This paper focuses on argumentation graphs whose nodes are arguments and edges represent supports, thus positive relations, between arguments. Furthermore, each argument has a weight reflecting its basic or intrinsic strength. For the sake of generality, the internal structure of arguments and the origin of arguments and their weights are unspecified. The paper tackles for the first time the question of evaluating the overall strengths of arguments in such graphs, thus of defining semantics for support graphs. It introduces a set of axioms that any semantics should satisfy. Then, it defines three semantics and evaluates them against the axioms.