# The interplay between ranking and communities in networks

arXiv: https://arxiv.org/abs/2112.12670 · HTML: https://mlsanity.com/paper/2112.12670/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 23 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Sync-Rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and Semidefinite Programming Synchronization](https://mlsanity.com/paper/1504.01070/) (2015)
- [Community detection with node attributes in multilayer networks](https://mlsanity.com/paper/2004.09160/) (2020)
- [A physical model for efficient ranking in networks](https://mlsanity.com/paper/1709.09002/) (2017)
- [Aspirational pursuit of mates in online dating markets](https://mlsanity.com/paper/1808.04840/) (2018)
- [Hierarchical community structure in networks](https://mlsanity.com/paper/2009.07196/) (2020)
- [Reciprocity, community detection, and link prediction in dynamic networks](https://mlsanity.com/paper/2112.09624/) (2021)
- [Generative model for reciprocity and community detection in networks](https://mlsanity.com/paper/2012.08215/) (2020)
- [Community detection and reciprocity in networks by jointly modeling pairs of edges](https://mlsanity.com/paper/2112.10436/) (2021)
- [Animal social networks: an introduction for complex systems scientists](https://mlsanity.com/paper/2005.09598/) (2020)

## Built on by (most cited first, 2 of 2)

- [Estimation of partial rankings from sparse, noisy comparisons](https://mlsanity.com/paper/2501.02505/) (2025)
- [A model for efficient dynamical ranking in networks](https://mlsanity.com/paper/2307.13544/) (2023)

## Abstract (arXiv)

Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative model based on an interplay between community and hierarchical structures. It assumes that each node has a preference in the interaction mechanism and nodes with the same preference are more likely to interact, while heterogeneous interactions are still allowed. The sparsity of the network is exploited for implementing a more efficient algorithm. We demonstrate our method on synthetic and real-world data and compare performance with two standard approaches for community detection and ranking extraction. We find that the algorithm accurately retrieves the overall node's preference in different scenarios, and we show that it can distinguish small subsets of nodes that behave differently than the majority. As a consequence, the model can recognize whether a network has an overall preferred interaction mechanism. This is relevant in situations where there is no clear "a priori" information about what structure explains the observed network datasets well. Our model allows practitioners to learn this automatically from the data.