMs

Five small networks from the ergmito R package

Discrete Exponential-family Models

  • ERGMs are a particular case of Random Markov fields.

  • We can use the ERGM framework for modeling vectors of binary outcomes, e.g., the consumption of {tobacco, MJ, alcohol}.

  • Moreover, similar to TERGMs (temporal ERGMs), we can model changes in these vectors over time.

You can learn more in the project’s website https://uofuepibio.github.io/defm/

Power analysis in ERGMs

  • Using conditional ERGMs, we can do power analysis for network samples (Vega Yon 2023).

  • With multi-network studies becoming increasingly common, the question of how many networks we need is now more important (for doing science and funding science).

Reproduced from Krivitsky, Coletti, and Hens (2023b)

Imaginary Network Motifs

  • Cognitive Social Structures [CSS] refers to individuals’ perception of social networks (usually their own).

  • In CSS studies, people are asked about different types of ties in the form of “Does i communicates/asks for advice/is friend of/etc j”.

Imaginary Network Motifs (cont.)

[I]individuals completely conceive or drop reciprocal structures to maintain a balanced structure in their perceptions – Tanaka and Vega Yon (2024)

Reproduced from Tanaka and Vega Yon (2024)

Two-step estimation ERGMs

  • Conditioning the ERGM on an observed statistic “drops” the associated coefficient.

  • Hypothesis: As n increases, conditional ERGM estimates are consistent with the full model:

Simulation study trying to demonstrate the concept (Work in progress)

Thanks!

Bonus track: Why network scientists don’t use ERGMs?

Attempts to overcome these problems by extending the blockmodel have focused particularly on the use of (more complicated) p∗ or exponential random graph models, but while these are conceptually appealing, they quickly lose the analytic tractability of the original blockmodel as their complexity increases.

– Karrer and Newman (2011)

References

Brandenberger, Laurence. 2020. “Interdependencies in Conflict Dynamics: Analyzing Endogenous Patterns in Conflict Event Data Using Relational Event Models.” In Computational Conflict Research, edited by Emanuel Deutschmann, Jan Lorenz, Luis G. Nardin, Davide Natalini, and Adalbert F. X. Wilhelm, 67–80. Computational Social Sciences. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-29333-8_4.
Butts, Carter T., Alessandro Lomi, Tom A. B. Snijders, and Christoph Stadtfeld. 2023. “Relational Event Models in Network Science.” Network Science 11 (2): 175–83. https://doi.org/10.1017/nws.2023.9.
Karrer, Brian, and M. E. J. Newman. 2011. “Stochastic Blockmodels and Community Structure in Networks.” Physical Review E 83 (1): 016107. https://doi.org/10.1103/PhysRevE.83.016107.
Koskinen, Johan, and Galina Daraganova. 2022. “Bayesian Analysis of Social Influence.” Journal of the Royal Statistical Society Series A: Statistics in Society 185 (4): 1855–81. https://doi.org/10.1111/rssa.12844.
Krivitsky, Pavel N., Pietro Coletti, and Niel Hens. 2023a. “A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks.” Journal of the American Statistical Association 0 (0): 1–21. https://doi.org/10.1080/01621459.2023.2242627.
———. 2023b. “Rejoinder to Discussion of ‘A Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks’.” Journal of the American Statistical Association 118 (544): 2235–38. https://doi.org/10.1080/01621459.2023.2280383.
Stadtfeld, Christoph, Tom A. B. Snijders, Christian Steglich, and Marijtje van Duijn. 2020. “Statistical Power in Longitudinal Network Studies.” Sociological Methods & Research 49 (4): 1103–32. https://doi.org/10.1177/0049124118769113.
Stivala, Alex D., H. Colin Gallagher, David A. Rolls, Peng Wang, and Garry L. Robins. 2020. “Using Sampled Network Data With The Autologistic Actor Attribute Model.” arXiv. https://doi.org/10.48550/arXiv.2002.00849.
Stivala, Alex, Garry Robins, and Alessandro Lomi. 2020. “Exponential Random Graph Model Parameter Estimation for Very Large Directed Networks.” PLoS ONE 15 (1): 1–23. https://doi.org/10.1371/journal.pone.0227804.
Tanaka, Kyosuke, and George G. Vega Yon. 2024. “Imaginary Network Motifs: Structural Patterns of False Positives and Negatives in Social Networks.” Social Networks 78 (July): 65–80. https://doi.org/10.1016/j.socnet.2023.11.005.
Vega Yon, George G. 2023. “Power and Multicollinearity in Small Networks: A Discussion of ‘Tale of Two Datasets: Representativeness and Generalisability of Inference for Samples of Networks’ by Krivitsky, Coletti & Hens.” Journal Of The American Statistical Association.
Vega Yon, George G., Andrew Slaughter, and Kayla de la Haye. 2021. “Exponential Random Graph Models for Little Networks.” Social Networks 64 (August 2020): 225–38. https://doi.org/10.1016/j.socnet.2020.07.005.
Wang, Zeyi, Ian E. Fellows, and Mark S. Handcock. 2023. “Understanding Networks with Exponential-Family Random Network Models.” Social Networks, August, S0378873323000497. https://doi.org/10.1016/j.socnet.2023.07.003.