Minimal spanning tree analysis

Minimal spanning tree analysis (Cartwright & Whitworth 2004; Cartwright et al. 2011) investigates the spatial distribution of a point pattern with focus on small scales, comparable to nearest neighbor analysis but with somewhat different properties. Two columns of x/y coordinates in a rectangular domain are expected. The method is based on a histogram of all the lengths of line segments in the minimal spanning tree (MST). The MST itself can be plotted in the XY graph module (Plot menu).

The expected curve from a random point pattern (blue curve) and its 95% confidence interval (red curves) are computed from 1000 Monte Carlo simulations of complete spatial randomness (CSR) in a rectangle of the same dimensions as the bounding rectangle of the original data. Thus, segment lengths where the histogram from the data (black curve) exceeds the upper red curve, have significantly higher frequencies than expected from a random pattern.

An overall significance test is based on the observed total mean length compared with the expected mean length from the Monte Carlo simulations.

The number of bins can be set by the user and should be small to reduce noise, but large enough to capture details.

The “Residual” option flattens the curves on the expected mean (blue curve), i.e. the expected mean is subtracted from the curves at all distances. This can make the figure clearer especially when the confidence interval is narrow.

A comparison between nearest neighbour and minimal spanning tree analysis for a geological data set is given by Cartwright et al. (2011).


Cartwright, A. & Whitworth, A.P. 2004. The statistical analysis of star clusters. Monthly Notices of the Royal Astronomical Society 348:589-597

Cartwright, A., Moss, J. & Cartwright, J. 2011. New statistical methods for investigating submarine pockmarks. Computers & Geosciences 37:1595-1601.

Published Aug. 31, 2020 8:57 PM - Last modified Aug. 31, 2020 8:57 PM