{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,28]],"date-time":"2023-02-28T05:44:39Z","timestamp":1677563079533},"reference-count":32,"publisher":"Proceedings of the National Academy of Sciences","issue":"11","license":[{"start":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T00:00:00Z","timestamp":1583107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1740850","CCF-1813165"]},{"DOI":"10.13039\/100000183","name":"DOD | United States Army | RDECOM | Army Research Office","doi-asserted-by":"publisher","award":["W911NF1910294"]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2020,3,17]]},"abstract":"Significance<\/jats:title>\n Our main message is that the popular method of low-dimensional embeddings provably cannot capture important properties of real-world complex networks. A widely used algorithmic technique for modeling these networks is to construct a low-dimensional Euclidean embedding of the vertices of the network, where proximity of vertices is interpreted as the likelihood of an edge. Contrary to common wisdom, we argue that such graph embeddings do not capture salient properties of complex networks. We mathematically prove that low-dimensional embeddings cannot generate graphs with both low average degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. 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