  In this paper we provide numerical evidence of the richer behavior of the
connectivity degrees in heterogeneous preferential attachment networks in
comparison to their homogeneous counterparts. We analyze the degree
distribution in the threshold model, a preferential attachment model where the
affinity between node states biases the attachment probabilities of links. We
show that the degree densities exhibit a power-law multiscaling which points to
a signature of heterogeneity in preferential attachment networks. This
translates into a power-law scaling in the degree distribution, whose exponent
depends on the specific form of heterogeneity in the attachment mechanism.
