[19] David Durfee, Rasmus Kyng, John Peebles, Anup B. Rao, and Sushant Sachdeva. Sampling random spanning trees faster than matrix multiplication. In Symposium on Theory of Computing, 2017.
[20] Aaron Schild. An almost-linear time algorithm for uniform random spanning tree generation. In Symposium on Theory of Computing, 2018.
[21] Aleksander Madry, Damian Straszak, and Jakub Tarnawski. Fast generation of random spanning trees and the effective resistance metric. In Symposium on Discrete Algorithms, 2014.
[22] Vedat Levi Alev, Nima Anari, Lap Chi Lau, and Shayan Oveis Gharan. Graph clustering using effective resistance. In arXiv preprint arXiv:1711.06530, 2017.
[23] Zhiqiang Zhao and Zhuo Feng. Effective-resistance preserving spectral reduction of graphs. In Proceedings of the Annual Design Automation Conference, 2019.
[24] Francesco Di Giovanni, Lorenzo Giusti, Federico Barbero, Giulia Louise, Pietro Lio', and Michael Bronstein. On over-squashing in message passing neural networks: The impact of width, depth, and topology. In International Conference on Machine Learning, 2023.
[25] Pradeep Banerjee, Kedar Karhadkar, and Guido Montúfar Yu Guang Wang, Uri Alon. Oversquashing in gnns through the lens of information contraction and graph expansion. In Allerton Conference on Communication, Control, and Computing, 2022.
[26] Mitchell Black, Amir Nayyeri, Zhengchao Wan, and Yusu Wang. Understanding oversquashing in gnu's through the lens of effective resistance. In International Conference on Machine Learning, 2023.
[27] Ameya Velingker, Ali Kemal Sinop, Ira Ktena, Petar Velivcković, and Sreenivas Gollapudi. Affinity-aware graph networks. In arXiv preprint arXiv:2206.11941, 2022.
[28] Arun Jambulapati and Aaron Sidford. Efficient  $\widetilde{O}(n/\epsilon)$  spectral sketches for the laplacian and its pseudoinverse. In Symposium on Discrete Algorithms, 2018.
[29] Lawrence Li and Sushant Sachdeva. A new approach to estimating effective resistances and counting spanning trees in expander graphs. In Symposium on Discrete Algorithms, 2022.
[30] Timothy Chu, Yu Gao, Richard Peng, Sushant Sachdeva, Saurabh Sawlani, and Junxing Wang. Graph sparsification, spectral sketches, and faster resistance computation, via short cycle decompositions. In Symposium on Foundations of Computer Science, 2018.
[31] Gramoz Goranci, Monika Henzinger, and Pan Peng. Dynamic effective resistances and approximate schur complement on separable graphs. In Embedded Systems and Applications, 2018.
[32] Michael Dinitz, Robert Krauthgamer, and Tal Wagner. Towards resistance sparsifiers, 2015.
[33] Cameron Musco, Praneeth Netrapalli, Aaron Sidford, Shashanka Ubara, and David P Woodruff. Spectrum approximation beyond fast matrix multiplication: Algorithms and hardness. In arXiv preprint arXiv:1704.04163, 2017.
[34] Virginia Vassilevska Williams and R. Ryan Williams. Subcubic equivalences between path, matrix, and triangle problems. In Symposium on Foundations of Computer Science, 2018.
[35] Ran Duan, Hongxun Wu, and Renfei Zhou. Faster matrix multiplication via asymmetric hashing. In https://arxiv.org/abs/2210.10173, 2023.
[36] Alexandr Andoni, Jiecao Chen, Robert Krauthgamer, Bo Qin, David P. Woodruff, and Qin Zhang. On sketching quadratic forms. In Proceedings of the Conference on Innovations in Theoretical Computer Science, 2015.
[37] Huan Li and Aaron Schild. Spectral subspace sparsification. In Symposium on Foundations of Computer Science, 2018.
[38] Jeff Cheeger. A lower bound for the smallest eigenvalue of the laplacian. In *Problems in Analysis*, 1971.
[39] William B. Johnson. Extensions of lipschitz mappings into hilbert space. In Contemporary mathematics, 1984.
[40] Dimitris Achlioptas. Database-friendly random projections. In Proceedings of the Symposium on Principles of Database Systems, 2001.