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Consider any complete signed graph ( on any number of nodes ) that is not balanced; i . e . it contains at least one
Consider any complete signed graph on any number of nodes that is not balanced; ie it contains at least one unbalanced triangle. A complete signed graph is a graph in which there is an edge between each pair of nodes, and each edge is labeled with either or A new node X wants to join this network, by attaching to each node using a positive or negative edge. When, if ever, is it possible for X to do this in such a way that it does not become involved in any unbalanced triangles? Give an explanation for your answer.
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