# Higher-Order Ranking and Link Prediction: From Closing Triangles to Closing Higher-Order Motifs

arXiv: https://arxiv.org/abs/1906.05059 · HTML: https://mlsanity.com/paper/1906.05059/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 5 of 5)

- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Neighborhood-aware Scalable Temporal Network Representation Learning](https://mlsanity.com/paper/2209.01084/) (2022)
- [Revisiting Link Prediction: A Data Perspective](https://mlsanity.com/paper/2310.00793/) (2023)
- [Higher-order Clustering and Pooling for Graph Neural Networks](https://mlsanity.com/paper/2209.03473/) (2022)
- [Neural Predicting Higher-order Patterns in Temporal Networks](https://mlsanity.com/paper/2106.06039/) (2021)

## Abstract (arXiv)

In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and recommendation. In such applications, real-time performance is critical. The proposed methods do not require any explicit training data, nor do they derive an embedding from the graph data, or perform any explicit learning. Existing methods with the above desired properties are all based on closing triangles (common neighbors, Jaccard similarity, and the ilk). In this work, we investigate higher-order network motifs and develop techniques based on the notion of closing higher-order motifs that move beyond closing simple triangles. All methods described in this work are fast with a runtime that is sublinear in the number of nodes. The experimental results indicate the importance of closing higher-order motifs for ranking and link prediction applications. Finally, the proposed notion of higher-order motif closure can serve as a basis for studying and developing better ranking and link prediction methods.