Expander Graphs

Emin Karayel 📧

March 3, 2023

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


Expander Graphs are low-degree graphs that are highly connected. They have diverse applications, for example in derandomization and pseudo-randomness, error-correcting codes, as well as pure mathematical subjects such as metric embeddings. This entry formalizes the concept and derives main theorems about them such as Cheeger's inequality or tail bounds on distribution of random walks on them. It includes a strongly explicit construction for every size and spectral gap. The latter is based on the Margulis-Gabber-Galil graphs and several graph operations that preserve spectral properties. The proofs are based on the survey papers/monographs by Hoory et al. and Vadhan, as well as results from Impagliazzo and Kabanets and Murtagh et al.


BSD License


Session Expander_Graphs