  In this extended abstract, we present a simple approach to convergence on
term graphs that allows us to unify term graph rewriting and infinitary term
rewriting. This approach is based on a partial order and a metric on term
graphs. These structures arise as straightforward generalisations of the
corresponding structures used in infinitary term rewriting. We compare our
simple approach to a more complicated approach that we developed earlier and
show that this new approach is superior in many ways. The only unfavourable
property that we were able to identify, viz. failure of full correspondence
between weak metric and partial order convergence, is rectified by adopting a
strong convergence discipline.
