Experiments on synthetic and real-world datasets show that GraphK outperforms existing methods, accurately learns graph structures, and generates synthetic graphs without explicit definitions.
Abstract
Graph generation models have advanced significantly with deep learning, yet they remain limited in scalability, flexibility, and ability to model underlying structures. We present GraphK, a novel encoder-sampler-decoder framework for graph generation that overcomes these challenges through structural flexibility and computational efficiency. Unlike autoregressive approaches constrained by vocabulary size (i.e. number of nodes in graph generation), GraphK allows for both upscaling (generating graphs with more nodes than the input) and downscaling, providing a flexible control over output graph size. By learning permutation-invariant latent representations and sampling new node embeddings via maximum likelihood estimation, GraphK generalizes across graph sizes and structures. For edge generation, we employ edge prediction with a KDTree-based top-k neighbor search in the latent space, reducing computational cost. Based on the manifold smoothness assumption, our method effectively captures graph properties. Experiments on synthetic and real-world datasets show that GraphK outperforms existing methods, accurately learns graph structures, and generates synthetic graphs without explicit definitions.
Graph representation learning has largely focused on designing increasingly sophisticated models to transform graph topology into vector representations, or embeddings. However, the extent to which embedding quality depends on model learning, rather than on the underlying topological transformations, remains unclear. Here, we show that informative embeddings can be derived without complicated model design and gradient-based training. Propagating random features through implicit hierarchical structures induced by random walks and anonymous walks yields embeddings that capture node proximity and structural role, respectively. These two training-free embeddings preserve complementary aspects of graph organization and perform competitively with classic and recent methods across various node-, edge-, and graph-level tasks. They often require substantially less computation, resulting in a favorable quality-efficiency trade-off. Combining the two types of embeddings further improves inference quality of some tasks compared with using either embedding type alone. Our results suggest that informative graph embeddings can arise from carefully chosen topological transformations before any learning operation is applied.
Meng Qin, Jinqiang Cui, Hongwei Zheng et al.· 0 citations
Generating categorical graphs requires choosing node and edge types that form a coherent structure without depending on node order. Many graph generators encode categories as fixed one-hot vectors, which can impose an artificial geometry in which categories are equidistant. We propose Embedded Graph Flows (EGF), a generative model that learns continuous embeddings for node and unordered-edge categories and transports Gaussian noise towards these learnt endpoints using a permutation-equivariant graph transformer. A terminal readout maps the embeddings back to discrete graph categories. Across molecular benchmarks, EGF achieved competitive performance. On QM9, EGF gives the best result on all four reported metrics among the three methods, including a Fr\'echet ChemNet Distance (FCD) of 0.150, compared with 0.717 for the categorical-diffusion baseline DiGress and 0.812 for the bridge-based baseline GruM. When applied to larger molecules in ZINC250k, EGF retains the lowest maximum mean discrepancy (MMD) using the neighbourhood subgraph pairwise distance kernel (NSPDK), indicating close agreement with the local substructures of the reference molecules. Our code is available at https://github.com/Trusted-System-Lab/EGF.
Ethan Ma, Zihan Wang, Chris Siu Yeung Chow et al.· 0 citations
This work introduces Topoformer, a lightweight and scalable framework for graph representation learning that encodes topological structure into attention-friendly sequences by decomposing a graph into a short, ordered sequence of topological tokens by slicing over node or edge filtrations.
Md Joshem Uddin, Astrit Tola, C. Akcora et al.· arXiv.org· 1 citation
The proposed DD-AG2m alternates between AG2m optimization on the original (global) graph and AG2m optimization on the partitioned graphs, and introduces a two-level variant that performs global optimization steps on a coarse graph obtained by randomly subsampling nodes within each subdomain.
Laurynas Varnas, Julien Herrmann, Alexander Heinlein et al.· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
