  Complex networks in natural, social, and technological systems generically
exhibit an abundance of rich information. Extracting meaningful structural
features from data is one of the most challenging tasks in network theory. Many
methods and concepts have been proposed to address this problem such as
centrality statistics, motifs, community clusters, and backbones, but such
schemes typically rely on external and arbitrary parameters. It is unknown
whether generic networks permit the classification of elements without external
intervention. Here we show that link salience is a robust approach to
classifying network elements based on a consensus estimate of all nodes. A wide
range of empirical networks exhibit a natural, network-implicit classification
of links into qualitatively distinct groups, and the salient skeletons have
generic statistical properties. Salience also predicts essential features of
contagion phenomena on networks, and points towards a better understanding of
universal features in empirical networks that are masked by their complexity.
