GridGraph[{m, n}] gives the grid graph with m*n vertices G m, n.GridGraph[{n_1, n_2, ..., n_k}] gives the k-dimensional grid graph with n_1*n_2*\[CenterEllipsis]*n_k vertices ...
RemoveProperty[{obj, item}] removes all properties associated with item in obj.RemoveProperty[{obj, item}, name] removes the property name associated with item in obj.
EdgeQ
(Built-in Mathematica Symbol) EdgeQ[g, e] yields True if e is an edge in the graph g and False otherwise.
SetProperty[{obj, item}, name -> value] sets the property name -> value for item in obj.
KirchhoffGraph[kmat] gives the graph with Kirchhoff matrix kmat.KirchhoffGraph[{v_1, v_2, ...}, kmat] gives the graph with vertices v_i and Kirchhoff matrix kmat.
PseudoDiameter[g] give the pseudo-diameter of the undirected graph g, and the two vertices that achieve this diameter.
GraphCenter[g] gives the set of vertices with minimum eccentricity in the graph g.