Clarity on ROS Master

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I have been intrigued by an aspect of the ROS Master that is not clear to me..

From ros.org

  "The ROS Master provides naming and registration servicesto the rest of the nodes 
  in the ROS system. It tracks publishers and subscribers to topics as well as
  services. The role of the Master is to enable individual ROS nodes to locate one
  another. Once these nodes have located each other they communicate with each other
  peer-to-peer."

There is also a great picture here:

My Question is:

I understand the ROS Master to be a very lightweight tool for the naming and coordination between ROS Nodes / Topics / Services etc.. The pictures and descriptions seem to entail that when information is given to a viewer or subscriber that the connection is there on only a peer-to-peer connection, where does the ROS Master fit into the peer-to-peer connection in order to know if the connection persists or even connected in the first place?