Matches in DBpedia 2016-04 for { ?s ?p "A gain graph is a graph whose edges are labelled \"invertibly\", or \"orientably\", by elements of a group G. This means that, if an edge e in one direction has label g (a group element), then in the other direction it has label g −1. The label function φ therefore has the property that it is defined differently, but not independently, on the two different orientations, or directions, of an edge e. The group G is called the gain group, φ is the gain function, and the value φ(e) is the gain of e (in some indicated direction). A gain graph is a generalization of a signed graph, where the gain group G has only two elements. See Zaslavsky (1989, 1991).A gain should not be confused with a weight on an edge, whose value is independent of the orientation of the edge."@en }
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- Gain_graph abstract "A gain graph is a graph whose edges are labelled \"invertibly\", or \"orientably\", by elements of a group G. This means that, if an edge e in one direction has label g (a group element), then in the other direction it has label g −1. The label function φ therefore has the property that it is defined differently, but not independently, on the two different orientations, or directions, of an edge e. The group G is called the gain group, φ is the gain function, and the value φ(e) is the gain of e (in some indicated direction). A gain graph is a generalization of a signed graph, where the gain group G has only two elements. See Zaslavsky (1989, 1991).A gain should not be confused with a weight on an edge, whose value is independent of the orientation of the edge.".