Interstellar internet hypothesis

I keep thinking about the idea of an interstellar internet, that would be possible within our current understanding of the laws of physics. No FTL needed, not even a need for quantum entangled communication. Let's say a civilisation sends out probes at sublight speed to a dozen neighbouring stars containing an archive of all its knowledge. The probes have the ability to self replicate and send copies of itself to other near stars with the most likelihood of intelligent life. These probes woul...