Topology-aware GNNs under structural perturbations: Empirical robustness across domains
- 1Faculty of Mathematics, University of Belgrade, Belgrade, Serbia
- 2School of Data Science and Analytics, Kennesaw State University, Kennesaw, Georgia, United States of America
Abstract
Graph neural networks learn from relational structure but can be sensitive to edge-level noise. We study a hybrid graph classifier that combines a message-passing branch (Graph Isomorphism Network, GIN) with a topological branch based on extended persistence diagrams and PersLay embeddings. Training optionally uses a paper-specific hinge penalty motivated by stable persistence-diagram representations and Lipschitz regularity, which we abbreviate as “HK-inspired.” On six TUDataset benchmarks, we compare five ablations (Full, GIN+PersLay, GIN + HK, GIN only, PersLay only) and measure robustness as accuracy drop under 10% random edge removal at test time, with persistence diagrams fixed from the original graphs; we also report targeted perturbations on MUTAG and PROTEINS and runtime on all six datasets. The regularized configurations reduce relative accuracy degradation where GIN-only is sensitive, particularly on smaller molecular and protein graphs, but do not consistently maximize clean or perturbed accuracy. On large social-network benchmarks, robustness differences are small and clean accuracy is the main differentiator. Adding PersLay to GIN can improve accuracy on several datasets, while PersLay alone performs worst. Training the full model increases per-epoch cost relative to GIN-only, with most overhead during training rather than inference. Overall, the results support a conditional empirical conclusion: combining structure, topology, and stability-oriented training can improve robustness under specified structural perturbations, with dataset-dependent accuracy–stability trade-offs rather than universal guarantees. Author summary: We study how graph neural networks behave when some edges in a graph are missing or altered. These models are widely used to classify molecules, proteins, and social networks, but their predictions can change if the observed connections are incomplete or noisy. We combine two complementary views of a graph: a standard message-passing network that looks at local neighborhoods, and a topological summary that captures global connectivity patterns through persistence diagrams. We also test a training penalty that discourages large prediction changes when inputs are perturbed. Across six public benchmarks, this combination can make predictions more stable under edge removal, especially on smaller molecular and protein graphs, but it does not always improve raw accuracy. On large social networks, ordinary message-passing models are already largely insensitive to removing 10% of edges. Our results therefore do not support a one-size-fits-all claim. Instead, they help practitioners decide when topology-aware features and stability-oriented training are worth the added cost, and when a simpler graph neural network is already sufficient.
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BibTeX
@article{losic2026topologyaware,
title = {{Topology-aware GNNs under structural perturbations: Empirical robustness across domains}},
author = {Jelena Losic and Charles Fanning},
journal = {PLOS Complex Systems},
year = {2026},
month = sep,
doi = {10.1371/journal.pcsy.0000125},
url = {https://journals.plos.org/complexsystems/article?id=10.1371/journal.pcsy.0000125},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Topology-aware GNNs under structural perturbations: Empirical robustness across domains
AU - Jelena Losic
AU - Charles Fanning
PY - 2026
DA - 2026/09/02
JO - PLOS Complex Systems
DO - 10.1371/journal.pcsy.0000125
UR - https://journals.plos.org/complexsystems/article?id=10.1371/journal.pcsy.0000125
AB - Graph neural networks learn from relational structure but can be sensitive to edge-level noise. We study a hybrid graph classifier that combines a message-passing branch (Graph Isomorphism Network, GIN) with a topological branch based on extended persistence diagrams and PersLay embeddings. Training optionally uses a paper-specific hinge penalty motivated by stable persistence-diagram representations and Lipschitz regularity, which we abbreviate as “HK-inspired.” On six TUDataset benchmarks, we compare five ablations (Full, GIN+PersLay, GIN + HK, GIN only, PersLay only) and measure robustness as accuracy drop under 10% random edge removal at test time, with persistence diagrams fixed from the original graphs; we also report targeted perturbations on MUTAG and PROTEINS and runtime on all six datasets. The regularized configurations reduce relative accuracy degradation where GIN-only is sensitive, particularly on smaller molecular and protein graphs, but do not consistently maximize clean or perturbed accuracy. On large social-network benchmarks, robustness differences are small and clean accuracy is the main differentiator. Adding PersLay to GIN can improve accuracy on several datasets, while PersLay alone performs worst. Training the full model increases per-epoch cost relative to GIN-only, with most overhead during training rather than inference. Overall, the results support a conditional empirical conclusion: combining structure, topology, and stability-oriented training can improve robustness under specified structural perturbations, with dataset-dependent accuracy–stability trade-offs rather than universal guarantees. Author summary: We study how graph neural networks behave when some edges in a graph are missing or altered. These models are widely used to classify molecules, proteins, and social networks, but their predictions can change if the observed connections are incomplete or noisy. We combine two complementary views of a graph: a standard message-passing network that looks at local neighborhoods, and a topological summary that captures global connectivity patterns through persistence diagrams. We also test a training penalty that discourages large prediction changes when inputs are perturbed. Across six public benchmarks, this combination can make predictions more stable under edge removal, especially on smaller molecular and protein graphs, but it does not always improve raw accuracy. On large social networks, ordinary message-passing models are already largely insensitive to removing 10% of edges. Our results therefore do not support a one-size-fits-all claim. Instead, they help practitioners decide when topology-aware features and stability-oriented training are worth the added cost, and when a simpler graph neural network is already sufficient.
SN - 2837-8830
ER -