- Luca Trevisan's series on expanders and their relation to Cayley graphs (one, two, three, four)
- Terry Tao's summary of expanders inspired by an Avi Wigderson talk.
- My note from SODA 2007 on the Alon/Schwartz/Schapira improved analysis of the replacement product.
- Dieter van Melkebeek's course on expanders
This doesn't mean that the zig-zag product is useless of course. In fact, there's a wonderful 'return to start' story here, which I'll attempt to convey. Essentially, as Luca describes, many early expander constructions proceeded via taking some special non-Abelian group and constructing its Cayley graph, which was then shown to be an expander. The zig-zag product is described "combinatorially" as a construction that takes two graphs and makes a third out of them, and one advantage of this representation is that it gives more explicit expander constructions. But it turned out that at the core of this hides a group operator ! In a certain sense, the zig zag product of the Cayley graph of two groups is the Cayley graph of the semidirect product of the groups ! This is a result of Alon, Lubotsky and Wigderson.