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 by

representing the ‘great circle‘: the shortest route between them. Knowing that the earth is a sphere, this results in rounded lines that give a really pleasant look to the map.

Python is an awesome tool to draw such a map due to the drawgreatcircle function of the basemap library.