  We describe two different bootstrap methods applied to the detection of a
minimum spanning tree obtained from a set of multivariate variables. We show
that two different bootstrap procedures provide partly distinct information
that can be highly informative about the investigated complex system. Our case
study, based on the investigation of daily returns of a portfolio of stocks
traded in the US equity markets, shows the degree of robustness and
completeness of the information extracted with popular information filtering
methods such as the minimum spanning tree and the planar maximally filtered
graph. The first method performs a "row bootstrap" whereas the second method
performs a "pair bootstrap". We show that the parallel use of the two methods
is suggested especially for complex systems presenting both a nested
hierarchical organization together with the presence of global feedback
channels.
