Essentially Every Unimodular Matrix Defines and Expander
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales
Random Structures & Algorithms
Revisiting the Efficiency of Malicious Two-Party Computation
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Note: Edge intersection graphs of systems of paths on a grid with a bounded number of bends
Discrete Applied Mathematics
Testing the expansion of a graph
Information and Computation
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Explicit construction of families of linear expanders and superconcentrators is relevant to theoretical computer science in several ways. There is essentially only one known explicit construction. Here we show a correspondence between the eigenvalues of the adjacency matrix of a graph and its expansion properties, and combine it with results on Group Representations to obtain many new examples of families of linear expanders. We also obtain better expanders than those previously known and use them to construct explicitly n-superconcentrators with 157.4 n edges, much less than the previous most economical construction.