2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138518Complex 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.5 pages, 3 figures. Published in EuroPhysics Letters 2007 EPL 77 18004, doiPhysics and Societytext