I’m interested in reconstructing networks/graphs where information is distributed via a gossip/epidemic/rumour protocol where each peer/node sends information to all of its neighbours, so that any piece of information eventually floods the network. Any peer can propagate new information. The number of neighbours of each peer should be much less than the total number of peer.

By connecting to all peers, we can measure the time that each peer sends a piece of information. Hopefully we can use that data to reconstruct the network, i.e. work out which peers are connected to which other peers.

Is anyone aware of research that has been done in this area? I’ve found quite a bit on locating the source of the information given this setup, but I’m really interested in reconstructing the graph.