Code covered by the BSD License

### Highlights from Random Regular generator

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# Random Regular generator

### golan pundak (view profile)

creates a random regular graph in the pairing model

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Description

the function:
A = createRandRegGraph(vertNum, deg)
create a simple d-regular undirected graph
vertNum - number of vertices.
deg - the degree of each vertex.
A is asparse matrix representation of the graph.
reference for "The pairing model":

MATLAB release MATLAB 7.11 (R2010b)
31 Jul 2013 golan pundak

### golan pundak (view profile)

Poormina: This code does (should) produce single undirected edge between nodes.
As a note: If you don't care about multiple edges and self loops there is a much simpler algorithm: pick d/2 permutations at random.
The reason this code is complicated is because it avoids multiple edges and self loops.

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31 Jul 2013 Poornima

### Poornima (view profile)

Dear Golan
Thank you. That was really a valuable suggestion! :)
Well, When I meant 'one edge', I meant undirected edges.... or a single edge bw nodes.

29 Jul 2013 golan pundak

### golan pundak (view profile)

Poormina:

You can add weights by multiplying the output with a random matrix
A_W = A.*rand(size(A,1), size(A,2))

Not sure what do you mean by 'one edge'. If you want to edges to be directed the nice property of d-regularity will be lost.

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29 Jul 2013 Poornima

### Poornima (view profile)

A very nice script. Thank you.

Is it possible to display the graph with just one edge between the nodes and not two with this code? Also, is it possible add weights to the edges? Thanks in advance...

h = view(biograph(G,[],'ShowArrows','Off','ShowWeights','on'));

26 Apr 2012 Felix Goldberg

### Felix Goldberg (view profile)

Overall, very nice.
But I'm afraid a bug may be lurking somewhere. Sometimes I call this function and get a zero matrix. Is this a bug or a feature?

12 Feb 2012 golan pundak

### golan pundak (view profile)

So it seems these are all problems of dynamically allocating memory and coping data. Here are 2 optimizations that can solve this:
1. Replace the sparse n*n matrix A by a preallocated n*d adjacency list, filled initially with -1.

2. Instead of recreating U (half edges), keep its size as a separate variable and only swap elements when updating it.

Maybe I'll get to it some day :)

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12 Feb 2012 Derek O'Connor

### Derek O'Connor (view profile)

This is a very useful function for graph-algorithm theoreticians and testers. However, its usefulness is limited by a severe bottleneck which occurs here:

5.61 75000 68 A(v1, v2)=1;
5.26 75000 69 A(v2, v1)=1;
70
71 %remove used half-edges
0.36 75000 72 v = sort([i1,i2]);
26.05 75000 73 U = [U(1:v(1)-1), U(v(1)+1:v(2)-1), U(v(2)+1:end)];
0.01 75000 74 end
0.65 75016 75 end

41.00 Total Time

As usual, the problem is caused by the inappropriate use of Matlab's powerful array manipulation operations.

Can the author devise a better way to remove the half-edges?

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