# Multi-order Graph Clustering with Adaptive Node-level Weight Learning

arXiv: https://arxiv.org/abs/2405.12183 · HTML: https://mlsanity.com/paper/2405.12183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 47 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 9 of 9)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [A Comprehensive Survey on Community Detection with Deep Learning](https://mlsanity.com/paper/2105.12584/) (2021)
- [20 years of network community detection](https://mlsanity.com/paper/2208.00111/) (2022)
- [Scalable motif-aware graph clustering](https://mlsanity.com/paper/1606.06235/) (2016)
- [EdMot: An Edge Enhancement Approach for Motif-aware Community Detection](https://mlsanity.com/paper/1906.04560/) (2019)
- [Path Sampling: A Fast and Provable Method for Estimating 4-Vertex Subgraph Counts](https://mlsanity.com/paper/1411.4942/) (2014)
- [Motif Clustering and Overlapping Clustering for Social Network Analysis](https://mlsanity.com/paper/1612.00895/) (2016)
- [Ranking Users in Social Networks with Motif-based PageRank](https://mlsanity.com/paper/1912.11817/) (2019)

## Abstract (arXiv)

Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based hypergraphs. However, these approaches often suffer from hypergraph fragmentation issue seriously, which degrades the clustering performance greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes participating in multiple motifs. A key challenge is how to achieve precise clustering results by integrating information from multiple motifs at the node level. In this paper, we propose a multi-order graph clustering model (MOGC) to integrate multiple higher-order structures and edge connections at node level. MOGC employs an adaptive weight learning mechanism to au tomatically adjust the contributions of different motifs for each node. This not only tackles hypergraph fragmentation issue but enhances clustering accuracy. MOGC is efficiently solved by an alternating minimization algo rithm. Experiments on seven real-world datasets illustrate the effectiveness of MOGC.