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Vaughan,

One thing you need to compute the small world statistics (described in Watt's book ) is to know how many nodes and ties your actual network has. This can be done quite easily using UCINet. Using the number of actual ties and nodes, you can compute clustering coefficients and path length for the random graphs to which your actual graphs can be compared. The detinition of these values are given in Watt's book as well.

Then you can also use UCINet to compute actual average pathlength in your network. This also can be done using UCINet option: Network-->Cohesion-->Distance.

The only catch is how to compute a clustering coefficient for your actual network. This can be implemented in VisualBasic or any other language that can deal with matrices in one way or another. I don't know of any software that does this computation.

One thing you need to watch out for is the isolated components in your network. If you have those, then the value of actual average path length doesn't make sense, because some nodes cannot reach other nodes by definition. Have a look at the following paper on how we dealt with this problem:

Baum, J.A.C., Shipilov, A., Rowley, T. Where do small worlds come from? 2003. Industrial and Corporate Change <http://icc.oupjournals.org/> (Special Issue in Honor of James March) Vol. 12 (3).

Good luck.

Andrew Shipilov

        -----Original Message-----
        From: Vaughan [mailto:[log in to unmask]]
        Sent: Sun 11/16/2003 5:26 PM
        To: [log in to unmask]
        Cc:
        Subject: Small world / scale free query



        *****  To join INSNA, visit http://www.sfu.ca/~insna/  *****

        Hello everyone,

        I am currently analysing the interconnectedness of a sub-set of web sites
        and have successfully coded the network and have a model which loads into
        either Pajek, NetDraw or UCINET.

        I would like to find out whether the network I have is a small world or
        scale free network (or neither), however it is not obvious to me which
        analysis in any of these software packages would tell me this.

        I have a background in psychology, rather than graph theory or sociology so
        some of the literature is a little mysterious to me. I have papers which
        define small world / scale free networks in mathematical terms but no
        pointers as to how (and if) this is implemented in relevant software
        packages.

        I have the Wasserman and Faust book ('Social Network Analysis') and two
        Watts books ('Six Degrees' and 'Small Worlds') so would be equally as happy
        to receive pointers as to what to read as to what to do !

        Many thanks,
        Vaughan Bell

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