Graphon Mixtures

• URL: http://arxiv.org/abs/2505.13864v1
• Date: Tue, 20 May 2025 03:19:29 GMT
• Title: Graphon Mixtures
• Authors: Sevvandi Kandanaarachchi, Cheng Soon Ong,
• Abstract summary: Social networks have a small number of large hubs, and a large number of small dense communities.<n>We propose a generative model that captures both hub and dense structures.<n>We show theoretically that we can estimate the normalized degree of the hubs, as well as estimate the graphon corresponding to sparse components of graph mixtures.
• Score: 6.822247359790484
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Social networks have a small number of large hubs, and a large number of small dense communities. We propose a generative model that captures both hub and dense structures. Based on recent results about graphons on line graphs, our model is a graphon mixture, enabling us to generate sequences of graphs where each graph is a combination of sparse and dense graphs. We propose a new condition on sparse graphs (the max-degree), which enables us to identify hubs. We show theoretically that we can estimate the normalized degree of the hubs, as well as estimate the graphon corresponding to sparse components of graph mixtures. We illustrate our approach on synthetic data, citation graphs, and social networks, showing the benefits of explicitly modeling sparse graphs.

Related papers

• Graph Community Augmentation with GMM-based Modeling in Latent Space [9.47065476904586]
  We propose an algorithm called the graph community augmentation (GCA)<n>We empirically demonstrate the effectiveness of GCA for generating graphs with a new community structure on synthetic and real datasets.
  arXiv  Detail & Related papers  (2024-12-02T06:05:10Z)
• Graph Mixup with Soft Alignments [49.61520432554505]
  We study graph data augmentation by mixup, which has been used successfully on images. We propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments.
  arXiv  Detail & Related papers  (2023-06-11T22:04:28Z)
• A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphs [13.954735096637298]
  We analyze how sparsity affects the graph spectra, and thus the performance of graph neural networks (GNNs) in node classification on dense and sparse graphs. We show that GNNs can outperform spectral methods on sparse graphs, and illustrate these results with numerical examples on both synthetic and real graphs.
  arXiv  Detail & Related papers  (2022-11-06T22:38:13Z)
• Joint Network Topology Inference via a Shared Graphon Model [24.077455621015552]
  We consider the problem of estimating the topology of multiple networks from nodal observations. We adopt a graphon as our random graph model, which is a nonparametric model from which graphs of potentially different sizes can be drawn.
  arXiv  Detail & Related papers  (2022-09-17T02:38:58Z)
• Graph Condensation via Receptive Field Distribution Matching [61.71711656856704]
  This paper focuses on creating a small graph to represent the original graph, so that GNNs trained on the size-reduced graph can make accurate predictions. We view the original graph as a distribution of receptive fields and aim to synthesize a small graph whose receptive fields share a similar distribution.
  arXiv  Detail & Related papers  (2022-06-28T02:10:05Z)
• G-Mixup: Graph Data Augmentation for Graph Classification [55.63157775049443]
  Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. We propose $mathcalG$-Mixup to augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs. Experiments show that $mathcalG$-Mixup substantially improves the generalization and robustness of GNNs.
  arXiv  Detail & Related papers  (2022-02-15T04:09:44Z)
• Graphon-aided Joint Estimation of Multiple Graphs [24.077455621015552]
  We consider the problem of estimating the topology of multiple networks from nodal observations. We adopt a graphon as our random graph model, which is a nonparametric model from which graphs of potentially different sizes can be drawn.
  arXiv  Detail & Related papers  (2022-02-11T15:20:44Z)
• Learning Graphon Autoencoders for Generative Graph Modeling [91.32624399902755]
  Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. We propose a novel framework called textitgraphon autoencoder to build an interpretable and scalable graph generative model. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons.
  arXiv  Detail & Related papers  (2021-05-29T08:11:40Z)
• Multilevel Graph Matching Networks for Deep Graph Similarity Learning [79.3213351477689]
  We propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects. To compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks.
  arXiv  Detail & Related papers  (2020-07-08T19:48:19Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)
• Searching for Stage-wise Neural Graphs In the Limit [38.929579739825066]
  A graphon is the limit of Cauchy sequence of graphs and a scale-free probabilistic distribution. We develop theoretically motivated techniques that search for and scale up small-capacity stage-wise graphs found on small datasets to large-capacity graphs that can handle ImageNet.
  arXiv  Detail & Related papers  (2019-12-30T09:17:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.