arXiv:2610. 07503v1 Announce Type: cross Abstract: Two populations of graphs often have to be compared without any correspondence between their vertices, for instance when networks come from different communities, or when a graph generative model is evaluated against held-out graphs.
arXiv:2506.02825v3 Announce Type: replace-cross Abstract: We present the OmniMatch algorithm for seeded multiple graph matching. In the setting of $d$-dimensional Random Dot Product Graphs (RDPG), we...
AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
arXiv:2511. 17240v3 Announce Type: replace-cross Abstract: We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes.
arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).
arXiv:2605. 22346v2 Announce Type: replace-cross Abstract: Two of the most widely used methods for analysing graph data, Adjacency Spectral Embedding and Laplacian Spectral Embedding, often produce different results when applied to the same graph.
arXiv:2607. 12026v1 Announce Type: cross Abstract: Finite groups are rigid algebraic objects, whose Cayley graphs expose a rich network geometry through which group-theoretic structure can be measured, compared, and learned.
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.
arXiv:2505. 03649v4 Announce Type: replace-cross Abstract: Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields.
arXiv:2609.26199v1 Announce Type: new Abstract: A large graph is often available only in part: a crawl stopped by its budget, a panel, a partial dump. When the sampled fraction $s$ is known by design...
arXiv:2601. 17130v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are widely used for tasks such as node classification and link prediction, but their use in sensitive settings raises concerns about training-data leakage.
The paper studies graphons—limits of graph sequences—by transforming sparse finite graphs into their line graphs. It identifies a property called the square‑degree property that ensures sparse graphs produce dense line graphs, allowing dense‑graph limit results to apply. Examples include star graphs and superlinear preferential attachment graphs, whose line graphs yield non‑zero graphons, while dense graphs such as Erdős–Rényi produce sparse line graphs and the zero graphon.