a bitcoin full node is normally "relaying" lots of transactions. another node that is connected to your node has no way of knowing whether a transaction that your node send it was originated from your node (if it is your transaction) or is it just another transaction that it received from a third node and is passing it along.
of course if you turn your relay off and only broadcast single tx messages it becomes apparent which transactions come from you.

it is not "little investigation" if the node is relaying all transactions. because they have to be connected to a very large number of nodes in the network to be able to figure out which node send a certain transaction first. it is so much harder nowadays since nodes add some randomness to how they broadcast txs.