EdgeCoverQ[g, elist] yields True if the edge list elist is an edge cover of the graph g and False otherwise.
EdgeDelete[g, e] makes a graph by deleting the edge e from the graph g.EdgeDelete[g, {e_1, e_2, ...}] deletes a collection of edges from g.EdgeDelete[g, patt] deletes all ...
EdgeForm[g] is a graphics directive which specifies that edges of polygons and other filled graphics objects are to be drawn using the graphics directive or list of ...
EdgeLabeling is an option for GraphPlot and related functions that specifies whether labeling specified for edges should be displayed by default.
EdgeLabelStyle is an option and property for Graph and related functions that specifies the style to use for edge labels.
EdgeList[g] gives the list of edges for the graph g. EdgeList[g, patt] gives a list of edges that match the pattern patt.
EdgeQ
(Built-in Mathematica Symbol) EdgeQ[g, e] yields True if e is an edge in the graph g and False otherwise.
EdgeRenderingFunction is an option for GraphPlot and related functions that gives a function to generate the graphics primitives to use in rendering each edge.
EdgeShapeFunction is an option and property for Graph and related functions that specifies a function to use to generate primitives for rendering each edge.
EdgeWeight is an option and property for Graph and related functions that specifies an edge weight.