GraphicQ[s] yields True if the list of integers s is a graphic sequence, and thus represents a degree sequence of some graph.
Harary
(Combinatorica Package Symbol) 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.
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.
VertexLabels is an option and property for Graph and related functions that specifies what labels and label positions should be used for vertices.
DegreeCentrality[g] gives a list of vertex degrees for the vertices in the underlying simple graph of g. DegreeCentrality[g, "InDegree"] gives a list of vertex ...
VertexLabeling is an option for GraphPlot and related functions which specifies whether labeling should be included by default for vertices in graphs.
VertexOutDegree[g] gives the list of vertex out-degrees for all vertices in the graph g.VertexOutDegree[g, v] gives the vertex out-degree for the vertex v.