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Scale-free power law structure describes complex networks derived from a widerange of real world processes. The extensive literature focuses almostexclusively on networks with power law exponent strictly larger than 2, whichcan be explained by constant vertex growth and preferential attachment. Thecomplementary scale-free behavior in the range between 1 and 2 has been mostlyneglected as atypical because there is no known generating mechanism to explainhow networks with this property form. However, empirical observations revealthat scaling in this range is an inherent feature of real world networksobtained from repeated interactions within a population, as in social,communication, and collaboration networks. A generative model explains theobserved phenomenon through the realistic dynamics of constant edge growth anda positive feedback mechanism. Our investigation, therefore, yields a novelempirical observation grounded in a strong theoretical basis for itsoccurrence.

Atypical scaling behavior persists in real world interaction networks