  Many systems in nature, society and technology can be described as networks,
where the vertices are the system's elements and edges between vertices
indicate the interactions between the corresponding elements. Edges may be
weighted if the interaction strength is measurable. However, the full network
information is often redundant because tools and techniques from network
analysis do not work or become very inefficient if the network is too dense and
some weights may just reflect measurement errors, and shall be discarded.
Moreover, since weight distributions in many complex weighted networks are
broad, most of the weight is concentrated among a small fraction of all edges.
It is then crucial to properly detect relevant edges. Simple thresholding would
leave only the largest weights, disrupting the multiscale structure of the
system, which is at the basis of the structure of complex networks, and ought
to be kept. In this paper we propose a weight filtering technique based on a
global null model (GloSS filter), keeping both the weight distribution and the
full topological structure of the network. The method correctly quantifies the
statistical significance of weights assigned independently to the edges from a
given distribution. Applications to real networks reveal that the GloSS filter
is indeed able to identify relevantconnections between vertices.
