I would be interested to know exactly what algorithms D3 uses to achieve the force-directed graph feature in the library. Having read Kobourov's summary of the history of force-directed graphs left me a bit baffled as to what is the exact algorithm or method (bination of algorithms / heuristics) used in the library.

D3 API reference says Barnes-Hut algorithm is used to calculate the charges acting on bodies, an O(N*log(N)) operation. Kobourov's article mentions that Quigley-Eades algorithm, and Hu's algorithm are multilevel algorithms that make use of Barnes-Hut. Is one of them utilized in some way in D3?

The API wiki futher says Verlet integration is used for particle positioning. The source code mentions Gauss-Seidel algorithm, which in turn is mentioned both in Hu's algorithm and Dwyer's graph layout paper. I guess the question I'm looking an answer to is what "integrative" algorithm D3 utilizes; Kobourov's article lists several and D3 force-directed features don't directly seem to fit any of those.

I would be interested to know exactly what algorithms D3 uses to achieve the force-directed graph feature in the library. Having read Kobourov's summary of the history of force-directed graphs left me a bit baffled as to what is the exact algorithm or method (bination of algorithms / heuristics) used in the library.

D3 API reference says Barnes-Hut algorithm is used to calculate the charges acting on bodies, an O(N*log(N)) operation. Kobourov's article mentions that Quigley-Eades algorithm, and Hu's algorithm are multilevel algorithms that make use of Barnes-Hut. Is one of them utilized in some way in D3?

The API wiki futher says Verlet integration is used for particle positioning. The source code mentions Gauss-Seidel algorithm, which in turn is mentioned both in Hu's algorithm and Dwyer's graph layout paper. I guess the question I'm looking an answer to is what "integrative" algorithm D3 utilizes; Kobourov's article lists several and D3 force-directed features don't directly seem to fit any of those.

• javascript
• algorithm
• d3.js
• graph-algorithm
• force-layout

Share Improve this question Follow edited Jun 16, 2014 at 15:05 VividD 10.5k88 gold badges6666 silver badges112112 bronze badges asked Oct 16, 2012 at 14:30 amerginamergin 99211 gold badge1313 silver badges3232 bronze badges 2

• You best email that question to Mike Bostock… – akuhn Commented Oct 25, 2012 at 8:59
• @akuhn: I haven't seen the creator's email on D3 website. I don't it would be appropriate to email such questions directly to him, then everyone in the munity would just do that. I have seen Mike answering questions here on SO so I think this is the right forum to ask. – amergin Commented Oct 25, 2012 at 11:20

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In the original d3 paper, Mike Bostock & al. wrote that Dwyer's implementation is used for the force graph layout :

The force layout bines physical simulation and iterative constraint relaxation [7] for stable graph layout.

[7] T. Dwyer. Scalable, versatile and simple constrained graph layout. In EuroVis, 2009.

For more information, Dwyer's paper describes in details the whole algorithm.

Well, this isn't an answer to your specific question, but on his demo page for force-directed layout, he says, "Layout algorithm inspired by Tim Dwyer and Thomas Jakobsen."

An overview of the Force-Layout algorithms can be found at https://github./mbostock/d3/wiki/Force-Layout