# Toward Universal Testing of Dynamic Network Models

## TL;DR

This paper develops a rigorous goodness of fit testing framework for dynamic network models, enabling comparison of observed network evolution against candidate models using non-stationary sampling methods.

## Contribution

It introduces a universal goodness of fit test for dynamic random graph models based on Markov processes, addressing a key challenge in network science.

## Key findings

- Proposes a formal goodness of fit testing methodology for dynamic networks.
- Develops a universal test applicable to a broad class of models.
- Analyzes the test's effectiveness and theoretical properties.

## Abstract

Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph models have been proposed to explain the macroscopic properties of these systems and to provide a foundation for statistical inferences and predictions. It is of interest to have a rigorous way to determine how well these models match observed networks. We thus ask the following goodness of fit question: given a sequence of observations/snapshots of a growing random graph, along with a candidate model M, can we determine whether the snapshots came from M or from some arbitrary alternative model that is well-separated from M in some natural metric? We formulate this problem precisely and boil it down to goodness of fit testing for graph-valued, infinite-state Markov processes and exhibit and analyze a universal test based on non-stationary sampling for a natural class of models.