I've checked the presentations from the recent Wolfram Technology Conference scanning for any improvements or ideas on how Graphs will be further developed (see WTC link). Unfortunately I did not find much which leaves me wondering what priority is being put on resolving the graph bugs.

I was one of the people posting to Mathematica StackExchange and have sent at least two bug reports several years ago on the FindMaximumFlow problem and I'm keen to see it solved for my application. It seems counter-productive that functional or algorithmic bugs go such a long time without being addressed.

My hope like many of those in this thread lies in the next release and the statements of Charles Pooh above.

@Charles Pooh:

Informations about algorithms are provided to users through Wolfram Technical Support or in public forum such as Wolfram Community.

Sometimes I find it a bit difficult to get information on methods and algorithms this way. Just now my request (through Support) for a reference to the method that GraphLayout -> "PlanarEmbedding" uses was refused. Thus I thought I would ask here, publicly (as you basically suggested):

Drawing a planar graph with straight edges and without edge crossings is a non-trivial problem. Since 1990, several algorithms have been published for constructing such drawings on integer grids. However, most of them do not produce a "nice" layout that is easy to interpret for humans. They often contain very small angles between edges or vertices so close to an edge that visually they overlap. I have been experimenting with using these algorithms (including Mathematica's) in more complicated practical schemes to produce more useful drawings. I want these schemes to be reproducible without Mathematica. Thus: which method does "PlanarEmbedding" implement? Can you give me a reference?

Another instance where I was unable to get information is the method used for random sampling from a "DegreeGraphDistribution". The usual method for sampling graphs with a given degree distribution fall into two categories: 1. Direct construction (such as the configuration model), which samples exactly uniformly 2. Markov chain based methods that repeatedly modify the graph (randomly), but only sample approximately uniformly (furthermore, the mixing times are usually unknown).

Clearly, knowing at least whether the sampling is exactly uniform is important for some applications. I asked W Support in 2012 (TS 44838) what sampling method is being used, and I was told that it is the configuration model. However, by experience, sampling is not exactly uniform (with the configuration model it should be): https://mathematica.stackexchange.com/q/167450/12

Thus, once again, I would like to know what method is being used for sampling from a DegreeGraphDistribution. I was not yet able to get a response about this (CASE:4027392).

I should also note that the documentation of DegreeGraphDistribution is in need of some expansion. I was unable to find any explicit statement about whether it represents a uniform distribution over the set of graphs with the given degree sequence ("degree graph distribution" is not a term used anywhere else than in the M Documentation, so it is of no help). Also, by experience, the distribution that RandomGraph[DegreeGraphDistribution[...]] samples from is not at all uniform if the degree sequence cannot be realized by a simple graph (which is actually expected from the configuration model—but the documentation never mentioned the configuration model). Without knowing the distribution it represents, this symbol is not very useful.

Hi Charles, Thx for your reply. Looking at the StackExchange issues logged there are some that seem more fundamental. Anyway I really appreciate your reply to give feedback on this subject. I agree that Graphs are seen as a fundamental part in the Wolfram system. What I would like and propose is that the dramatic expansions in the Graphs and Networks functionality as you mentioned might be shown in a Wolfram Twitch session. This way feedback can also be given directly. Thx for time to reply.

Wolfram has most definitely not abandoned Graphs & Networks functionality. It is true that all projects at Wolfram go through periods of different intensity of development and the most intense development phase for Graphs & Networks certainly spanned Version 8, 9 and 10. Currently there is a lot of functionality being added and planned, with a focus on several vertical functionalities such as neural networks, chemistry, general trees and geometry. In fact, graphs and networks are being deeply integrated into areas which stress them in new and interesting ways.

The functionality is also being maintained. Here are some recent bug fix statistics: WL 10.0 - 62, WL 11.0 - 27, WL 11.3 - 97. As of today, the number of open bugs is 208. We will have another major batch of bugs fixed in the coming release. Interestingly we find that 70-90% of the bugs we track, are found internally. Of the 24 issues published in an earlier post, the following 5 are fixed in 11.3:

• IsomorphicGraphQ issues?
• HighlightGraph Problem
• GraphAutomorphismGroup bug or my misunderstanding?
• EdgeAdd function not adding edges to a RandomGraph[ ] with edges
• Self-loops in Graph may not display correctly or export correctly to PDF

And many more issues are already fixed in our development version.

Functions such as NeighborhoodGraph, preserve the layout of the input graph. This can be computationally expensive for a large GridGraph[{50,50,50}] with 125 000 vertices and 367 500 edges. Here is a workaround if performance is the primary goal.

g = GridGraph[{50, 50, 50}];
NeighborhoodGraph[g, 123,  GraphLayout -> None]

Informations about algorithms are provided to users through Wolfram Technical Support or in public forum such as Wolfram Community.

We are looking forward to dramatic expansions in Graphs & Networks functionality. We are even more excited about its many applications across different domains and the graph related functions in the pipeline. This is a very strong framework that will continue to evolve quite a bit and it is getting integrated in so much functionality that we are starting to take it for granted and becomes part of the everyday fabric of the system.

I think Henrik captured the essence of the issue. Unless there is a strong foundation, syntax sugar is irrelevant.

I even started with Mathematica just because the graph functionality. I'm not a very heavy user with special demands but Szabolcs work helped me out very often. I thinks graphs are a fundamental need in such frameworks and I have hope that wri will address the issues. We'll see but some support statements from wri would help.

The closest I've seen was on Tree Structures https://www.twitch.tv/videos/228665929

I am a user of the built-in Graph functionality (not a heavy user) but i am seriously concerned after what you have mentioned in your post. WRI has to fix the past bugs and catch up with R and python when it comes to Graphs

Here are the at present 24 unresolved bugs I got via a quick-and-dirty query of the StackExchange API:

• Does DegreeGraphDistribution sample uniformly?
• Querying for multiple vertex properties using PropertyValue does not work
• Question about TransitiveReductionGraph
• IsomorphicGraphQ issues?
• How to take a subgraph of an edge-weighted graph and preserve weights?
• VertexReplace destroys edge labels
• Graph3D - Double Arrow in 3rd Dimension
• HighlightGraph Problem
• Why equivalent Graph objects yield different results?
• EdgeAdd function not adding edges to a RandomGraph[ ] with no edges
• Why does adding an edge to an empty graph not work as expected?
• Is this memory leak in VertexDelete a bug?
• Finding all Minimal Cut Sets for Site Percolation?
• Arrows from GraphicsComplex not converted to Normal form correctly
• Odd behaviors of FindKPlex
• Set new edge capacity
• FindVertexCut & FindEdgeCut
• FindMaximumFlow generates a weird result
• TreePlot EdgeLabeling Style
• GraphAutomorphismGroup bug or my misunderstanding?
• Self-loops in Graph may not display correctly or export correctly to PDF (due to BezierCurve problem)
• What's the meaning of FindVertexCut?
• TreePlot, VertexRenderingFunction and stretched vertices issue
• GraphDistance gives incorrect result in weighted multigraph

Some of these are rather inconsequential (but annoying), e.g. Graph3D - Double Arrow in 3rd Dimension, but some are absolutely fundamental and absolutely need to be fixed, e.g. GraphDistance gives incorrect result in weighted multigraph or Why equivalent Graph objects yield different results?

And keep in mind this list is just those left open, which is a fraction of the total number reported by Szabolcs (and possibly only partially fixed).

I find it odd the lack of evolution (or basic maintenance) of this functionality, as graphs seem to be used more and more in other fields being integrated in the WL. But I guess that the functionality is probably good enough for these applications (that are basically representation related?).

I think that I would also have fallen on your problem, as graphs functionality focus was considerable when it was presented (and I have the sensation that it never really stopped), with multiple blog posts talking of it. I even remembered a post on Spacetime that seemed to point to the need of considerable graph capabilities.

(for version 12, at the 30th anniversary, I would be very happy with just functionality polishing)

Hi Szabolcs,

My voting routine still uses the original Combinatorica package by Sriram V. Pemmaraju and Steven S. Skiena. This uses a somewhat other format, and I did not want to get lost in brackets. It is still included in Mathematica. If I recall it correctly, Mathematica's graphs & networks have been based upon Combinatorica, which might explain that WRI hasn't its heart on the issue as you suggest or show. I am not in graphs & networks as a topic myself, only such a user. I can only hope for you that there is such a community that would support you on this issue.

You might like my earler text "Beating the software jungle", now included here: https://zenodo.org/record/291974

Best regards, Thomas