  Many data-rich industries are interested in the efficient discovery and
modelling of structures underlying large data sets, as it allows for the fast
triage and dimension reduction of large volumes of data embedded in high
dimensional spaces. The modelling of these underlying structures is also
beneficial for the creation of simulated data that better represents real data.
In particular, for systems testing in cases where the use of real data streams
might prove impractical or otherwise undesirable. We seek to discover and model
the structure by combining methods from topological data analysis with
numerical modelling. As a first step in combining these two areas, we examine
the recovery of the abstract graph $G$ structure, and model a linear embedding
$|G|$ given only a noisy point cloud sample $X$ of $|G|$.
