Besides the random initializing the centroids, what could a reason for this bizarre graph(1st one) that it has given? I am yet to understand this simple algorithm to full extent.
If you choose the right-bottom-most two objects as starting points, the centers will remain stuck there, and never move to the top right.
The green points are closest to the green center, and will remain there.
This is a common problem with k-means because of random starting. A heuristic such as k-means++ is less likely to choose this starting situation.