Examples
- If every circle belongs to B, and there are no half-edges, Ω is balanced. A balanced biased graph is (for most purposes) essentially the same as an ordinary graph.
- If B is empty, Ω is called contrabalanced. Contrabalanced biased graphs are related to bicircular matroids.
- If B consists of the circles of even length, Ω is called antibalanced and is the biased graph obtained from an all-negative signed graph.
- The linear class B is additive, that is, closed under repeated symmetric difference (when the result is a circle), if and only if B is the class of positive circles of a signed graph.
- Ω may have underlying graph that is a cycle of length n ≥ 3 with all edges doubled. Call this a biased 2Cn . Such biased graphs in which no digon (circle of length 2) is balanced lead to spikes and swirls (see Matroids, below).
- Some kinds of biased graph are obtained from gain graphs or are generalizations of special kinds of gain graph. The latter include biased expansion graphs, which generalize group expansion graphs.
Read more about this topic: Biased Graph
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