  Though algorithms promise many benefits including efficiency, objectivity and
accuracy, they may also introduce or amplify biases. Here we study two
well-known algorithms, namely PageRank and Who-to-Follow (WTF), and show to
what extent their ranks produce inequality and inequity when applied to
directed social networks. To this end, we propose a directed network model with
preferential attachment and homophily (DPAH) and demonstrate the influence of
network structure on the rank distributions of these algorithms. Our main
findings suggest that (i) inequality is positively correlated with inequity,
(ii) inequality is driven by the interplay between preferential attachment,
homophily, node activity and edge density, and (iii) inequity is driven by the
interplay between homophily and minority size. In particular, these two
algorithms reduce, replicate and amplify the representation of minorities in
top ranks when majorities are homophilic, neutral and heterophilic,
respectively. Moreover, when this representation is reduced, minorities may
improve their visibility in the rank by connecting strategically in the
network. For instance, by increasing their out-degree or homophily when
majorities are also homophilic. These findings shed light on the social and
algorithmic mechanisms that hinder equality and equity in network-based ranking
and recommendation algorithms.
