Graph Neural Networks Applications Across Domains: All Insights You Need

Neural Message Passing on Structural Interaction Graphs for Fully-Inductive Graph Neural Networks

A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework

Learning and Clustering on Temporal Graphs: Principles, Primitives, and Pooling

This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?

Collective Node Classification through Neuro-Symbolic Integration

Statistical Edge Graphs for Tabular Learning with Graph Neural Networks

Tabular data are central to many real-world applications, yet deep learning models often underperform compared to tree-based methods due to limited relational inductive bias. We propose a unified framework that models each tabular instance as an instance-level statistical feature graph to enable learning with Graph Neural Networks (GNNs). In this representation, features are treated as nodes, and edges encode pairwise statistical relationships derived from Z-score similarity, covariance, Pearson correlation, or Euclidean distance. This formulation explicitly captures inter-feature dependencies rather than relying solely on implicitly learned interactions. We evaluate the framework across four classification and four regression datasets spanning diverse domains and feature dimensionalities. Results demonstrate competitive and, in several cases, superior performance compared to strong baselines including Random Forests, XGBoost, and multilayer perceptrons. Correlation- and covariance-based edge constructions consistently provide robust performance across tasks. Furthermore, empirical analysis indicates that performance gains become more pronounced in higher-dimensional datasets, suggesting that graph-based representations are particularly effective at modeling complex feature interactions. Overall, this work provides a systematic examination of statistical graph construction for tabular learning and highlights the potential of GNNs as a structured alternative to conventional tabular models.

Mapping the DAG-ness Landscape: Structural Archetypes in Complex Networks

Directed networks arise across biological, social, informational, and engineered systems, yet most analyses treat directedness as a binary property: a network is either a directed acyclic graph (DAG) or it is not. This binary classification obscures the rich spectrum of hierarchical, recurrent, and modular structure present in real systems. In this paper, we empirically evaluate the DAG-ness framework, a four-component measure that quantifies acyclicity, flow alignment, cyclic locality, and pathway complexity across a corpus of 107 networks drawn from twelve structurally diverse domains. Rather than aligning with traditional disciplinary boundaries, our results reveal unexpected cross-domain convergence: diverse systems resolve into four universal structural archetypes. We find that macroscopic acyclicity is pervasive even in feedback-rich systems, and that domains as disparate as neural connectomes and abstract informational networks frequently converge on identical topological constraints. These findings demonstrate that DAG-ness provides a unified, interpretable, and domain-agnostic lens for understanding the hidden laws of directed structure in complex systems.

Graph Classification via Network Usable Information: From Representation Evaluation to Structure Selection

A training-free NUI estimation procedure based on clustering consistency with ground-truth labels is introduced, providing a proxy for task-relevant information without supervised learning, and a strong correlation between estimated NUI and downstream classification accuracy is observed, validating NUI as an effective measure of representation utility.