Fig. 3

Impact of node attribute-based noise on the representation of minority nodes in rankings on synthetic networks. We visualize the fraction of minority in the top 1% (top 100) nodes as a function of the retain parameter \(\rho\). Note that low values of \(\rho\) correspond to a strong noise (noise decreases from left to right in every subplot). We increase the homophily parameter h from the leftmost to the rightmost panel. The main plots show the representation of the minority in a degree-based ranking while the insets show the impact of \(\rho\) on the number of edges in the network. We can see that in heterophilic regimes the original minority representation is already affected by relatively weak noise. In contrast, the representation in homophilic regimes is only affected for much stronger noise. This shows that node attribute-based, systematic noise can have a variety of effects which depends on the homophily of the network