  We describe two kinds of regular invariant measures on the boundary path
space of a second countable topological graph, which allows us to describe all
extremal tracial weights on the graph C$^{*}$-algebra which are not
gauge-invariant. Using this description we prove that all tracial weights on
the C$^{*}$-algebra of a second countable topological graph are gauge-invariant
when the graph is free. This in particular implies that all tracial weights are
gauge-invariant when the graph C$^{*}$-algebra is simple and separable.
