How can I conveniently call igraph from Mathematica?

Question

Mathematica has lots of functions for working with graphs and networks, but there are still some functionality holes that are provided by other packages. Also, due to the nature of graph theory, often it is very hard (in practice impossible) to verify results returned by Mathematica without having an alternative implementation.

For these reasons it would be very useful to have access to another graph analysis library. igraph is one of the most mature open source network analysis packages. How can we access it from Mathematica?

Answer 1

Update: I am no longer maintaining IGraphR. I recommend that you transition to IGraph/M instead. If you need a feature that IGraph/M does not yet have, please submit a feature request.

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I wrote a small package for this. The main reason why I'm posting it here is to get some feedback on how to improve it. I'm new both R and RLink.

You can get the package here. Please see the installation instructions in README.md, especially if you're a Mac user (important!).

How does it work?

RLink does not play well with igraph objects, so an edge-list representation is used to transfer data between R and Mathematica. Using a simple edge-list is good for performance and transparency too. On the R side, edge lists are marked with the mmaDirectedGraph attribtue. On the Mathematica side, Graph objects are auto-converted to R edge lists using RLink's RDataTypeRegister mechanism.

The function to be called and the argument list are passed separately to R. On the R side a function takes care of converting the egde lists to proper igraph objects, and then calls the function. If the return value is a graph, it also converts that back to an edge list.

Usage examples

Mac users will need to load RLink like this first (again, follow the instructions on github!!):

<< RLink`

SetEnvironment[
  "DYLD_LIBRARY_PATH" -> 
   "/Library/Frameworks/R.Framework/Resources/lib"];

InstallR["RHomeLocation" -> 
  "/Library/Frameworks/R.Framework/Resources"]

Note: if using Mathematica 10.0.1, also specify the R version, e.g.

InstallR["RHomeLocation" -> 
  "/Library/Frameworks/R.Framework/Resources", "RVersion" -> "3.1"]

Examples:

IGraph["vertex.connectivity"][CycleGraph[5]]

(* ==> {2.} *)

IGraph["barabasi.game"][50]

Answer 2

To overcome some limitations of RLink with regard to performance and parallelizability, I also created a LibraryLink based interface to igraph:

• IGraph/M

Since the original release, IGraph/M has grown into a large package of over 300 functions that is much more than just an igraph interface, and provides many unique functions for working with graphs in Mathematica.

Functionality highlights:

• Graph theory:

  • Isomorphism: vertex/edge coloured graphs, multigraphs, subgraph finding
  • Fast exact graph colouring
  • Work with planar graphs and combinatorial embeddings
  • Degree sequences: check graphicality, construct realizations, random sampling
  • Replacement for most of Combinatorica's functions that are not yet built into the Wolfram Language
  • ...

• Network analysis:

  • Implementations for many random graph models
  • Centrality measures: support for weighted graphs, multigraphs
  • Find network motifs
  • Community detection algorithms (fully documented and referenced)
  • Random walks on graphs
  • Fast shortest path histogramming
  • Additional graph layouts
  • ...

• Geometrical computation:

  • Mesh/graph conversion
  • Proximity graphs (Delaunay graph, Gabriel graph, $\beta$-skeletons)
  • Lattice generation

• Utility functions:

  • Quick and easy edge/vertex property handling and transformations
  • Convenient graph styling based on stored or computed properties
  • ...

• Many other things such as useful graph generators, finding/counting all cliques, minimum feedback arc set, edge rewiring, bipartite graph handling, matching, alternative algorithms for multiple built-ins, etc.

Compatibility: 64-bit Windows/macOS/Linux or Raspberry Pi; Mathematica 11.0 or later. Version 0.5 and earlier will run with Mathematica 10.0.2 or later.

I recommend using IGraph/M instead of IGraphR if the functionality you need is already included. It is faster and more robust than IGraphR.

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After installing the package, load it as

<<IGraphM`

and open the documentation notebook with

IGDocumentation[]

It contains many examples.

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I am hoping that eventually IGraph/M will become a community project. Contributions of all kinds are welcome: comments/suggestions on features & the API, editing usage message and documentation, adding more cool examples, converting the documentation to a format compatible with the Documentation Centre, implementing new functionality, etc.