Here's the effect I'm going for, maybe a bit more glow and lines do not need to arc like that: http://image.shutterstock.com/display_pic_with_logo/504532/504532,1275 514960,1/stock-photo--d-illustration-render-of-a-global-network-focus- on-europe-54442234.jpg
I'm having a couple of problems: 1) if I put the network lines on the map it looks too flat so I think I need to apply them to a slightly larger invisible sphere; 2) when I add a blur/outer glow to the lines they do not wrap cleanly on the sphere, they kind of break up and distort. Plain lines do not seem to have this problem but objects with effects do.
Any tips on how to do this? Thanks!
I'm sure the lines in your examples were drawn individually with the pen tool but for the lines below the sphere in the second example you can use the arc tool and draw a bunch of random lines with it in one go if you hold the ~ key on your keyboard when you drag with the arc tool. this is how I made the lines on the image below in one second, then I used the eraser tool to make the ends uneven and added some glowing dots which I had to duplicate on top of each other to increase the glow.