Explicit Concentrators from Generalized N -Gons

Concentrators are graphs used in the construction of switching networks that exhibit high connectivity. A technique for establishing the concentration properties of a graph by analysis of its eigenvalues is given. If the ratio of the subdominant eigenvalue to the dominant eigenvalue is small, the graph is a good concentrator. Generalized $N$-gons are very sparse, locally tree-like graphs for which the eigenvalues can be calculated with relative ease. The eigenvalue ratios for the known $N$-gons are calculated and show that the $N$-gons are excellent concentrators.