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Hello, are you aware of any open source implementation of this algorithm ?
Some nice presentations on the topic: - https://www.irif.fr/~habib/Documents/cours_4-2015.pdf - http://igm.univ-mlv.fr/AlgoB/algoperm2012/04Paul.pdf - http://www.lirmm.fr/~paul/Talks/talk-06-algo-sem-McGill.pdf
>See table 3 from https://arxiv.org/abs/1811.10705 This is with $n=50$ nodes. It seems that the behavior is not the same for $n$ large: - I think that in a large ER, if the proba of connection $p$ is not too large or too small, then it is rare to find a group of nodes with the same neighbors outside the group (i.e. find a module). Can you prove that? - I don't think that the code https://github.com/antonovvk/decmod is buggy.
[Almost all finite graphs are asymmetric](https://en.wikipedia.org/wiki/Asymmetric_graph#Random_graphs). There is no pair of vertices with common neighborhood.
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An improvement to Boldi-Vigna WebGraph. It uses Huffman coding, asymmetric numeral systems (a form of arithmetic coding) and a new hybrid integer encoding schema. The paper also mentions other algorithms like [Log(Graph) by Besta et al.](https://www.youtube.com/watch?v=j98N9nthr0M) and Apostolico-Drovandi method together with $k^2$-trees, 2D block trees, ZipG graph store... Author suggest the [Besta-Hoefler survey (2018) with more than 460 references](https://arxiv.org/abs/1806.01799) to any reader interested in lossless graph compression methods. The paper does not consider node permutations. The code is in [google's github account](https://github.com/google/zuckerli).
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Furthermore, Apostolico and Drovandi suggest to use $\pi$-code, see Section 4 from [their paper](https://papers-gamma.link/paper/178), when the power law distribution have an exponent close to 1. It actually pushes me to ask, maybe a naive question: is there any standard method to construct such a code when the distribution of the gaps is given or estimated from the data?
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Clever algorithm. The java code is [available on the net](https://github.com/drovandi/GraphCompressionByBFS). In 2009, it was almost simultaneously published with [Permuting Web and Social Graphs](https://papers-gamma.link/paper/177) of Boldi et al. At this time it is better than Boldi et al. solution in many cases. The Apostolico-Drovandi paper is mentioned as "The only coordinate-free compression algorithm we are aware of" in [another](https://papers-gamma.link/paper/105) Boldi et al. paper which was published after a while. At that time Boldi et al. provide better results.
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