Graph machine learning

Although data that can be naturally represented as graphs is widespread in real-world applications across diverse industries, popular graph ML benchmarks for node property prediction only cover a surprisingly narrow set of data domains, and graph neural networks (GNNs) are often evaluated on just a few academic citation networks. This issue is particularly pressing in light of the recent growing interest in designing graph foundation models. These models are supposed to be able to transfer to diverse graph datasets from different domains, and yet the proposed graph foundation models are often evaluated on a very limited set of datasets from narrow applications. To alleviate this issue, we introduce GraphLand: a benchmark of 14 diverse graph datasets for node property prediction from a range of different industrial applications. GraphLand allows evaluating graph ML models on a wide range of graphs with diverse sizes, structural characteristics, and feature sets, all in a unified setting. Further, GraphLand allows investigating such previously underexplored research questions as how realistic temporal distributional shifts under transductive and inductive settings influence graph ML model performance. To mimic realistic industrial settings, we use GraphLand to compare GNNs with gradient-boosted decision trees (GBDT) models that are popular in industrial applications and show that GBDTs provided with additional graph-based input features can sometimes be very strong baselines. Further, we evaluate currently available general-purpose graph foundation models and find that they fail to produce competitive results on our proposed datasets.

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives a better understanding of the graph distance underlying the diversity measure.

Homophily is a graph property describing the tendency of edges to connect similar nodes. There are several measures used for assessing homophily but all are known to have certain drawbacks: in particular, they cannot be reliably used for comparing datasets with varying numbers of classes and class size balance. To show this, previous works on graph homophily suggested several properties desirable for a good homophily measure, also noting that no existing homophily measure has all these properties. Our paper addresses this issue by introducing a new homophily measure — unbiased homophily — that has all the desirable properties and thus can be reliably used across datasets with different label distributions. The proposed measure is suitable for undirected (and possibly weighted) graphs. We show both theoretically and via empirical examples that the existing homophily measures have serious drawbacks while unbiased homophily has a desirable behavior for the considered scenarios. Finally, when it comes to directed graphs, we prove that some desirable properties contradict each other and thus a measure satisfying all of them cannot exist.