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How can you determine the "hub" nodes in a small-world graph especially when the degree distribution is fairly symmetric? I imagine what constitutes a hub or not is fairly arbitrary, or is there some criterion?

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These metrics are called 'centralities' in network theory. The one most likely to be useful to you is betweenness centrality. The betweenness centrality of a node is the proportion of all shortest path lengths in the graph that go through that node.

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  • $\begingroup$ Thanks, and just to follow up - how can a small-world graph have a fairly symmetric degree distribution? That seems to eliminate the possibility of hubs, or not? $\endgroup$
    – user95199
    Jul 15, 2022 at 16:22
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    $\begingroup$ @user2561523 No, it doesn't necessarily eliminate hubs. You can even have a regular graph with hubs - see researchgate.net/figure/…. You can't get more symmetric of a degree distribution than that, but the central node is clearly a hub! $\endgroup$
    – Brady Gilg
    Jul 15, 2022 at 17:07

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