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In mathematics, a biased graph is a graph with a list of distinguished circles (edge sets of simple cycles), such that if two circles in the list are contained in a theta graph, then so is the third circle of the theta graph. A biased graph is a generalization of the combinatorial essentials of a gain graph and in particular of a signed graph. Formally, a biased graph Ω is a pair (''G'', ''B'') where ''B'' is a linear class of circles; this by definition is a class of circles that satisfies the theta-graph property mentioned above. A subgraph or edge set whose circles are all in ''B'' (and which contains no half-edges) is called balanced. For instance, a circle belonging to ''B'' is ''balanced'' and one that does not belong to ''B'' is ''unbalanced''. Biased graphs are interesting mostly because of their matroids, but also because of their connection with multiary quasigroups. See below. ==Technical notes== A biased graph may have half-edges (one endpoint) and loose edges (no endpoints). The edges with two endpoints are of two kinds: a link has two distinct endpoints, while a loop has two coinciding endpoints. Linear classes of circles are a special case of linear subclasses of circuits in a matroid. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「biased graph」の詳細全文を読む スポンサード リンク
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