research-article

GRASP: Scalable Graph Alignment by Spectral Corresponding Functions

Authors:

Judith Hermanns,

Konstantinos Skitsas,

Anton Tsitsulin,

Marina Munkhoeva,

Alexander Kyster,

Alexander M. Bronstein,

Panagiotis KarrasAuthors Info & Claims

ACM Transactions on Knowledge Discovery from Data, Volume 17, Issue 4

Article No.: 50, Pages 1 - 26

https://doi.org/10.1145/3561058

Published: 24 February 2023 Publication History

Abstract

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph.

In this article, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

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Cited By

Zhou HLai PSun ZChen XChen YWu HWang Y(2024)AdaMotif: Graph Simplification via Adaptive Motif DesignIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.345632131:1(688-698)Online publication date: 10-Sep-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3456321
Shen BNiu QZhu S(2024)Adaptive Softassign via Hadamard-Equipped Sinkhorn2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.01670(17638-17647)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.01670

Index Terms

GRASP: Scalable Graph Alignment by Spectral Corresponding Functions

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Published In

cover image ACM Transactions on Knowledge Discovery from Data

ACM Transactions on Knowledge Discovery from Data Volume 17, Issue 4

May 2023

364 pages

ISSN:1556-4681

EISSN:1556-472X

DOI:10.1145/3583065

Editor:
Charu Aggarwal
IBM T. J. Watson Research, USA

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 24 February 2023

Online AM: 15 September 2022

Accepted: 19 August 2022

Revised: 18 August 2022

Received: 05 December 2021

Published in TKDD Volume 17, Issue 4

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Cited By

Zhou HLai PSun ZChen XChen YWu HWang Y(2024)AdaMotif: Graph Simplification via Adaptive Motif DesignIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2024.345632131:1(688-698)Online publication date: 10-Sep-2024
https://dl.acm.org/doi/10.1109/TVCG.2024.3456321
Shen BNiu QZhu S(2024)Adaptive Softassign via Hadamard-Equipped Sinkhorn2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.01670(17638-17647)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.01670

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