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Plotting graph on top of World map

I'm trying to plot a graph representing a P2P network on top of a world map. I want to be able to draw vertices and edges, and it has to work with several thousands of veritces/edges on a map.

Is there a python library that allows me to do so?

The matplotlib package with the basemap toolkit might work for you. See here for some examples of its use.

You could use the canvas object in the tkinter library for basic drawing. http://effbot.org/tkinterbook/canvas.htm

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