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As a mathematician, my immediate reaction was: duh! Of course! Why is this interesting? The go-to example would be a person having 10 friends, being the only f
by romwell 4y ago
As a mathematician, my immediate reaction was: duh! Of course! Why is this interesting?
The go-to example would be a person having 10 friends, being the only friend for each of them. It's not too hard to generalize from there, or at least to have an intuition.
The interesting part for me was this:
> If there are only enough vaccines for a small fraction of the population, an effective strategy is to vaccinate a random friend of each randomly chosen person.
Oh. Makes sense!
Somehow, something like that didn't occur to me even when the math felt intuitive.
- mkehrt 4y agoWell, the interesting thing isn't that such graphs exist, so finding an arbitrary graph with this property isn't really relevant. It's that certain distributions of random graphs, when sampled tend to produce graphs with this property and human social networks are one of them.
- romwell 4y agoTrue. My comment was to highlight how wrong my initial intuition was. Looking around, this article[1] by Arun Maiya and Tanya Berger-Wolf explores this in the context of social networks. Fascinating stuff! [1] https://arxiv.org/pdf/1109.3911.pdf https://arxiv.org/pdf/1109.3911.pdf
- woopwoop 4y agoNo, this statement is true for every graph that doesn't have constant degree. It's not really to do with random graphs. Rather it's the fact that a random neighbor of a random node draws from a different distribution than a random node, and the former distribution puts more mass on nodes of higher degree.
- mkehrt 4y agoAh, oops, you are correct.
- kinban123 4y agoDoes this logic extend? What if i reached out to a random friend of a random friend of a random node - basically to degree 3 of the network. Is that better than degree 2 ? If so, then is there a degree where the spreading is optimal ?