  Based on the formation of triad junctions, the proposed mechanism generates
networks that exhibit extended rather than single power law behavior. Triad
formation guarantees strong neighborhood clustering and community-level
characteristics as the network size grows to infinity. The asymptotic behavior
is of interest in the study of directed networks in which (i) the formation of
links cannot be described according to the principle of preferential
attachment; (ii) the in-degree distribution fits a power law for nodes with a
high degree and an exponential form otherwise; (iii) clustering properties
emerge at multiple scales and depend on both the number of links that newly
added nodes establish and the probability of forming triads; and (iv) groups of
nodes form modules that feature less links to the rest of the nodes.
