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We quantify the structure of a very large number of Galactic open clustersand look for evidence of mass segregation for the most massive stars in theclusters. We characterise the structure and mass segregation ratios of 1276clusters in the Milky Way Stellar Cluster (MWSC) catalogue containing each atleast 40 stars and that are located at a distance of up to $\approx 2$ kpc fromthe Sun. We use an approach based on the calculation of the minimum spanningtree of the clusters, and for each one of them, we calculate the structureparameter \Q\ and the mass segregation ratio $\Lambda_{\rm MSR}$. Our findingsindicate that most clusters possess a \Q\ parameter that falls in the range0.7-0.8 and are thus neither strongly concentrated nor do they show significantsubstructure. Only 27\% can be considered centrally concentrated with \Q\values $> 0.8$. Of the 1276 clusters, only 14\% show indication of significantmass segregation ($\Lambda_{\rm MSR} > 1.5$). Furthermore, no correlation isfound between the structure of the clusters or the degree of mass segregationwith their position in the Galaxy. A comparison of the measured \Q\ values forthe young open clusters in the MWSC to N-body numerical simulations that followthe evolution of the \Q\ parameter over the first 10 Myrs of the clusters lifesuggests that the young clusters found in the MWSC catalogue initiallypossessed local mean volume densities of $\rho_{*} \approx 10-100$ M$_{\odot}$pc$^{-3}$.

Structure and mass segregation in Galactic stellar clusters