# The impossibility of low-rank representations for triangle-rich complex networks

@article{Comandur2020TheIO, title={The impossibility of low-rank representations for triangle-rich complex networks}, author={Seshadhri Comandur and Aneesh Sharma and Andrew Stolman and Ashish Goel}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={2020}, volume={117}, pages={5631 - 5637} }

Significance 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… CONTINUE READING

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