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Is there any software which will give me a graphical representation of the dependency relationships between all packages installed on my system? That would make it easier for me to optimize my system by pruning large branches that provided few applications.
I don't know of a graphical software, but you might be able to write a script using dpkg --get-selections and apt-cache depends packagename, then count up then number of times each package appears on a line starting with "Depends:". Then you could probably use apt-cache whatdepends packagename on the earlier results and compare which packages are on your system.