# An information-theoretic, all-scales approach to comparing networks

arXiv: https://arxiv.org/abs/1804.03665 · HTML: https://mlsanity.com/paper/1804.03665/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

## Built on by (most cited first, 8 of 8)

- [Challenges of Generating Structurally Diverse Graphs](https://mlsanity.com/paper/2409.18859/) (2024)
- [Multiscale Graph Comparison via the Embedded Laplacian Discrepancy](https://mlsanity.com/paper/2201.12064/) (2022)
- [An embedding-based distance for temporal graphs](https://mlsanity.com/paper/2401.12843/) (2024)
- [Graph Similarity Description: How Are These Graphs Similar?](https://mlsanity.com/paper/2105.14364/) (2021)
- [Dynamic Vertex Replacement Grammars](https://mlsanity.com/paper/2303.11553/) (2023)
- [Visualization Tasks for Unlabeled Graphs](https://mlsanity.com/paper/2504.14115/) (2025)
- [A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks](https://mlsanity.com/paper/2511.00768/) (2025)
- [A temporal graph dissimilarity measure capturing epidemic spreading behavior](https://mlsanity.com/paper/2610.16456/) (2026)

## Abstract (arXiv)

As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is network comparison, developing a similarity or distance measure between networks so that meaningful comparisons can be drawn. The best means to accomplish this task remains an open area of research. Here we introduce a new measure to compare networks, the Network Portrait Divergence, that is mathematically principled, incorporates the topological characteristics of networks at all structural scales, and is general-purpose and applicable to all types of networks. An important feature of our measure that enables many of its useful properties is that it is based on a graph invariant, the network portrait. We test our measure on both synthetic graphs and real world networks taken from protein interaction data, neuroscience, and computational social science applications. The Network Portrait Divergence reveals important characteristics of multilayer and temporal networks extracted from data.