AddEdge[g, e] returns a graph g with the new edge e added. e can have the form {a, b} or the form {{a, b}, options}.

AddEdges[g, edgeList] gives graph g with the new edges in edgeList added. edgeList can have the form {a, b} to add a single edge {a, b} or the form {{a, b}, {c, d}, ...}, to ...

AddVertex[g] adds one disconnected vertex to graph g. AddVertex[g, v] adds to g a vertex with coordinates specified by v.

AddVertices[g, n] adds n disconnected vertices to graph g. AddVertices[g, vList] adds vertices in vList to g. vList contains embedding and graphics information and can have ...

Algorithm is an option that informs functions such as ShortestPath, VertexColoring, and VertexCover about which algorithm to use.

AllPairsShortestPath[g] gives a matrix, where the (i, j)\[Null]^th entry is the length of a shortest path in g between vertices i and j. AllPairsShortestPath[g, Parent] ...

AlternatingGroupIndex[n, x] gives the cycle index of the alternating group of size n permutations as a polynomial in the symbols x[1], x[2], ..., x[n]}.

AlternatingGroup[n] generates the set of even-size n permutations, the alternating group on n symbols. AlternatingGroup[l] generates the set of even permutations of the list ...

AlternatingPaths[g, start, ME] returns the alternating paths in graph g with respect to the matching ME, starting at the vertices in the list start. The paths are returned in ...

AnimateGraph[g, l] displays graph g with each element in the list l successively highlighted. Here l is a list containing vertices and edges of g. An optional flag, which ...