4 ms·

I know this is HN but can someone ELI-don't-have-a-PhD-in-mathematics?

• alextheparrot 10y ago
  The math is tough to grok, but it appears they are using some set constructions to show that given a certain cycle size (4 or more) within a graph, those cycles are stable (Irreducible) based on some previous work. Thus, network stability is contingent on those cycles and you can extend this to say that the reason social networks don't dissolve is because these subsets give stability to the graph?
  • M_Grey 10y ago
    Honestly, I've had easier times reading through representation theory concerning quantum mechanics! I think I see what it's trying to say though, which appears to be some mathematical basis for what we experience online; communities form, fragment, and it's exceedingly difficult to halt or reverse that process of fragmentation and isolation. Eventually, this trend results in the decoherence of the network. Is that about it?
• Kenji 10y ago
  You don't need a PhD in mathematics. Firstly, they explain the (already existing) concept of a closure (think for example transitive closure, which seems to be exactly what they're going for). Y.ϕ is a notation that means we apply operator ϕ on Y. It seems like they work with a closure operator that goes akin to "if we have a graph G where A relates to B and B relates to C, then G.ϕ additionally has A relating to C". Then they look at how a social network evolves under the (formalized) assumption that no two individuals become one individual. Then they prove, under this condition, that, as the network evolves, some separate sets remain separate. That is, certain structures in the graph remain stable. That's a broad overview, I think. I only spent like 15 minutes reading and writing this, so I might be mistaken.