Version 0.6.5 is now released, just in time for Christmas! :-) Please upgrade to this release, especially if you are using Mathematica 13.2.

Hello Flavio,

And sorry about the slow response. I was on holidays when you originally wrote.

IGraph/M provides many new operations to work with Mathematica's built-in Graph expressions. Most IGraph/M functions are concerned with analysing networks, or with building new networks.

Graph expressions can represent any kind of graph, including the ones you mention. However, they don't really do anything, they just represent a structure. This distinguishes them from things like NetGraph where the primary purpose is not just to represent, but perform a function: you give it some inputs and it computes the output.

If I understand your question, you may be looking for a system to propagate a signal through a network, or perhaps to perform some computation with it. Graph can provide an underlying structure for this, but if you have a specific way to propagate signals through it, you would need to implement that yourself. There are some functions in IGraph/M which can be though of as "signal propagation", but they are all for specific purposes, so I am not sure this is what you are looking for. For example, there is IGRandomWalk which simulates a random walker on the network. There is IGSIRProcess, which models epidemic spread through a network. There are many classic network metrics that IGraph/M can compute (in more flexible ways than Mathematica's builtins) which can tell us something about how various signals would propagate: PageRank is based on the idea of a random walker (a rando web-surfer clicking through pages) that occasionally jumps to an arbitrary node. Betweenness centrality tells us something about which nodes the signal will pass through most often if it takes a shortest path. And so on.

I hope this helps a bit.

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Great work!

IGraph/M 0.3.112 is now released with some critical bug fixes and new functions. Please upgrade.

There are new functions for testing graph symmetry and regularity. Here's a demonstration:

Needs["IGraphM`"]

graphs = {StarGraph[4], IGSquareLattice[{2, 3}, "Periodic" -> True], 
   HypercubeGraph[3], GraphData[{"Rook", {4, 4}}], 
   GraphData["ShrikhandeGraph"], GraphData["HoltGraph"], 
   GraphData["Tutte12Cage"], GraphData[{"Paulus", {25, 1}}]};

functions = <|"regular" -> IGRegularQ, 
   "strongly regular" -> IGStronglyRegularQ, 
   "distance regular" -> IGDistanceRegularQ, 
   "vertex transitive" -> IGVertexTransitiveQ, 
   "edge transitive" -> IGEdgeTransitiveQ, 
   "arc transitive" -> IGEdgeTransitiveQ@*DirectedGraph, 
   "distance transitive" -> IGDistanceTransitiveQ|>;

TableForm[
  Through[Values[functions][#]] & /@ graphs, 
  TableHeadings -> {Show[#, ImageSize -> 60] & /@ graphs, Keys[functions]}, 
  TableDirections -> Row
]

Prerelease 0.3.91 is now available. If you tried the previous prerelease, please upgrade.

• https://github.com/szhorvat/IGraphM/releases

This release includes bug fixes, documentation improvements, and a few new functions.

Let me know if you find any problems, or have any suggestions.

Don't worry about the red colouring here. This is only because the builtin HierarchicalClustering package hasn't been updated to make use of SyntaxInformation. These options work correctly. The highlighting can be safely ignored.

IGraph/M 0.3.0 is now available.

This release fixes compatibility with Mathematica 11.1.

It also introduces new functions, performance improvements, bug fixes and polish. Upgrading is recommended for all users.

IGraph/M 0.2.0 is released now with many improvements. It can be downloaded from https://github.com/szhorvat/IGraphM/releases as usual.

Highlights for this release:

• Significant performance improvements for many functions
• New and extended functions for shortest path calculations (extended IGDistanceMatrix, IGDistanceCounts, IGDistanceHistogram, IGDiameter, IGFindDiameter)
• Support for weighted clique calculations (IGWeightedCliques, IGMaximalWeightedCliques, IGLargestWeightedCliques, IGWeightedCliqueNumber)
• Additional new functions
• Syntax highlighting for functions
• Raspberry Pi support
• Compatibility with Mathematica 10.4 on OS X.
• Bug fixes

I would appreciate any testing people can do on platforms I didn't have access to (priorities in decreasing order: Linux, Windows, OS X, pre-10.3 Mathematica versions).

IGraph/M version 0.1.3 is released now, with expanded coverage for igraph functions and a lot of polish for the already covered ones.

Highlights for this release:

• Community detection algorithms
• Automorphism group for vertex coloured graphs; multigraph isomorphism
• Additional centrality measures with support for weighted graphs

Thank you for letting me know! This is now fixed in version 0.1.2. There are few changes in this version; its main purpose was to fix a bug on Windows where some functions were not working at all.