  Much of the structure in social networks has been explained by two seemingly
independent network evolution mechanisms: triadic closure and homophily. While
it is common to consider these mechanisms separately or in the frame of a
static model, empirical studies suggest that their dynamic interplay is the
very process responsible for the homophilous patterns of association seen in
off- and online social networks. By combining these two mechanisms in a minimal
solvable dynamic model, we confirm theoretically the long-held and empirically
established hypothesis that homophily can be amplified by the triadic closure
mechanism. This research approach allows us to estimate how much of the
observed homophily in various friendship and communication networks is due to
amplification for a given amount of triadic closure. We find that the
cumulative advantage-like process leading to homophily amplification can, under
certain circumstances, also lead to the widely documented core-periphery
structure of social networks, as well as to the emergence of memory of previous
homophilic constraints (equivalent to hysteresis phenomena in physics). The
theoretical understanding provided by our results highlights the importance of
early intervention in managing at the societal level the most adverse effects
of homophilic decision-making, such as inequality, segregation and online echo
chambers.
