KMS weights on graph C⁎-algebras

The paper contains a study of the gauge invariant KMS weights for a generalized gauge action on a graph C⁎-algebra. When the graph is irreducible and has the property that there are at most countably many roads to infinity in the graph, a complete description is given of the structure of KMS weights for the gauge action. The structure is very rich and is identical with the structure of KMS states for the restriction of the action to any corner defined by a projection in the fixed point algebra.