Mathematica Import/Export Format

Sparse6 (.s6)

sparse6 graph data format.
Used for storing undirected graphs.
ASCII format.
Stores connectivity information for multiple undirected graphs.
Suitable for large sparse graphs, stores up

vertices.
Related to graph6 which is optimized for small graphs or large dense graphs.
Developed by Brendan McKay at the Australian National University.

Import and Export fully support the sparse6 file format.

IMPORT AND EXPORT

Import["file.s6"]gives a graphical rendering of the first graph stored in the specified file.

Export["file.s6", expr] exports an adjacency matrix or edge information for one graph or multiple graphs to the sparse6 format.

Import["file.s6"] imports the first graph from file and returns it as a GraphPlot.

Import["file.s6", elem] imports the specified element from a sparse6 file.

Import["file.s6", {elem, sub_a, sub_b, ...}] imports a subelement.

Import["file.s6", {{elem₁, elem₂, ...}}] imports multiple elements.

The import format can be specified with Import["file", "Sparse6"] or Import["file", {"Sparse6", elem, ...}].

Export["file.s6", expr, elem] creates a sparse6 file by treating expr as specifying element elem.

Export["file.s6", {expr₁, expr₂, ...}, {{elem₁, elem₂, ...}}] treats each expr_i as specifying the corresponding elem_i.

Export["file.s6", expr, opt₁->val₁, ...] exports expr with the specified option elements taken to have the specified values.

Export["file.s6", {elem₁->expr₁, elem₂->expr₂, ...}, "Rules"] uses rules to specify the elements to be exported.

See the reference pages for full general information on Import and Export.

ImportString and ExportString support the sparse6 format.

ELEMENTS

General Import elements:

	"Elements"	list of elements and options available in this file
	"Rules"	full list of rules for each element and option
	"Options"	list of rules for options, properties and settings

Data representation elements:

	"AdjacencyMatrix"	edge information for all graphs in this file, given as a list of sparse matrices
	"EdgeRules"	connectivity data for all graphs, given as an array of rules
	"Graphics"	first graph stored in this file, rendered as GraphPlot
	"GraphicsList"	all graphs stored in this file, given as a list of Graphics objects
	"VertexCount"	number of vertices in each graph, given as a list of integers

Import uses the "Graphics" element by default.

Element specifications for sparse6 files containing multiple graphs:

	elem, n	data representation element elem for the n graph in this file
	elem, {n₁,n₂,...}	element elem for graphs n₁, n₂, ...
	elem, All	element elem for all graphs, given as a list

Import["file.s6", {"Graphics", All}] gives a list of Graphics objects, each representing a rendering of a graph stored in file.s6.

When importing a graph6 file using the "EdgeRules" element, no rules are returned for possible unconnected vertices.

Graphs including unconnected vertices can be fully specified using the "AdjacencyMatrix" element, or as a combination of "EdgeRules" and "VertexCount".

OPTIONS

General Import option:

ImageSize

Automatic

specifies the overall size of the image to display for a graph