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Berhie,

If you are not satisfied with 'arbitrary' choice of the shortest path when the two path have the same length, you might want to try other kinds of betweenness .  I believe you would be happy with Newman's random walks betweenness centrality. It does not count only the shortest paths. It considers all possible paths between nodes and gives weight according to the inverse of the path length so that the shortest path gives more weight.  See how such idea is implemented:

http://www.sciencedirect.com/science/article/pii/S0378873304000681

Yongha



On Sun, Jun 22, 2014 at 10:26 AM, Minseok Kim <[log in to unmask]> wrote:
Berhie
I think Saboya is coming to the point.
I had a chance to discuss about calculating choice value with Turner, former developer of Depthmap.
The way of 'randomly choosing' is adapted to then version of Depthmap.
Meanwhile, their is another software tool for Grid Map analysis, 'SaVisibility'.
It is a kind of AutoCAD addin, and it can calculate many SS indices, such as connectivity, mean depth, integration, choice, etc.
Surely, the way of 'randomly choosing' is adapted to it.
It is available at:  http://ladonara.blogspot.com



2014-06-22 10:23 GMT+09:00 Renato Saboya <[log in to unmask]>:

Berhie,
Did you solve the connectivity issue before testing the random assignment possibility? If not, maybe Depthmap isn't even detecting the equivalent shortest paths in the first place.

Tasos probably knows better, but in my defense I found the paper in which I read about my "hypothesis" (see attached file). I was not able to ascertain its date, but it seems rather old and lots of things may have changed since.

"However, in rare cases, there will be two  (or more) routes with exactly the same path length.  In this case we choose one or other node at random,  as shown in  the pseudocode.  This has a side effect that in the extremely rare case where there are two identical shortest paths, one or other will be chosen at random.  Of course, given that there are many nodes in the system, in general the paths will distribute  their weight evenly."

Best,
Renato.


On Sat, Jun 21, 2014 at 5:49 PM, Berhie, Girmay <[log in to unmask]> wrote:
I realized the email I sent earlier didn't go through, I am informed to resend it. Here was my email.

Thank you Tasos and Renato
Renato said  the machine randomly picks one when it faces more than one shorter path between two spaces,
Tasos said the machine just takes the first path from the list. These two are significantly different statements for me. If the machine were to pic randomly,there is a probabilistic chance for each of them to be chosen (the probability will be determined by the number of possible shortest paths). If it was the case I have tried the same map many times I would have seen different results. Tasos's statement seems the case, if the machine picks the first path there is no chance for different result no mater how many times I tried.
However, I would like to ask Tasos whether randomizing the choice is possible. 
I know this is not a big problem as you said since there is no such perfect symmetries, But I am curious what effect could it have in more grid American cities specially at a local level. By the way if I tried by hand, I would split the values among these possible paths. 
Regards

Girmay K. Berhie
Texas Tech University
College of Architecture
Land Use Planning Management and Design (LPMD)
Mailling Address 
2008 56th Street Unite B
Lubbock TX, 79412






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  Minseok Kim
  Assistant Professor.
  Ph.D. in Architecture and Architectural Engineering.
  Department of Architecture, Pukyong National University.
  (Tel: +82-51-629-6085,  Fax: +82-51-629-6083)
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Yongha HWANG
Ph.D candidate in Architecture
The University of Michigan
Taubman College of Architecture and Urban Planning