  Complex networks with high numbers of nodes or links are often difficult to
analyse. However, not all elements contribute equally to their structural
patterns. A small number of elements (the hubs) seem to play a particularly
relevant role in organizing the overall structure around them. But other parts
of the architecture (such as hub-hub connecting elements) are also important.
In this letter we present a new type of substructure, to be named the
$K$-scaffold subgraph, able to capture all the essential network components.
Their key features, including the so called critical scaffold graph, are
analytically derived.
