ShortestPathSpanningTree[g, v] constructs a shortest-path spanning tree rooted at v, so that a shortest path in graph g from v to any other vertex is a path in the tree.

ToAdjacencyLists[g] constructs an adjacency list representation for graph g. ToAdjacencyLists[g, EdgeWeight] returns an adjacency list representation along with edge weights.

ToAdjacencyMatrix[g] constructs an adjacency matrix representation for graph g. ToAdjacencyMatrix[g, EdgeWeight] returns edge weights as entries of the adjacency matrix with ...

VertexColoring[g] uses Brelaz's heuristic to find a good, but not necessarily minimal, vertex coloring of graph g.

New functions SymmetricPolynomial and SymmetricReduction have been added to the built-in Mathematica kernel.

The symbolic functions in Calculus`FourierTransform` have been added to the built-in Mathematica kernel. The numerical functionality in Calculus`FourierTransform` is now ...

As of Version 7, the Geodesy Package has been integrated into the Mathematica kernel.

Plot, ListPlot, and similar functions have new Filling and FillingStyle options.

ContourPlot in the built-in Mathematica kernel now accepts equations.

All the functionality in Miscellaneous`BlackBodyRadiation` is now available through the newly created Black Body Radiation Package.