Specific constructions

This chapter presents network-generating models which cannot be neatly categorized as growing, nor as defined primarily through a target degree distribution. They are best understood as mechanistic constructions designed to elucidate a particular feature of the network. In the first sub-section, the Watts–Strogatz model is introduced and motivated as a construction to achieve both a high degree of clustering and a low average path length. Geometric graphs, in their Euclidian flavour, are shown to be a natural choice for broadcast networks. The Hyperbolic variant is informally described, because it is known to be a natural space in which to embed hierarchical graphs. Planar graphs have very specific real-world applications, but are extraordinarily challenging to analyze mathematically. Finally, weighted graphs allow for concepts such as traffic to be incorporated into the random graph model.