# Hairball Graphs (data)

## Dataset Description

A simple model generating random graphs with cohesive groups that are connected into a small world is the planted partition model (PPM).

Let $\mathcal{C}=\{C_1, \ldots, C_k\}$ be a partition of $V$ for a graph G = (V,E). Then $\mathcal{C}$ is called a clustering of G with class $c(v) \in \mathcal{C}$ for a vertex $v\in V$. The probability of an edge (u,v) is pin if c(u) = c(v) and pout if $c(u)\neq c(v)$.

$p(u,v)=\begin{cases} p_\text{in} &\mbox{if } c(u)=c(v) \text{ (intra-cluster)}\\ p_\text{out} & \mbox{if } c(u)\neq c(v) \text{ (inter-cluster)} \end{cases}.$

We generated 50 graphs from a PPM with 500 vertices, k = 9, pin = 0.3, and pout = 0.01. On top of that, we ran a random noise model with pin = pout = 0.1 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.