# A generalised significance test for individual communities in networks

arXiv: https://arxiv.org/abs/1712.00298 · HTML: https://mlsanity.com/paper/1712.00298/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2017.

## Built on by (most cited first, 1 of 1)

- [Agentic Analysis for Agentic Infrastructure: An LLM-Powered Pipeline for Comparative Governance of DAO and Corporate AI Protocols](https://mlsanity.com/paper/2606.26203/) (2026)

## Abstract (arXiv)

Many empirical networks have community structure, in which nodes are densely interconnected within each community (i.e., a group of nodes) and sparsely across different communities. Like other local and meso-scale structure of networks, communities are generally heterogeneous in various aspects such as the size, density of edges, connectivity to other communities and significance. In the present study, we propose a method to statistically test the significance of individual communities in a given network. Compared to the previous methods, the present algorithm is unique in that it accepts different community-detection algorithms and the corresponding quality function for single communities. The present method requires that a quality of each community can be quantified and that community detection is performed as optimisation of such a quality function summed over the communities. Various community detection algorithms including modularity maximisation and graph partitioning meet this criterion. Our method estimates a distribution of the quality function for randomised networks to calculate a likelihood of each community in the given network. We illustrate our algorithm by synthetic and empirical networks.