Re: Swiftest code to turn list of ordered pairs into Markov matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg29701] Re: [mg29683] Swiftest code to turn list of ordered pairs into Markov matrix
• From: Rob Pratt <rpratt at email.unc.edu>
• Date: Wed, 4 Jul 2001 03:08:26 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Perhaps you can modify the FromOrderedPairs command in the
DiscreteMath`Combinatorica` package.  FromOrderedPairs creates a graph,
but you can do Edges[FromOrderedPairs[oplist]] to get the adjacency
matrix.  The Edges[] matrix has entries in {0, 1}, so some modification is
needed if you want to count duplicate edges.

Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill

rpratt at email.unc.edu

http://www.unc.edu/~rpratt/

On Tue, 3 Jul 2001, Seth Chandler wrote:

> Suppose one has a list of ordered pairs oplist such as
> {{1,5},{1,6},{2,3},{2,3} ... }. All the values in the list are positive
> integers. The highest value in oplist is known to be some value z.
>
> Now one wishes to form a matrix such that the value at element i,j is equal
> to
> Count[oplist,{i,j}]. One terribly slow way to do this is
>
> Table[Count[oplist,{i,j}],{i,1,z},{j,1,z}]
>
> A faster way to do this is as follows:
> Fold[ReplacePart[#,Extract[#,#2]+1,{#2}]&,Table[0,{z},{z}],oplist]
>
> Does anyone have a considerably faster way? A speed up of 100% or more would
>
> For what it's worth Count[oplist,{something_,_}] is the same for all values
> of something.
>
> P.S. The problem arises in converting a representation of a directed graph
> into a Markov transition matrix.
>
> Thanks,
>
> Seth J. Chandler
> Associate Professor of Law
> University of Houston Law Center

```

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