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Thanks Carter and others who has posted me - being the constant SNA
newbie, it's much appreciated!

The application in question is economic-geographic so I have looked at
the network-shape measurements which were applied in the 60's (Kansky,
Garrison et al). Kansky developed a shape measurement for valued
non-directional graphs that works like this:

Pi index = C/d
Where C=sum of all edge values (total mileage), and d=total edge value
for the graph's topological diameter

d is calculated first by measuring the topological diameter (i.e. the
largest min-nbr-of-edges-traversed for all pair of nodes), setting d to
be the total mileage for this diameter. If there are several possible
paths which fulfils this minimum-step criteria, d is set as the average
mileage for these paths. Using this measurement, Kansky calculates a
Pi-shape index for the railway system in France to be up to 30 (close to
a total graph), while the shape of Bolivia's railway network is close to
one (elongated network).

Although this index has been somewhat criticised, I find it quite
interesting and valuable. Which measurement of shape in the standard (or
non-standard) repertoire of SNA tools is theoretically similar? C/P?

/Carl
-----
Carl Nordlund, BA, PhD student
carl.nordlund(at)humecol.lu.se
Human Ecology Division, Lund university
www.humecol.lu.se


-----Ursprungligt meddelande-----
Från: Social Networks Discussion Forum [mailto:[log in to unmask]] För
Carter T. Butts
Skickat: den 24 oktober 2003 01:11
Till: [log in to unmask]
Ämne: Re: Measurements on network shapes


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Carl Nordlund wrote:
> *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****  Are
> there any established SNA indices that describe the shape of networks,

> preferably which makes it possible to do comparisons between the
> shapes of networks?
>

There are many.  For starters, try the various graph-level indices
described in Wasserman and Faust; if you're interested in tree-like
structure, you should also take a look at Krackhardt's "Graph
Theoretical Dimensions of Informal Organizations" in K. Carley and M. J.
Prietula (1994), _Computational Organization Theory_.  If your interests
are application-specific (e.g., disease transmission), you can find
many, many more in the literature (see especially various papers in
_Social Networks_).

Hope that helps,

-Carter

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