  Scale-free power law structure describes complex networks derived from a wide
range of real world processes. The extensive literature focuses almost
exclusively on networks with power law exponent strictly larger than 2, which
can be explained by constant vertex growth and preferential attachment. The
complementary scale-free behavior in the range between 1 and 2 has been mostly
neglected as atypical because there is no known generating mechanism to explain
how networks with this property form. However, empirical observations reveal
that scaling in this range is an inherent feature of real world networks
obtained from repeated interactions within a population, as in social,
communication, and collaboration networks. A generative model explains the
observed phenomenon through the realistic dynamics of constant edge growth and
a positive feedback mechanism. Our investigation, therefore, yields a novel
empirical observation grounded in a strong theoretical basis for its
occurrence.
