Combinatorica Package >

DeleteEdge

DeleteEdge[g, e]
gives graph g minus e. If g is undirected, then e is treated as an undirected edge, otherwise it is treated as a directed edge. If there are multiple edges between the specified vertices, only one edge is deleted.
DeleteEdge[g, e, All]
will delete all edges between the specified pair of vertices. Using the tag Directed as a third argument in DeleteEdge is now obsolete.
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