Local Weak Limits and Unimodularity
Local weak limits of finite graphs are unimodular (involution-invariant)
random countable locally-finite rooted graphs.
Is the converse true -- does every such infinite graph arise as some local weak limit?
Posed in our 2007 paper this has been called the
See the 2014 Hatami - Lovasz - Szegedy survey
Limits of locally-globally convergent graph sequences
for discussion of this general topic.