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Well, 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 distributio
by mkehrt 4y ago
Well, 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.