VertexCoordinateRules is an option for GraphPlot and related functions which specifies rules for determining the coordinates at which vertices should be placed.
FindGraphIsomorphism[g_1, g_2] finds an isomorphism that maps the graph g_1 to g_2 by renaming vertices.
AcyclicGraphQ[g] yields True if the graph g is an acyclic graph and False otherwise.
DirectedGraph[g] gives a directed graph from the undirected graph g.DirectedGraph[g, conv] gives a directed graph using the conversion conv.
VertexQ
(Built-in Mathematica Symbol) VertexQ[g, v] yields True if v is a vertex in the graph g and False otherwise.
Subgraph[g, {v_1, v_2, ...}] gives the subgraph of the graph g generated by the vertices v_i.Subgraph[g, {e_1, e_2, ...}] gives the subgraph generated by the edges ...
VertexWeight is an option and property for Graph and related functions that specifies a vertex weight.
DirectedGraphQ[g] yields True if the graph g is a directed graph and False otherwise.
LineGraph[g] gives the line graph of the graph g.
EdgeWeight is an option and property for Graph and related functions that specifies an edge weight.