  In this contribution we discuss some approaches of network analysis providing
information about single links or single nodes with respect to a null
hypothesis taking into account the heterogeneity of the system empirically
observed. With this approach, a selection of nodes and links is feasible when
the null hypothesis is statistically rejected. We focus our discussion on
approaches using (i) the so-called disparity filter and (ii) statistically
validated network in bipartite networks. For both methods we discuss the
importance of using multiple hypothesis test correction. Specific applications
of statistically validated networks are discussed. We also discuss how
statistically validated networks can be used to (i) pre-process large sets of
data and (ii) detect cores of communities that are forming the most close-knit
and stable subsets of clusters of nodes present in a complex system.
