NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

TransitiveClosure[g] finds the transitive closure of graph g, the supergraph of g that contains edge {x, y} if and only if there is a path from x to y.

Mathematica's matrix operations handle both numeric and symbolic matrices, automatically accessing large numbers of highly efficient algorithms. Mathematica uses ...

BitSet[n, k] sets to 1 the bit corresponding to the coefficient of 2^k in the integer n.

BitShiftLeft[n, k] shifts the binary bits in the integer n to the left by k places, padding with zeros on the right.BitShiftLeft[n] shifts one bit to the left.

Distributed[x, dist] or x \[Distributed] dist asserts that the random variable x is distributed according to the probability distribution dist.Distributed[{x_1, x_2, ...}, ...

FindHamiltonianCycle[g] finds a Hamiltonian cycle in the graph g if one exists.

GroupActionBase is an option to specify a base for a group.

GroupElementQ[group, g] returns True if the object g is an element of group and False otherwise.