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Suppose we have a complete graph on 10 nodes and we need to mark each edge as positive or negative and satisfy the Weak Balance

Suppose we have a complete graph on 10 nodes and we need to mark each edge as positive or negative and satisfy the Weak Balance property. Suppose we do it in all the ways possible and get a total of M different signed networks. For each network, we are able to divide it into some specific number of non-empty groups such that there is no antagonism within groups and no friendship between groups. For network i, call that number ki. Call the set of ki K. What numbers belong to K?

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