Abstract
In this paper we present a framework for the extension of the Barabási-Albert model to heterogeneous complex networks. We define a class of heterogeneous preferential attachment models where node properties are described by fixed states in an arbitrary space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the degree distributions in heterogeneous preferential attachment networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in the presence of heterogeneity.