Your animations are really smooth and flow pretty nicely, but the actual movement isn't necessarily as realistic as it could be. When a four legged animal runs, the back feet hit the ground first, not the front feet. You should try animating that kind of movement and see how it feels.
That diagram is pretty accurate, but it starts off at a weird place in the cycle. At the end, you can kind of see how the front leg is coming down just as the back leg is lifting up, although if you look at slow motion videos of dogs or horses running, you can see a little more clearly that the front legs usually touch the ground before the back legs lift up again. This is because the back legs (at least in horses) tend to do most of the pushing and the front legs are a secondary support to keep the body level until the animal's feet touch the ground again.