Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform other state-of-the-art approaches in both accuracy and computational efficiency.

We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes followanorder.

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Technically,various methods of both categories exploit the link between graph data and linear algebra by representing graphs by their (normalized) adjacency matrix. Such methods are often defined or can be interpreted in terms ofwalks. On the other hand, the Weisfeiler-Leman heuristic for graph isomorphism testing has attracted great interest in machine learning [33, 34].

In recent years, graph neural networks (GNNs) have become the de facto tool for performing machine learning tasks on graphs. Most GNNs belong to the family of message passing neural networks (MPNNs).

Identifying such a metric is particularly challenging for non-Euclidean data such as graphs.

Graphs are the most popular mathematical abstractions for relational data structures.