# Choosing to Grow a Graph: Modeling Network Formation as Discrete Choice

arXiv: https://arxiv.org/abs/1811.05008 · HTML: https://mlsanity.com/paper/1811.05008/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2018.

## Built on by (most cited first, 9 of 9)

- [Network Formation and Dynamics Among Multi-LLMs](https://mlsanity.com/paper/2402.10659/) (2024)
- [TempME: Towards the Explainability of Temporal Graph Neural Networks via Motif Discovery](https://mlsanity.com/paper/2310.19324/) (2023)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Graph-Based Methods for Discrete Choice](https://mlsanity.com/paper/2205.11365/) (2022)
- [Investigating and Modeling the Dynamics of Long Ties](https://mlsanity.com/paper/2109.10523/) (2021)
- [Cost-based feature selection for network model choice](https://mlsanity.com/paper/2101.07766/) (2021)
- [Fast Learning of MNL Model from General Partial Rankings with Application to Network Formation Modeling](https://mlsanity.com/paper/2112.15575/) (2021)
- [Learning the mechanisms of network growth](https://mlsanity.com/paper/2404.00793/) (2024)
- [When AI Writes, Who Gets Cited? Evidence of Citation Monoculture Across Language Models](https://mlsanity.com/paper/2608.19230/) (2026)

## Abstract (arXiv)

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another node, based on (generic) features of the other nodes available to make a connection. This perspective on network formation unifies existing models such as preferential attachment, triadic closure, and node fitness, which are all special cases, and thereby provides a flexible means for conceptualizing, estimating, and comparing models. The lens of discrete choice theory also provides several new tools for analyzing social network formation; for example, the significance of node features can be evaluated in a statistically rigorous manner, and mixtures of existing models can be estimated by adapting known expectation-maximization algorithms. We demonstrate the flexibility of our framework through examples that analyze a number of synthetic and real-world datasets. For example, we provide rigorous methods for estimating preferential attachment models and show how to separate the effects of preferential attachment and triadic closure. Non-parametric estimates of the importance of degree show a highly linear trend, and we expose the importance of looking carefully at nodes with degree zero. Examining the formation of a large citation graph, we find evidence for an increased role of degree when accounting for age.