What sort of leds are you talking about? just plain LED's or LED lamp fittings? The diagram isn't clear either. It has two contacts on the led not four!
If you are talking about just plain LED's which are about 2v, I think you are connecting the leds in series in the first diagram and in parallel in the second. It is more normal to do a combination of the two to avoid problems. You place say four in series with a resistor so that they will run off 12V, then repeat that connecting each one in parallel for how many times you need. The reason for this is the losses with 12V are less significant than with 2V so the cables connecting them can be longer and if they are all just in series then it can be difficult to find an appropriate power supply. You can though go to a maximum of say 24V before it starts getting a tad dangerous ( will make the kids scream if they stick it in their mouth! ). If the LEDs are far apart then I would just put a resister on each one and place them all in parallel.