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RandomHypergraph #510

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daneelsan opened this issue Nov 2, 2020 · 2 comments · Fixed by #511
Closed

RandomHypergraph #510

daneelsan opened this issue Nov 2, 2020 · 2 comments · Fixed by #511
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@daneelsan
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feature New functionality, or change in existing functionality wolfram language Requires Wolfram Language implementation

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@daneelsan
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The problem

Implement the RandomHypergraph function.

Possible solution

A possible implementation and API is found in the WFR:

RandomHypergraph[{n_Integer, {e_Integer, a_Integer}}] := 
 RandomInteger[{1, n}, {e, a}]

RandomHypergraph[{n_Integer, sig : {{_Integer, _Integer} ..}}] := 
 Catenate[RandomInteger[{1, n}, #] & /@ sig]

image

In[]:= RandomHypergraph[{10, {5, 2}}]
Out[]= {{5, 4}, {7, 8}, {7, 6}, {7, 1}, {4, 9}}
In[]:= RandomHypergraph[{10, {{5, 2}, {4, 3}}}]
Out[]= {{1, 2}, {2, 9}, {6, 1}, {3, 3}, {10, 10}, {1, 8, 8}, {5, 7, 9}, {5, 
  7, 6}, {5, 3, 3}}
@daneelsan daneelsan added feature New functionality, or change in existing functionality wolfram language Requires Wolfram Language implementation labels Nov 2, 2020
@daneelsan daneelsan self-assigned this Nov 2, 2020
@daneelsan daneelsan mentioned this issue Nov 2, 2020
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@maxitg
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maxitg commented Nov 2, 2020

I think another useful API would be just specifying the total number of hyperedge parts (essentially, the "complexity").

E.g., for {{1, 2, 3}, {3, 4}, {4, 5, 6}}, this number will be 8.

This way, one can generate any possible hypergraph by varying just one parameter. This will be even more useful for enumeration.

@daneelsan daneelsan mentioned this issue Nov 3, 2020
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@maxitg
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maxitg commented Nov 4, 2020

It might also be useful to generate connected hypergraphs (maybe with an option).

@maxitg maxitg mentioned this issue Nov 4, 2020
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daneelsan added a commit that referenced this issue Nov 9, 2020
@daneelsan
RandomHypergraph (#511)
d3e9126 
## Changes
* Close #510.
* Implements `RandomHypergraph` function.

## Comments
* Missing option `"Connected" -> True` to specifically generate random connected hypergraphs.

## Examples

```wl
In[] := SeedRandom[2]; RandomHypergraph[8]
Out[] = {{2, 3}, {8}, {1, 6}, {7, 7}, {1}}

In[] := RandomHypergraph[8, 10]
Out[] = {{3, 7, 7}, {1, 7}, {10, 2, 6}}

In[] := RandomHypergraph[{5, 2}]
Out[] = {{5, 1}, {10, 7}, {9, 3}, {3, 2}, {4, 6}}

In[] := RandomHypergraph[{{5, 2}, {4, 3}}, 2]
Out[] = {{1, 1}, {1, 1}, {2, 2}, {1, 1}, {1, 2}, {1, 2, 2}, {1, 1, 2}, {1, 2, 2}, {2, 1, 1}}
```

```wl
In[]:= SeedRandom[111];
Grid[Partition[
  Table[Labeled[WolframModelPlot@#, # -> i] &[
    RandomHypergraph[i]], {i, 1, 12}], 3, 3, 1], Frame -> All]
```
![image](https://user-images.githubusercontent.com/40190339/98330685-e886ca00-1fc8-11eb-92ab-1aca157be21c.png)

## Documentation

![image](https://user-images.githubusercontent.com/40190339/98401650-05a4b280-2034-11eb-9ae3-fd2b14f17c46.png)

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feature New functionality, or change in existing functionality wolfram language Requires Wolfram Language implementation
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RandomHypergraph maxitg/SetReplace
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