  An explicitly-gauge-invariant expansion in powers of $e/\hbar$ times the
magnetic flux density is formally obtained for the density of states (as
characterized by the trace of the resolvent $\widehat G$ = $(\omega - \hat
h)^{-1}$) of a charged particle moving on a Hermitian quantum network that is
embedded in a Euclidean background that supports a uniform magnetic flux
density. The explicit expressions, given here up to third order in the flux
density, are also valid for the ``local trace'' (the trace of $\widehat P_i
\widehat G$, where $\widehat P_i$ is the projector on a network node), and do
not appear to have been previously given.
