Structure and mass segregation in Galactic stellar clusters
  We quantify the structure of a very large number of Galactic open clusters
and look for evidence of mass segregation for the most massive stars in the
clusters. We characterise the structure and mass segregation ratios of 1276
clusters in the Milky Way Stellar Cluster (MWSC) catalogue containing each at
least 40 stars and that are located at a distance of up to $\approx 2$ kpc from
the Sun. We use an approach based on the calculation of the minimum spanning
tree of the clusters, and for each one of them, we calculate the structure
parameter \Q\ and the mass segregation ratio $\Lambda_{\rm MSR}$. Our findings
indicate that most clusters possess a \Q\ parameter that falls in the range
0.7-0.8 and are thus neither strongly concentrated nor do they show significant
substructure. Only 27\% can be considered centrally concentrated with \Q\
values $> 0.8$. Of the 1276 clusters, only 14\% show indication of significant
mass segregation ($\Lambda_{\rm MSR} > 1.5$). Furthermore, no correlation is
found between the structure of the clusters or the degree of mass segregation
with their position in the Galaxy. A comparison of the measured \Q\ values for
the young open clusters in the MWSC to N-body numerical simulations that follow
the evolution of the \Q\ parameter over the first 10 Myrs of the clusters life
suggests that the young clusters found in the MWSC catalogue initially
possessed local mean volume densities of $\rho_{*} \approx 10-100$ M$_{\odot}$
pc$^{-3}$.
