K-Scaffold Subgraphs of Complex Networks

Complex networks with high numbers of nodes or links are often difficult to analyze. 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.