Looking for resources on irregular expander graphs

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I've been reading up on Expander graphs on the web, papers, books and surveys.

However, all the resources I could find on Google is about regular, connected, non-bipartite (undirected) graphs. The only thing I managed to find about irregular expander graphs is this question. The answer to that directs to "Recent Progress In General Topology III" which I have been unable to get my hands on.

I would appreciate if anyone could point me to a readily available resource about non-regular expanders (directed ones if possible) as I would like to know how the lack of regularity would affect the properties of expanders. Specifically, I would like to know if there is a variant of the the "Expander Mixing Lemma" for general digraphs.

Any help would be appreciated!