Wolfram Language & System 10.0 (2014)|Legacy Documentation

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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 to 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 ExportImport and Export

  • Import["file.s6"] imports the graphs stored in the specified file, given as a single Graph object or a list of graphs.
  • Export["file.s6",expr] exports an adjacency matrix or edge information for one graph or multiple graphs to the sparse6 format.
  • 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 as specifying the corresponding .
  • 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.


  • 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 matrices
    "EdgeRules"connectivity data for all graphs, given as an array of rules
    "Graph"first graph stored in the file, given as a Graph object
    "Graphics"first graph stored in this file, rendered as a graph plot
    "GraphicsList"all graphs, given as a list of graphics objects
    "GraphList"all graphs given as a list of Graph objects
    "VertexCount"number of vertices in each graph, given as a list of integers
    "VertexList"list of integers representing the vertices
  • Import by default uses for simple sparse6 files and for multi-graph sparse6 files.
  • 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
    elem,Allelement elem for all graphs, given as a list
  • Import["file.s6","GraphList"] gives a list of all graphs in the file, rendered as a Graph object.
  • Import["file.s6",{"GraphList",n}] gives a rendering of the n^(th) graph in the file.
  • When importing a sparse6 file using the element, no rules are returned for possible unconnected vertices.
  • Graphs including unconnected vertices can be fully specified using the element, or as a combination of and .


ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Import a sparse6 example file, giving a visual representation:

Click for copyable input

Read the adjacency matrix of the above example and render it as MatrixPlot:

Click for copyable input

Export a Graph object to the sparse6 format:

Click for copyable input

Export the adjacency matrix of a graph to the sparse6 format:

Click for copyable input

Export edge rules:

Click for copyable input
Introduced in 2007
| Updated in 2010