Power in graphs with classes

We introduce a new family of power indices for nodes in graphs with classes. We provide an axiomatic characterization of this family and prove the independence of the axioms. Furthermore, we show that these indices coincide with the Shapley values of a family of subadditive transferable-utility games defined on such graphs. These normative results yield a general framework for quantifying structural influence in complex networks. In particular, we identify the normative conditions under which power in technological sharing networks can be represented by our family of indices. Importantly, the proposed axiomatic framework also applies to influence flows that generate negative effects.