VertexQ (Built-in Mathematica Symbol)

VertexQ[g, v] yields True if v is a vertex in the graph g and False otherwise.

Subgraph (Built-in Mathematica Symbol)

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 (Built-in Mathematica Symbol)

VertexWeight is an option and property for Graph and related functions that specifies a vertex weight.

DirectedGraphQ (Built-in Mathematica Symbol)

DirectedGraphQ[g] yields True if the graph g is a directed graph and False otherwise.

LineGraph (Built-in Mathematica Symbol)

LineGraph[g] gives the line graph of the graph g.

EdgeWeight (Built-in Mathematica Symbol)

EdgeWeight is an option and property for Graph and related functions that specifies an edge weight.

Mathematical Data Formats (Mathematica Guide)

PropertyList (Built-in Mathematica Symbol)

PropertyList[{obj, item}] lists the properties available for item in obj.

SimpleGraphQ (Built-in Mathematica Symbol)

SimpleGraphQ[g] yields True if the graph g is a simple graph and False otherwise.

Properties (Built-in Mathematica Symbol)

Properties is an option that allows specification of properties to objects and items of objects.