  Representing various networked data as multiplex networks, networks of
networks and other multilayer networks can reveal completely new types of
structures in these system. We introduce a general and principled graphlet
framework for multilayer networks which allows one to break any multilayer
network into small multilayered building blocks. These multilayer graphlets can
be either analyzed themselves or used to do tasks such as comparing different
systems. The method is flexible in terms of multilayer isomorphism,
automorphism orbit definition, and the type of multilayer network. We
illustrate our method for multiplex networks and show how it can be used to
distinguish networks produced with multiple models from each other in an
unsupervised way. In addition, we include an automatic way of generating the
hundreds of dependency equations between the orbit counts needed to remove
redundant orbit counts. The framework introduced here allows one to analyze
multilayer networks with versatile semantics, and these methods can thus be
used to analyze the structural building blocks of myriad multilayer networks.
