Investigating the structure of star-forming regions using INDICATE
  The ability to make meaningful comparisons between theoretical and
observational data of star-forming regions is key to understanding the star
formation process. In this paper we test the performance of INDICATE, a new
method to quantify the clustering tendencies of individual stars in a region,
on synthetic star-forming regions with sub-structured, and smooth, centrally
concentrated distributions. INDICATE quantifies the amount of stellar
affiliation of each individual star, and also determines whether this
affiliation is above random expectation for the star-forming region in
question. We show that INDICATE cannot be used to quantify the overall
structure of a region due to a degeneracy when applied to regions with
different geometries. We test the ability of INDICATE to detect differences in
the local stellar surface density and its ability to detect and quantify mass
segregation. We then compare it to other methods such as the mass segregation
ratio $\Lambda_{\rm{MSR}}$, the local stellar surface density ratio
$\Sigma_{\rm{LDR}}$ and the cumulative distribution of stellar positions.
INDICATE detects significant differences in the clustering tendencies of the
most massive stars when they are at the centre of a smooth, centrally
concentrated distribution, corresponding to areas of greater stellar surface
density. When applied to a subset of the 50 most massive stars we show INDICATE
can detect signals of mass segregation. We apply INDICATE to the following
nearby star-forming regions: Taurus, ONC, NGC 1333, IC 348 and $\rho$ Ophiuchi
and find a diverse range of clustering tendencies in these regions.
