A computer network in which some of the links between nodes are carried by open connections or virtual circuits in a larger network, such as the internet, instead of by physical wires is a

A virtual private network carries some links over open connections or virtual circuits in a larger public network like the internet.

Virtual public network is not the standard name for this private, tunnelled arrangement.

Virtual private net is an incomplete form and not the accepted term.

Virtual public net is likewise not a real networking term.

A VPN encrypts traffic so a shared public link behaves like a private line.

VPNs are widely used for secure remote access to an organisation's resources.