Final answer:
The nerve branch network that supplies the head, neck, upper chest, and shoulder is the cervical plexus.
Step-by-step explanation:
The nerve branch network that supplies the head, neck, upper chest, and shoulder is the cervical plexus. The cervical plexus is composed of axons from spinal nerves C1 through C5 and branches into nerves in the posterior neck and head. In addition, it includes the phrenic nerve, which connects to the diaphragm. Therefore, the correct answer is b) Cervical plexus.