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Much of the structure in social networks has been explained by two seeminglyindependent network evolution mechanisms: triadic closure and homophily. Whileit is common to consider these mechanisms separately or in the frame of astatic model, empirical studies suggest that their dynamic interplay is thevery process responsible for the homophilous patterns of association seen inoff- and online social networks. By combining these two mechanisms in a minimalsolvable dynamic model, we confirm theoretically the long-held and empiricallyestablished hypothesis that homophily can be amplified by the triadic closuremechanism. This research approach allows us to estimate how much of theobserved homophily in various friendship and communication networks is due toamplification for a given amount of triadic closure. We find that thecumulative advantage-like process leading to homophily amplification can, undercertain circumstances, also lead to the widely documented core-peripherystructure of social networks, as well as to the emergence of memory of previoushomophilic constraints (equivalent to hysteresis phenomena in physics). Thetheoretical understanding provided by our results highlights the importance ofearly intervention in managing at the societal level the most adverse effectsof homophilic decision-making, such as inequality, segregation and online echochambers.

Cumulative effects of triadic closure and homophily in social networks