Tracial weights on topological graph algebras

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${}^{\ast }$-algebra which are not gauge-invariant. Using this description we prove that all tracial weights on the C${}^{\ast }$-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${}^{\ast }$-algebra is simple and separable.