UCINET is a Windows program. To run it on another platform you will need a Windows partition (such as Boot Camp), a Windows emulator (such as VMware Fusion or Parallels), or a "compatibility layer" such as Wine. Boot Camp and the emulators work best: Wine does not allow full functionality (such as calling Excel from within UCINET, or using shortcut keys) but it is free. Here are instructions for running UCINET with Wine.
You need download two pieces of software in addition UCINET: XQuartz and WineBottler