# Link Prediction Based on Graph Neural Networks

## TL;DR

This paper introduces a novel GNN-based approach for link prediction that learns heuristics from local subgraphs, unifying existing heuristics under a new theory and demonstrating superior performance across various network datasets.

## Contribution

The paper develops the $$-decaying heuristic theory and proposes a GNN-based algorithm to learn link prediction heuristics from local subgraphs, surpassing traditional methods.

## Key findings

- Unifies various heuristics under the $\u0013$-decaying framework.
- Shows local subgraphs contain rich information for link prediction.
- Achieves state-of-the-art results across multiple datasets.

## Abstract

Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, every heuristic has a strong assumption on when two nodes are likely to link, which limits their effectiveness on networks where these assumptions fail. In this regard, a more reasonable way should be learning a suitable heuristic from a given network instead of using predefined ones. By extracting a local subgraph around each target link, we aim to learn a function mapping the subgraph patterns to link existence, thus automatically learning a `heuristic' that suits the current network. In this paper, we study this heuristic learning paradigm for link prediction. First, we develop a novel $\gamma$-decaying heuristic theory. The theory unifies a wide range of heuristics in a single framework, and proves that all these heuristics can be well approximated from local subgraphs. Our results show that local subgraphs reserve rich information related to link existence. Second, based on the $\gamma$-decaying theory, we propose a new algorithm to learn heuristics from local subgraphs using a graph neural network (GNN). Its experimental results show unprecedented performance, working consistently well on a wide range of problems.