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 \mathcal { Q } and the mass segregation ratio \Lambda _ { MSR } .
Our findings indicate that most clusters possess a \mathcal { 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 \mathcal { Q } values > 0.8 .
Of the 1276 clusters , only 14 % show indication of significant mass segregation ( \Lambda _ { 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 \mathcal { Q } values for the young open clusters in the MWSC to N-body numerical simulations that follow the evolution of the \mathcal { 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 } .