Degree is popularity, not influence

The useful first count can become the misleading headline. Degree centrality is often the first graph metric people understand because it counts direct connections. That makes it valuable. It also makes it easy to overclaim. What degree sees Degree sees immediate neighbors. In an undirected graph, that is the number of adjacent nodes. In directed graphs, in-degree and out-degree separate incoming attention from outgoing activity. In weighted graphs, you may also care about weighted degree, where connection strength matters. What degree misses Degree does not see position beyond one hop. It cannot tell whether a node connects separate groups, whether…

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