Numerous recent works have analyzed the expressive power of message-passing graph neural networks (MPNNs), primarily utilizing combinatorial techniques such as the $1$-dimensional Weisfeiler--Leman test ($1$-WL) for the graph isomorphism problem. However, the graph isomorphism objective is inherently binary, not giving insights into the degree of similarity between two given graphs.

A key challenge in graph out-of-distribution (OOD) detection lies in the absence of ground-truth OOD samples during training. Existing methods are typically optimized to capture features within the in-distribution (ID) data and calculate OOD scores, which often limits pre-trained models from representing distributional boundaries, leading to unreliable OOD detection. Moreover, the latent structure of graph data is often governed by multiple underlying factors, which remains less explored. To address these challenges, we propose a novel test-time graph OOD detection method, termed BaCa, that calibrates OOD scores using dual dynamically updated dictionaries without requiring fine-tuning the pre-trained model. Specifically, BaCa estimates graphons and applies a mix-up strategy solely with test samples to generate diverse boundary-aware discriminative topologies, eliminating the need for exposing auxiliary datasets as outliers. We construct dual dynamic dictionaries via priority queues and attention mechanisms to adaptively capture latent ID and OOD representations, which are then utilized for boundary-aware OOD score calibration. To the best of our knowledge, extensive experiments on real-world datasets show that BaCa significantly outperforms existing state-of-the-art methods in OOD detection.

In this work we develop a theory of hierarchical clustering for graphs. Our modelling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary setting for recent progress in the statistical theory of graph clustering. We define what it means for an algorithm to produce the ``correct clustering, give sufficient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.

In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary setting for recent progress in the statistical theory of graph clustering. We define what it means for an algorithm to produce the "correct" clustering, give sufficient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.

A network, which is used to model interactions or communications among a set of agents or nodes, is arguably among one of the most common and important representations for modern complex data.

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