We propose a novel peer-to-peer (P2P) distributed control architecture for the shared haptic interaction among remotely located users over partially connected and undirected unreliable Internet communication network with varying delay, packet loss, data swapping/duplication, etc. Each user simulates and interacts with their own local copy of the shared deformable virtual object (for haptic responsiveness against latency), while these local copies are synchronized via a proportional-derivative type consensus control over the Internet communication network (for haptic experience consistency among the users). Our proposed architecture enforces passivity, thereby, rendering itself to be interaction stable, portable, and scalable for heterogeneous (passive) users and devices. Configuration consensus among the local copies and force balance among the users are also shown. The issue of optimizing communication network topology is also addressed with some relevant experimental results.