Harry Crane Rutgers University
I discuss two challenges in modeling networks:
1. modeling temporal variation in network structure and
2. accounting for common structural properties in a natural way.
In both cases, I consider how to specify models with logical properties necessary for sensible inference.
For 1., I show how certain minimal assumptions constrain the class of dynamic network models to a relatively restricted class of processes.
For 2., I discuss how basic properties of sparsity and power law, which cannot be accommodated by conventional network models that assume exchangeability with respect to vertex relabeling, are better handled by a new invariance principle of edge exchangeability. (This is joint work with Walter Dempsey, U. Michigan.)