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Does anyone knows If there is a way to calculate Geary's index of spatial autocorrelation on open source gis?

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You might want to take a look at this question (How to implement Spatial Autocorrelation using QGIS or PostgreSQL (or any free application)?) and look at programmatic solutions like R. QGIS may be another option as well.

This website outlines different formulas and measures for spatial autocorrelation that may also be of interest to you

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You can also use:

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