Could a scientist use the internet to detect gravitational waves? According to my understanding (I'm not a physicist just a fan), LIGO measures the changes in two path's lengths to detect gravitational waves by sending a particle down each path at the constant speed of light and measuring the time it takes. In networking, we use pings to measure how long a packet takes to reach a destination. Could the ping be used like LIGO to detect gravitational waves? Of course, this wouldn't be as accurate as LIGO, but the internet is a massive and (essentially) free infrastructure so you could use averages to compensate for errors.
 A: Gravitational waves are tidal effects so they cause a very small difference in forces acting on  two freely-suspended masses separated  by a few kilometers.  
LIGO uses  its intereferometer to detect the relative motion of the two masses due to to the different gravitational forces that they experience. It is not using the interferometer to measure redshifts or a difference in elapsed time.
The ends of an optical fibre are not freely suspended so you cannot measure the forces although you could ask about time delays due to redshifts.
Indeed  you can use elapsed time measurements to detect gravitational effects. High-precision atomic clocks can detect the  $(\Delta t)/t =gh/c^2$  elapsed time difference between two clocks with $h= 1$m of vertical separation after running for a day.  However it is much easier to measure the same $gh$ potential  difference by using a spring balance or a pendulum to find $g$ and a meter stick to find $h$.  LIGO is like the pendulum and meterstick but still has a hard time to detect the waves. Imagine how much harder it would be using timing differences.      
