Definition:Balanced Signed Graph
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Definition
Let $G = \struct {V, E}$ be a signed graph.
Then $G$ is balanced if and only 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
Also see
- Results about balanced signed graphs can be found here.