  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.
