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This will get you a winning modularity score.
You divide by the number of stubs so that whatever the size of the graph, the maximum modularity score is 1, which facilitates comparisons across graphs.
So you start this divisive clustering process by dividing the graph into two communities so the modularity score is maximized.
By that, I mean if you place Adams in community 1, you'll calculate his piece of the total modularity score by
You're trying to maximize the total modularity scores, so Adams' score will want to rise until it bumps up against the lowest of these two constraining formulas.
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