Visual graphs for image classification: does the structure affect performance?

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph structure of neural networks and their predictive performance, they often limit themselves to a narrow range of model networks, particularly lacking mesoscale structures such as communities. Our work advances this area by conducting a more comprehensive investigation, incorporating realistic network structures characterized by heterogeneous degree distributions and community structures, which are typical characteristics of many real networks. These community structures offer a nuanced perspective on network architecture. Our analysis employs model networks such as random and scale-free networks, alongside a comparison with a biological neural network and its subsets for more detailed analysis. We examine the impact of these structural attributes on the performance of image classification tasks. Our findings reveal that structural properties do affect performance to some extent. Specifically, within moderate-depth architectures, networks featuring coherent, densely interconnected communities demonstrate enhanced learning capabilities. Crucially, we find that this advantage is strictly depth-dependent: extending the architecture to eight layers reverses the effect entirely. This comparison with the biological neural network emphasizes the relevance of our findings to real-world structures, suggesting an intriguing connection worth further exploration. This study contributes meaningfully to network science and machine learning, providing insights that could inspire the design of more biologically informed neural networks.

The quality of graph-structured data is fundamental to the success of modern graph analysis techniques such as Graph Neural Networks (GNNs). However, real-world graph data is often suboptimal, suffering from issues such as noise and incomplete connections. Graph Structure Learning (GSL) has emerged as a promising technique that adaptively optimizes node connections. However, we observe that the effectiveness of GSL often comes at the cost of a dramatic expansion in edge count, resulting in significant storage and computational overhead. In this work, we reveal that this limitation stems from the prevalent use of similarity-based edge construction, which predominantly connects highly similar neighbors based on their embeddings, introducing substantial structure redundancy. To address this, we propose a novel Informative Graph Structure Learning method (InGSL), which jointly considers both similarity and diversity in edge construction by incorporating a mutual-information-guided learning strategy. Notably, InGSL serves as a plug-in module that can be seamlessly integrated into existing GSL frameworks. Through extensive experiments on six representative GSL methods, we demonstrate that InGSL achieves significant performance improvements at a reduced number of edges.

Graphs are a fundamental data structure underlying many problems in the natural and social sciences. Over the past decade, Graph Neural Networks (GNNs) have dominated graph machine learning, supported by solid theoretical foundations. Yet scientists often understand graph structure through vision: chemists read molecular diagrams and social scientists inspect network visualizations. Despite decades of work on graph visualization, most graph learning pipelines still treat graphs purely as symbolic structures, rarely leveraging the visual form of graphs. We argue that this gap deserves renewed attention in the era of powerful vision and vision-language models. This survey provides a first systematic overview of the emerging area we term vision meets graphs, which treats visual depictions of graphs as first-class inputs for reasoning and learning. We organize existing work into three threads. Vision for Graph Reasoning studies how models can use visual depictions of graphs to understand structure and carry out multi-step reasoning. Vision for Graph Learning explores how visual features can complement or augment graph encoders beyond known limitations of message passing. Scientific Graphs examines domains where standardized depiction conventions support both reasoning and learning. Our goal is to clarify what current methods can and cannot do, and to outline a path toward foundation models that perceive and reason about graphs as scientists do.