# Questions tagged [nauty]

Questions about the program Nauty (No AUTomorphisms, Yes?) used for studying isomorphisms of graphs.

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### nauty/traces orbit sizes for colored graph?

I'm given a graph $G$ (<1000 vertices, large automorphism group), and a large number (~10^6-10^10) of different colorings of said graph. I have two tasks.
Calculate the canonical coloring. I can ...

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### Edit distance vs. canonical adjacency matrix distance

Let $G$ and $G'$ be two simple random graphs on the same set of nodes. Let $d_{edit}$ be the edit distance between $G$ and $G'$. Let $\mathbf{A}$ and $\mathbf{A'}$ be the adjacency matrices of the ...

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### Generate all non-isomorphic partitions $\pi = \{ \{1, …, n-1\}, \{n\} \}$ for all graphs of order $n$

Let $G$ be any connected, undirected, and unweighted graph of order $n$.
Let $\pi = \{ \{ 1, ..., n-1 \}, \{ n \} \}$ be partitioning of $G$ such that always $n-1$ vertices are in the first cluster ...

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### Details of generation programs supplied with nauty

The program nauty comes with gtools which contains, among others, several generation programs like geng, genbg, ... I was ...

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**1**answer

187 views

### Generating k-partite graphs

Does there exist an efficient algorithm for generating all non-isomorphic k-partite graphs up to a certain order $n$? I've read through the nauty tutorial, but it doesn't look like anything beyond ...

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302 views

### An example of when nauty, on two different platforms, gives different canonical labels for the same input graph? [closed]

Let $G$ be a graph. I've heard that, if we use nauty to canonically label $G$ on two different platforms, it's possible to obtain distinct labels. However, I've never actually seen this occur.
The ...

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278 views

### Is there a canonical labelling package optimised for small graphs?

Recently, I've been looking into motifs in networks (directed graphs) -- small connected induced subgraphs that appear significantly more frequently than in a "similar random graph".
In practice, we ...