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based on an earlier version of the Wolfram Language.
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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 2^(18)-1 vertices.
Related to graph6 which is optimized for small graphs or large dense graphs.
Developed by Brendan McKay at the Australian National University.
  • 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, suba, subb, ...}] 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 expri as specifying the corresponding elemi.
  • 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.
"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, ndata representation element elem for the n^(th) graph in this file
elem, {n1,n2,...}element elem for graphs n1, n2, ...
elem, Allelement 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".
ImageSizeAutomaticspecifies the overall size of the image to display for a graph