  In this paper we present a framework for the extension of the preferential
attachment (PA) model to heterogeneous complex networks. We define a class of
heterogeneous PA models, where node properties are described by fixed states in
an arbitrary metric space, and introduce an affinity function that biases the
attachment probabilities of links. We perform an analytical study of the
stationary degree distributions in heterogeneous PA 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 presence of heterogeneity.
