Definition:Balanced Signed Graph

Let $$G = \left({V, E}\right)$$ be a signed graph.

Then $$G$$ is balanced if it is possible to partition $$V$$ into two subsets $$A, B$$ such that:


 * the positive edges have both ends in $$A$$ or both ends in $$B$$;


 * the negative edges have one end in $$A$$ and the other end $$B$$.

It is a frequent practice to apply a different colour to the vertices in each set to enhance clarity.

Example

 * BalancedSignedGraph.png