# Revealing consensus and dissensus between network partitions

arXiv: https://arxiv.org/abs/2005.13977 · HTML: https://mlsanity.com/paper/2005.13977/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 7 of 7)

- [Normalized mutual information is a biased measure for classification and community detection](https://mlsanity.com/paper/2307.01282/) (2023)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [Multilayer Networks for Text Analysis with Multiple Data Types](https://mlsanity.com/paper/2106.15821/) (2021)
- [Descriptive vs. inferential community detection in networks: pitfalls, myths, and half-truths](https://mlsanity.com/paper/2112.00183/) (2021)
- [Implicit models, latent compression, intrinsic biases, and cheap lunches in community detection](https://mlsanity.com/paper/2210.09186/) (2022)
- [Estimation of partial rankings from sparse, noisy comparisons](https://mlsanity.com/paper/2501.02505/) (2025)
- [Scalable inference of spatial regions and temporal signatures from time series](https://mlsanity.com/paper/2605.05008/) (2026)

## Abstract (arXiv)

Community detection methods attempt to divide a network into groups of nodes that share similar properties, thus revealing its large-scale structure. A major challenge when employing such methods is that they are often degenerate, typically yielding a complex landscape of competing answers. As an attempt to extract understanding from a population of alternative solutions, many methods exist to establish a consensus among them in the form of a single partition "point estimate" that summarizes the whole distribution. Here we show that it is in general not possible to obtain a consistent answer from such point estimates when the underlying distribution is too heterogeneous. As an alternative, we provide a comprehensive set of methods designed to characterize and summarize complex populations of partitions in a manner that captures not only the existing consensus, but also the dissensus between elements of the population. Our approach is able to model mixed populations of partitions where multiple consensuses can coexist, representing different competing hypotheses for the network structure. We also show how our methods can be used to compare pairs of partitions, how they can be generalized to hierarchical divisions, and be used to perform statistical model selection between competing hypotheses.