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However, someone with full access to your network connection (your ISP, the NSA, etc) can see if you sent a transaction that you didn't already receive from another peer, which proves that transaction is yours and you're not relaying someone else's transaction.
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Thats not necessarily true. I could potentially create a signed transaction and send it to e.g. Danny via PM/(Snail)mail/SMS/OTR/DVBT/etc. for broadcasting. Or - even easier - broadcast it from a public WiFi at a remote coffee shop in my city. There are several miners and services that allow you to push a TX via their node.
Thanks. I just want to know the information about nodes connected.
If you just want information about the nodes your node is connected to you can use
getpeerinfo it will include IP addresses.