Here's a diagram of the Circle of Willis (after Thomas Willis, 17th century anatomist).
Blood reaches the brain via 2 major arterial systems - the carotid arteries (which enter at the front) and the vertebral arteries (which enter from the back). These arterial inputs are linked together in a circle so that blood can be shunted from left to right and front to back and vice versa keeping the flow steady. The ability of this system to compensate for vascualr disease means that it is not uncommon to see patients with a carotid artery that is completely blocked on one side. The brain on that side is receiving blood shunted across the Circle of Willis from the carotid on the other side, and from the vertebral arteries behind.
The posterior communicating arteries are part of this circle, but their absence, in the absence of any other disease, is not harmful.

(From Henry Gray (1825–1861). Anatomy of the Human Body. 1918)
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