This R code explores an old graph-partitioning algorithm. The algorithm's end-goal is to find a minimal-edge, hierarchical digraph which preserves the reachability properties of a given digraph. This algorithm used to be a major part of Interpretive Structural Modelling (ISM). I am referring specficially to the algorithms described in the work of J.N Warfield:
- Warfield (1976) Societal Systems ISBN 0-471-01569-5 esp. Ch.9 and 10
- Warfield (1974) 10.1109/TSMC.1974.4309336
- Warfield (1973) doi 10.1109/TSMC.1973.4309270
Today the term ISM has mutated - and now refers to some wishy-washy parody of the original, rigorous approach. Over the past decades, academics have unilaterally decided to strip ISM off its most characteristic computational devices. As rigour decreased, the number of publications claiming to apply ISM grew (or vice versa? but I digress...). Long story short, i am wary of published ISM research today. For a better articulated rant feel free to dig some work in progress of mine, available as a preprint at http://dx.doi.org/10.2139/ssrn.3622934 Utilmately, the code is meant for use as supporting materials for such paper.
There are not many options that I know of to implement ISM calculations transparently on a computer. The J.N. Warfield IP Trust kindly provides ISM software free of charge (see: https://www.jnwarfield.com/ism-software.html). Yet the software is not open source and I'm not sure which parts of the original algorithm are implemented - if any - and how.
Therefore, this code is my two pennies worth contribution to making ISM available to those interested in
- looking under the hood of this technique
- reclaiming the rigour of the original procedures, which is lost in the incumbent academic literature - I think;
The code explores surprising, but unnoticed similarities with other well-known algorithms. Namely, the code includes a function for finding strongly connected components (SCC) by Depth-First Search, which is borrowed from my other repository (https://github.com/Dr-Eti/RtarD-Tarjans_DFS_in_R.git). It also provides a block-triangular permutation of the corresponding adjacency matrix. There's lots in common between ISM; finding SCC in a digraph; and working out a block triangular permutation of the adjacency matrix of said digraph. You might argue DFS can do that quite efficiently - although it was not quite as popular when the original ISM work came out, and hence never acknowledged. But don't tell those academics who publish what they claim to be ISM - I love that they don't have a clue of what on earth they're trying to do as they go through the moves of something reminiscent of ISM. Let them have a good sweat.