KaryTree[n] gives a binary tree with n vertices. KaryTree[n, k] gives a k-ary tree with n vertices.

In Mathematica, graphs can be constructed in a variety of ways. They can be built from vertices and edges directly in a symbolic form. They can come from built-in curated ...

DirectedEdges is an option for Graph, GraphPlot, and related functions that specifies whether edges should be taken to be directed.

GraphLayout is an option to Graph and related functions that specifies what layout to use.

TreePlot lays out the vertices of a graph in a tree of successive layers, or a collection of trees. If the graph g is not a tree, TreePlot lays out its vertices on the basis ...

EdgeCount[g] gives a count of the number of edges in the graph g. EdgeCount[g, patt] gives a count of the number of edges that match the pattern patt.

VertexCount[g] gives a count of the number of vertices in the graph g. VertexCount[g, patt] gives a count of the number of vertices that match the pattern patt.

CompleteKaryTree[n] gives the complete binary tree with n levels. CompleteKaryTree[n, k] gives the complete k-ary tree with n levels.

As of Version 8, much of the functionality covered by Combinatorica has been implemented in the Mathematica kernel. BooleanAlgebra CodeToLabeledTree HasseDiagram ...

KCoreComponents[g, k] gives the k-core components of the underlying simple graph of g. KCoreComponents[g, k, "In"] gives the k-core components with vertex in-degrees at least ...