VertexReplace[g, {v_1 -> w_1, v_2 -> w_2, ...}] replaces each vertex v_i in the graph g by w_i.
VertexShape is an option and property for Graph and related functions that specifies the graphics used for vertices.
VertexSize is an option and property for Graph and related functions that specifies the size used for vertices.
VertexStyle is an option and property for Graph and related functions that specifies what style to use for vertices.
WattsStrogatzGraphDistribution[n, p] represents the Watts\[Dash]Strogatz graph distribution for n-vertex graphs with rewiring probability p.WattsStrogatzGraphDistribution[n, ...
WeightedAdjacencyMatrix[g] gives the adjacency matrix of edge weights of the graph g.
Xnor
(Built-in Mathematica Symbol) Xnor[e_1, e_2, ...] is the logical XNOR (not XOR) function. It gives True if an even number of the e_i are True, and the rest are False. It gives False if an odd number of ...
DifferenceRootReduce[expr, n] attempts to reduce expr to a single DifferenceRoot object as a function of n.
DifferentialRoot[lde] represents a function that solves the linear differential equation specified by lde[y, x].
QBinomial[n, m, q] gives the q-binomial coefficient (n; m)_q.