In order to function a circuit must contain at least one loop so it cannot be hierarchical ( = a tree structure).
However there is a relationship between the number nodes and loops which determines the number of equations you have generate and solve to solve a particular circuit.
Further more complicated circuits may be planar or non planar. Planar networks can be created (drawn) in a plane without two elements crossing (intersecting) except at nodes.
Non planar networks cannot.
A further complication arises if you consider polyphase systems and delta - star configurations where series and parallel don't mean the same.
Then, of course, whilst you can have series and/or parallel winding on a transformer, the relationship of primary to secondary is neither series nor parallel.