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. Existing solutions either require auxiliary information such as node attributes, or provide a single-scale view of the graph by translating the problem into aligning node embeddings.
In this paper, 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 captures multiscale structural characteristics from the eigenvectors of the graph’s Laplacian and uses this information to align two graphs.Our experimental study, featuring noise levels higher than anything used in previous studies, shows that GRASP outperforms state-of-the-art methods for graph alignment across noise levels and graph types.
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Notes
- 1.
Solutions to the problem of aligning graphs with unequal numbers of nodes can rest on solutions to this basic problem form.
- 2.
In our experiments we select \(q=100\) values evenly spaced in the range [0.1, 50].
- 3.
\(\mu =0.132\) in our experiments.
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Hermanns, J., Tsitsulin, A., Munkhoeva, M., Bronstein, A., Mottin, D., Karras, P. (2021). GRASP: Graph Alignment Through Spectral Signatures. In: U, L.H., Spaniol, M., Sakurai, Y., Chen, J. (eds) Web and Big Data. APWeb-WAIM 2021. Lecture Notes in Computer Science(), vol 12858. Springer, Cham. https://doi.org/10.1007/978-3-030-85896-4_4
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