{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T06:29:28Z","timestamp":1776493768776,"version":"3.51.2"},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"01","license":[{"start":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T00:00:00Z","timestamp":1563321600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.aaai.org"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically\u2014showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.<\/jats:p>","DOI":"10.1609\/aaai.v33i01.33014602","type":"journal-article","created":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T07:36:53Z","timestamp":1567409813000},"page":"4602-4609","source":"Crossref","is-referenced-by-count":755,"title":["Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks"],"prefix":"10.1609","volume":"33","author":[{"given":"Christopher","family":"Morris","sequence":"first","affiliation":[]},{"given":"Martin","family":"Ritzert","sequence":"additional","affiliation":[]},{"given":"Matthias","family":"Fey","sequence":"additional","affiliation":[]},{"given":"William L.","family":"Hamilton","sequence":"additional","affiliation":[]},{"given":"Jan Eric","family":"Lenssen","sequence":"additional","affiliation":[]},{"given":"Gaurav","family":"Rattan","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Grohe","sequence":"additional","affiliation":[]}],"member":"9382","published-online":{"date-parts":[[2019,7,17]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/4384\/4262","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/4384\/4262","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,7]],"date-time":"2022-11-07T06:29:38Z","timestamp":1667802578000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/4384"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,17]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,7,23]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v33i01.33014602","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2019,7,17]]}}}