Definition:Balanced Signed Graph

Definition

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