Though centrality of vertices in social networks has been extensively studied, all past efforts assume that centrality of a vertex solely depends on the structural properties of graphs. However, with the emergence of online "semantic" social networks where vertices have properties (e.g. gender, age, and other demographic data) and edges are labeled with relationships (e.g. friend, follows) and weights (measuring the strength of a relationship), it is essential that we take semantics into account when measuring centrality. Moreover, the centrality of a vertex should be tied to a diffusive property in the network - a Twitter vertex may have high centrality w.r.t. jazz, but low centrality w.r.t. Republican politics. In this paper, we propose a new notion of diffusion centrality (DC) in which semantic aspects of the graph, as well as a diffusion model of how a diffusive property p is spreading, are used to characterize the centrality of vertices. We present a hypergraph based algorithm to compute DC and report on a prototype implementation and experiments showing how we can compute DCs (using real YouTube data) on social networks in a reasonable amount of time. We compare DC with classical centrality measures like degree, closeness, betweenness, eigenvector and stress centrality and show that in all cases, DC produces higher quality results. DC is also often faster to compute than both betweenness, closeness and stress centrality, but slower than degree and eigenvector centrality.