# k-hop Graph Neural Networks

## TL;DR

This paper introduces k-hop GNNs, an architecture that enhances the expressive power of standard GNNs by aggregating information from k-hop neighborhoods, enabling the identification of fundamental graph properties.

## Contribution

The paper proposes k-hop GNNs, a more expressive architecture that overcomes limitations of standard GNNs in identifying key graph properties.

## Key findings

- k-hop GNNs can identify fundamental graph properties.
- Experimental results show k-hop GNNs perform better or comparably to standard GNNs.
- Theoretical analysis confirms increased expressive power.

## Abstract

Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot identify fundamental graph properties such as connectivity and triangle freeness. We show that GNNs also suffer from the same limitation. To address this limitation, we propose a more expressive architecture, k-hop GNNs, which updates a node's representation by aggregating information not only from its direct neighbors, but from its k-hop neighborhood. We show that the proposed architecture can identify fundamental graph properties. We evaluate the proposed architecture on standard node classification and graph classification datasets. Our experimental evaluation confirms our theoretical findings since the proposed model achieves performance better or comparable to standard GNNs and to state-of-the-art algorithms.