  The law of a finite graph is a probability measure induced by the orbits of
the graph under its automorphism group. Every law satisfies the intrinsic mass
transport principle, which is also known as unimodularity. We discuss the
convergence of sequences of laws of finite graphs. Of particular importance is
a conjecture proposed by Aldous and Lyons that claims every unimodular measure
is a limit of a sequence of laws. Aside from this open problem, other
directions of research are also mentioned. We work out in detail a number of
results and examples, some of which are new, and others that have been
previously stated without proofs. These results include a new characterization
of laws of finite connected graphs, a description of the topological space of
paths, and a proof that the compact space of weak limits of laws is convex.
