Federico Musciotto, Luca Marotta, Salvatore Miccichè, Rosario N. Mantegna

Proximity based networks are widely used in many econophysics investigations. Here we evaluate the robustness of minimum spanning trees and of planar maximally filtered graphs by performing bootstrap sampling of the analyzed data. The bootstrap validation confirms the robustness of the proximity based network estimation and highlights both the links that are statistically robust and the links that have a poor bootstrap frequency, i.e. those links that are not often detected in bootstrap replicas. The bootstrap is performed with two distinct approaches and the difference between them is discussed.