Counting road intersections and blocks

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I have a shp file that consists of the road system of Mexico City. I would like to count the number of road intersections (crossings) and blocks (which I would define as a segment starting from one intersection and ending in another). This within a buffer of a certain size: a circle centered in a polygon within another shp file.

I am mainly using ArcGIS but am quite familiar with R, Python and QGIS if the solution is simpler on any of those. I realize their are a few similar questions around here but havent been able to use any of the information provided there.



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