In this paper we discuss potentially practical ways to produce expander graphs with good spectral properties and a compact description. We focus on several classes of uniform and bipartite expander graphs defined as random Schreier graphs of the general linear group over the finite field of size two. We perform numerical experiments and show that such constructions produce spectral expanders that can be useful for practical applications. To find a theoretical explanation of the observed experimental results, we used the method of moments to prove upper bounds for the expected second largest eigenvalue of the random Schreier graphs used in our constructions. We focus on bounds for which it is difficult to study the asymptotic behaviour but it is possible to compute non-trivial conclusions for relatively small graphs with parameters from our numerical experiments (e.g., with less than 2^200 vertices and degree at least logarithmic in the number of vertices).

翻译：本文讨论具有良好谱性质及紧凑描述的实际可构造扩张图生成方法。我们聚焦于定义在大小为2的有限域上一般线性群的几类均匀及二分随机施赖尔图。通过数值实验表明，此类构造产生的谱扩张图可应用于实际场景。为解释实验观测结果的理论机制，我们采用矩方法证明所用随机施赖尔图期望第二大特征值的上界。重点研究难以分析渐近行为却能在数值实验参数范围内（如顶点数少于2^200、度至少为顶点数对数级）得出非平凡结论的界。