  We introduce the Graph TT (GTT) and Graph OSPA (GOSPA) metrics based on
optimal assignment, which allow us to compare not only the edge structures but
also general vertex and edge attributes of graphs of possibly different sizes.
We argue that this provides an intuitive and universal way to measure the
distance between finite simple attributed graphs. Our paper discusses useful
equivalences and inequalities as well as the relation of the new metrics to
various existing quantifications of distance between graphs. By deriving a
representation of a graph as a pair of point processes, we are able to
formulate and study a new type of (finite) random graph convergence and
demonstrate its applicability using general point processes of vertices with
independent random edges. Computational aspects of the new metrics are studied
in the form of an exact and two heuristic algorithms that are derived from
previous algorithms for similar tasks. As an application, we perform a
statistical test based on the GOSPA metric for functional differences in
olfactory neurons of Drosophila flies.
