# Significant Scales in Community Structure

arXiv: https://arxiv.org/abs/1306.3398 · HTML: https://mlsanity.com/paper/1306.3398/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2013.

## Built on by (most cited first, 3 of 3)

- [Bayan Algorithm: Detecting Communities in Networks Through Exact and Approximate Optimization of Modularity](https://mlsanity.com/paper/2209.04562/) (2022)
- [Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection](https://mlsanity.com/paper/2210.09186/) (2022)
- [Robust Markov stability for community detection at a scale learned based on the structure](https://mlsanity.com/paper/2504.11621/) (2025)

## Abstract (arXiv)

Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem shows foremost in multi-resolution methods. We here introduce an efficient method for scanning for resolutions in one such method. Additionally, we introduce the notion of "significance" of a partition, based on subgraph probabilities. Significance is independent of the exact method used, so could also be applied in other methods, and can be interpreted as the gain in encoding a graph by making use of a partition. Using significance, we can determine "good" resolution parameters, which we demonstrate on benchmark networks. Moreover, optimizing significance itself also shows excellent performance. We demonstrate our method on voting data from the European Parliament. Our analysis suggests the European Parliament has become increasingly ideologically divided and that nationality plays no role.