In this paper, we fill the missing parts by investigating different perspectives of the "node similarity". Conventional homophily metrics quantify the "similarity" as an indicator function of whether

Graph neural networks (GNNs) have emerged as powerful models for learning representations of graph data showing state of the art results in various tasks. Nevertheless, the superiority of these methods is usually supported by either evaluating their performance on small subset of benchmark datasets or by reasoning about their expressive power in terms of certain graph isomorphism tests. In this paper we critically analyse both these aspects through a transductive setting for the task of node classification. First, we delve deeper into the case of multi-label node classification which offers a more realistic scenario and has been ignored in most of the related works. Through analysing the training dynamics for GNN methods we highlight the failure of GNNs to learn over multi-label graph datasets even for the case of abundant training data. Second, we show that specifically for transductive node classification, even the most expressive GNN may fail to learn in absence of node attributes and without using explicit label information as input. To overcome this deficit, we propose a straightforward approach, referred to as GNN-MultiFix, that integrates the feature, label, and positional information of a node. GNN-MultiFix demonstrates significant improvement across all the multi-label datasets. We release our code at https://anonymous.4open.science/r/Graph-MultiFix-4121.

Graph Neural Networks (GNNs) and their message passing framework that leverages both structural and feature information, have become a standard method for solving graph-based machine learning problems. However, these approaches still struggle to generalise well beyond datasets that exhibit strong homophily, where nodes of the same class tend to connect. This limitation has led to the development of complex neural architectures that pose challenges in terms of efficiency and scalability. In response to these limitations, we focus on simpler and more scalable approaches and introduce Graph-aware Logistic Regression (GLR), a non-neural model designed for node classification tasks. Unlike traditional graph algorithms that use only a fraction of the information accessible to GNNs, our proposed model simultaneously leverages both node features and the relationships between entities. However instead of relying on message passing, our approach encodes each node's relationships as an additional feature vector, which is then combined with the node's self attributes. Extensive experimental results, conducted within a rigorous evaluation framework, show that our proposed GLR approach outperforms both foundational and sophisticated state-of-the-art GNN models in node classification tasks. Going beyond the traditional limited benchmarks, our experiments indicate that GLR increases generalisation ability while reaching performance gains in computation time up to two orders of magnitude compared to it best neural competitor.

Graph Neural Networks (GNNs) have achieved state-of-the-art results in node classification tasks. However, most improvements are in multi-class classification, with less focus on the cases where each node could have multiple labels. The first challenge in studying multi-label node classification is the scarcity of publicly available datasets. To address this, we collected and released three real-world biological datasets and developed a multi-label graph generator with tunable properties. We also argue that traditional notions of homophily and heterophily do not apply well to multi-label scenarios. Therefore, we define homophily and Cross-Class Neighborhood Similarity for multi-label classification and investigate $9$ collected multi-label datasets. Lastly, we conducted a large-scale comparative study with $8$ methods across nine datasets to evaluate current progress in multi-label node classification. We release our code at \url{https://github.com/Tianqi-py/MLGNC}.

In recent years, continual learning (CL) techniques have made significant progress in learning from streaming data while preserving knowledge across sequential tasks, particularly in the realm of euclidean data. To foster fair evaluation and recognize challenges in CL settings, several evaluation frameworks have been proposed, focusing mainly on the single- and multi-label classification task on euclidean data. However, these evaluation frameworks are not trivially applicable when the input data is graph-structured, as they do not consider the topological structure inherent in graphs. Existing continual graph learning (CGL) evaluation frameworks have predominantly focussed on single-label scenarios in the node classification (NC) task. This focus has overlooked the complexities of multi-label scenarios, where nodes may exhibit affiliations with multiple labels, simultaneously participating in multiple tasks. We develop a graph-aware evaluation (\agale) framework that accommodates both single-labeled and multi-labeled nodes, addressing the limitations of previous evaluation frameworks. In particular, we define new incremental settings and devise data partitioning algorithms tailored to CGL datasets. We perform extensive experiments comparing methods from the domains of continual learning, continual graph learning, and dynamic graph learning (DGL). We theoretically analyze \agale and provide new insights about the role of homophily in the performance of compared methods. We release our framework at https://github.com/Tianqi-py/AGALE.

Graph Neural Networks (GNNs) have shown state-of-the-art improvements in node classification tasks on graphs. While these improvements have been largely demonstrated in a multi-class classification scenario, a more general and realistic scenario in which each node could have multiple labels has so far received little attention. The first challenge in conducting focused studies on multi-label node classification is the limited number of publicly available multi-label graph datasets. Therefore, as our first contribution, we collect and release three real-world biological datasets and develop a multi-label graph generator to generate datasets with tunable properties. While high label similarity (high homophily) is usually attributed to the success of GNNs, we argue that a multi-label scenario does not follow the usual semantics of homophily and heterophily so far defined for a multi-class scenario. As our second contribution, we define homophily and Cross-Class Neighborhood Similarity for the multi-label scenario and provide a thorough analyses of the collected $9$ multi-label datasets. Finally, we perform a large-scale comparative study with $8$ methods and $9$ datasets and analyse the performances of the methods to assess the progress made by current state of the art in the multi-label node classification scenario. We release our benchmark at https://github.com/Tianqi-py/MLGNC.