High Quality Content by WIKIPEDIA articles! In the area of graph theory in mathematics, a signed graph is a graph in which each edge has a positive or negative sign. Formally, a signed graph ? is a pair (G, ?) that consists of a graph G = (V, E) and a sign mapping or signature ? from E to the sign group {+,?}. The graph may have loops and multiple edges as well as half-edges (with only one endpoint) and loose edges (with no endpoints). Half and loose edges do not receive signs. (In the terminology of the article on graphs, it is a multigraph, but we say graph because in signed graph theory it is usually unnatural to restrict to simple graphs.) The sign of a circle (this is the edge set of a simple cycle) is defined to be the product of the signs of its edges; in other words, a circle is positive if it contains an even number of negative edges and negative if it contains an odd number of negative edges. The fundamental fact about a signed graph is the list of positive circles, which we write B(?).

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