ReadGraph[f] reads a graph represented as edge lists from file f and returns a graph object.

PathGraph[{v_1, v_2, ...}] yields a path with vertices v_i and edges between v_i and v i +\[ThinSpace]1 .PathGraph[{e_1, e_2, ...}] yields a path with edges ...

DegreeSequence[g] gives the sorted degree sequence of graph g.

GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.

Harary[k, n] constructs the minimal k-connected graph on n vertices.

VertexSize is an option and property for Graph and related functions that specifies the size used for vertices.

Mathematica supports many formats, with many subformats, variants, and options.

TeleportProbability is an option to PageRanks, PageRankVector, LinkRanks, and LinkRankMatrix that specifies the probability that an internet user may choose to visit a vertex ...

Spectrum[g] gives the eigenvalues of graph g.

UndirectedQ[g] yields True if graph g is undirected.