“…On one hand, in the presence of noisy network generation, there are many empirical studies (Lakhina et al, 2003, Banerjee et al, 2013, Breza et al, 2020, Zhu and Yang, 2020 and many that try to estimate or recover the true network without involving centrality (Butts, 2003, Handcock and Gile, 2010, Chandrasekhar and Lewis, 2011, Le et al, 2018, Newman, 2018, Rohe, 2019. On the other hand, many researchers focus on the network regression model with centralities while ignoring the noise of the centrality estimation inherited from the noise of the network (Ahern, 2013, Hochberg et al, 2007, Shao et al, 2018, Richmond, 2019, Allen et al, 2019, Liu, 2019, Banerjee et al, 2019, Bovet and Makse, 2019, Fogli and Veldkamp, 2021.…”