Abstract
Abstract A cycle in a signed graph is a positive cycle if the number of negative edges is even and is a negative cycle if the number of negative edges is odd. A signed graph is balanced if and only if each cycle is a positive cycle, and unbalanced otherwise; equivalently, a signed graph is balanced if we can colour each vertex red or green in such a way that positive edges have ends of the same colour and negative edges have ends of different colours. Signed graphs are used in the social sciences, with positive edges corresponding to positive relationships and negative edges corresponding to negative ones. Balanced signed graphs correspond to social situations in which there is no ‘tension’.
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