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Weisfeiler-Lehman goes dynamic: An analysis of the expressive power of Graph Neural Networks for attributed and dynamic graphs

dc.date.accessioned2024-03-13T10:52:28Z
dc.date.available2024-03-13T10:52:28Z
dc.date.issued2024-02-28
dc.identifierdoi:10.17170/kobra-202403139766
dc.identifier.urihttp://hdl.handle.net/123456789/15551
dc.description.sponsorshipGefördert im Rahmen des Projekts DEAL
dc.language.isoeng
dc.rightsNamensnennung 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectGraph Neural Networkeng
dc.subjectDynamic graphseng
dc.subjectGNN expressivityeng
dc.subjectUnfolding treeseng
dc.subjectWeisfeiler-Lehman testeng
dc.subject.ddc004
dc.subject.ddc600
dc.titleWeisfeiler-Lehman goes dynamic: An analysis of the expressive power of Graph Neural Networks for attributed and dynamic graphseng
dc.typeAufsatz
dcterms.abstractGraph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler–Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence. Moreover, the proof of the approximation capability is mostly constructive and allows us to deduce hints on the architecture of GNNs that can achieve the desired approximation.eng
dcterms.accessRightsopen access
dcterms.creatorBeddar-Wiesing, Silvia
dcterms.creatorD’Inverno, Giuseppe Alessio
dcterms.creatorGraziani, Caterina
dcterms.creatorLachi, Veronica
dcterms.creatorMoallemy-Oureh, Alice
dcterms.creatorScarselli, Franco
dcterms.creatorThomas, Josephine Maria
dcterms.extent16 Seiten
dc.relation.doidoi:10.1016/j.neunet.2024.106213
dc.subject.swdGraphger
dc.subject.swdAlgorithmusger
dc.subject.swdNeuronales Netzger
dc.type.versionpublishedVersion
dcterms.source.identifiereissn:0893-6080
dcterms.source.journalNeural Networkseng
dcterms.source.volumeVolume 173
kup.iskupfalse
dcterms.source.articlenumber106213


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