Hairball Graphs (data)
A simple model generating random graphs with cohesive groups that are connected into a small world is the planted partition model (PPM).
Let be a partition of $V$ for a graph . Then is called a clustering of with class for a vertex . The probability of an edge is if and if .
We generated 50 graphs from a PPM with vertices, , , and . On top of that, we ran a random noise model with to obfuscate the underlying groups. The resulting graphs are very dense, have a low diameter, and are real hairballs without any visible structure when laid out using force-directed methods.