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Given a positive function on the set of edges of an arbitrary directed graph$E=(E^0,E^1)$, we define a one-parameter group of automorphisms on theC*-algebra of the graph $C^*(E)$, and study the problem of finding KMS statesfor this action. We prove that there are bijective correspondences between KMSstates on $C^*(E)$, a certain class of states on its core, and a certain classof tracial states on $C_0(E^0)$. We also find the ground states for this actionand give some examples.

KMS states for the generalized gauge action on graph algebras