# Detecting communities using asymptotical Surprise

arXiv: https://arxiv.org/abs/1503.00445 · HTML: https://mlsanity.com/paper/1503.00445/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2015.

## Built on by (most cited first, 6 of 6)

- [Bayan Algorithm: Detecting Communities in Networks Through Exact and Approximate Optimization of Modularity](https://mlsanity.com/paper/2209.04562/) (2022)
- [Analyzing Modularity Maximization in Approximation, Heuristic, and Graph Neural Network Algorithms for Community Detection](https://mlsanity.com/paper/2310.10898/) (2023)
- [Heuristic Modularity Maximization Algorithms for Community Detection Rarely Return an Optimal Partition or Anything Similar](https://mlsanity.com/paper/2302.14698/) (2023)
- [Network Report: A Structured Description for Network Datasets](https://mlsanity.com/paper/2206.03635/) (2022)
- [Learning dynamic representations of the functional connectome in neurobiological networks](https://mlsanity.com/paper/2402.14102/) (2024)
- [Robust Markov stability for community detection at a scale learned based on the structure](https://mlsanity.com/paper/2504.11621/) (2025)

## Abstract (arXiv)

Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity, and may find communities where modularity fails to discern any structure.