  We discuss three related models of scale-free networks with the same degree
distribution but different correlation properties. Starting from the
Barabasi-Albert construction based on growth and preferential attachment we
discuss two other networks emerging when randomizing it with respect to links
or nodes. We point out that the Barabasi-Albert model displays dissortative
behavior with respect to the nodes' degrees, while the node-randomized network
shows assortative mixing. These kinds of correlations are visualized by
discussig the shell structure of the networks around their arbitrary node. In
spite of different correlation behavior, all three constructions exhibit
similar percolation properties.
