We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and increasing average degree as a function of the network size. Our experiments are based on three Twitter at-mention networks and three more from the Koblenz Network Collection. We observe that popular network models cannot explain decreasing power-law degree distribution exponent and increasing average degree at the same time. We propose a model that is the combination of exponential growth, and a power-law developing network, in which new "homophily" edges are continuously added to nodes proportional to their current homophily degree. Parameters of the average degree growth and the power-law degree distribution exponent functions depend on the ratio of the network growth exponent parameters. Specifically, we connect the growth of the average degree to the decreasing exponent of the power-law degree distribution. Prior to our work, only one of the two cases were handled. Existing models and even their combinations can only reproduce some of our key new observations in growing information networks.