Discovering Bitcoin network topology For a research I am doing I would love to have a graph with the network of reachable Bitcoin nodes. Active reachable nodes can be extracted by using getaddr messages (e.g. bitnodes project). However direct inbound/outbounds connections cannot be discovered at least you have access to the node and you can run the RPC command getpeerinfo. 

Is there any way to get a detailed graph of the network?
No, due to different reasons.

First, the network is always in flux, nodes are appearing and disappearing, and connections are even more dynamic, so even if there were an API you could use to ask a node for its connections, that information would be outdated quickly.

Second, privacy is part of the reason why crypto currencies exist. Divulging the list of peers of every node would run counter to this goal, so node software would be ill-designed if it provided such an interface.