# On clustering network-valued data

arXiv: https://arxiv.org/abs/1606.02401 · HTML: https://mlsanity.com/paper/1606.02401/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 9 of 9)

- [Graphon based Clustering and Testing of Networks: Algorithms and Theory](https://mlsanity.com/paper/2110.02722/) (2021)
- [Network two-sample test for block models](https://mlsanity.com/paper/2406.06014/) (2024)
- [On the Number of Edges of the Frechet Mean and Median Graphs](https://mlsanity.com/paper/2105.14397/) (2021)
- [Network Clustering for Latent State and Changepoint Detection](https://mlsanity.com/paper/2111.01273/) (2021)
- [Differentially Describing Groups of Graphs](https://mlsanity.com/paper/2201.04064/) (2021)
- [Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA](https://mlsanity.com/paper/2202.04719/) (2022)
- [Nested stochastic block model for simultaneously clustering networks and nodes](https://mlsanity.com/paper/2307.09210/) (2023)
- [A Multilayer Correlated Topic Model](https://mlsanity.com/paper/2101.02028/) (2021)
- [Fitting Low-rank Models on Egocentrically Sampled Partial Networks](https://mlsanity.com/paper/2303.11230/) (2023)

## Abstract (arXiv)

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being able to cluster within a network is important, there are emerging needs to be able to cluster multiple networks. This is largely motivated by the routine collection of network data that are generated from potentially different populations. These networks may or may not have node correspondence. When node correspondence is present, we cluster networks by summarizing a network by its graphon estimate, whereas when node correspondence is not present, we propose a novel solution for clustering such networks by associating a computationally feasible feature vector to each network based on trace of powers of the adjacency matrix. We illustrate our methods using both simulated and real data sets, and theoretical justifications are provided in terms of consistency.