Connection Map
A connection map allows to show the connection between several positions on a map. The link between 2 places can be drawn with a straight line, or more commonly using great circles: the shortest route between them. The earth beeing a sphere, it results in arcs that give a really pleasant look to the map.
Background map with Basemap
Basemap is probably the best option to draw a connection map with python. It provides a function calleddrawgreatcircle() that draws the connection using great circles. Great circles are arcs that gives a better appearance than straight lines.
This is the result when you visualize the connection between 7 major world cities:
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