A notification platform for distribution of notification content in an on-line social network system, on-line and in near real time, is described. As a new notification is detected in the continuous stream of notifications triggered by time-sensitive events, the near real time notifications distribution system determines member profiles representing potential recipients of the notification by traversing a relationship graph. The relationship graph has nodes representing member profiles, as well as other entities maintained in the on-line social network system. The edges of the relationship graph represent relationships between entities represented by the associated nodes. For each member profile representing a potential recipient of the notification, the near real time notifications distribution system generates a relevance score, which is used to determine whether the notification is to be delivered to the potential recipient.