AlternatingGroup[n] generates the set of even-size n permutations, the alternating group on n symbols. AlternatingGroup[l] generates the set of even permutations of the list ...

Diameter[g] gives the diameter of graph g, the maximum length, among all pairs of vertices in g, of a shortest path between each pair.

EdgeConnectivity[g] gives the minimum number of edges whose deletion from graph g disconnects it. EdgeConnectivity[g, Cut] gives a set of edges of minimum size whose deletion ...

GraphPower[g, k] gives the k\[Null]^th power of graph g. This is the graph whose vertex set is identical to the vertex set of g and that contains an edge between vertices i ...

InDegree[g, n] returns the in-degree of vertex n in directed graph g. InDegree[g] returns the sequence of in-degrees of the vertices in directed graph g.

NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...

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, ...

OutDegree[g, n] returns the out-degree of vertex n in directed graph g. OutDegree[g] returns the sequence of out-degrees of the vertices in directed graph g.

RadialEmbedding[g, v] constructs a radial embedding of the graph g in which vertices are placed on concentric circles around v depending on their distance from v. ...