st: Social Network Analysis shortest path centrality

[Michael Goodwin <michael.goodwin@endeavor.org>]

Hi,

I am trying to do some light social network analysis on a dataset
containing a list of edges. I have the dataset organized such that
there are two variables, Source and Target. Bot the Source and Target
are companies, and the connection between indicates that an employee
from Source went on to found Target. The relationship between these
two variables is indeterminate (i.e. m:m) and although the variables
start as strings, I've converted them to numeric values using encode
(and ensured
that the numeric values in both Target and Source are equal to one another).

I am attempting to determine the number of first, second, third,...,n
degree connections that each Source has. For example if an employees
from Company A went on to found Company B and then employees from
Company B went on to found Companies C and D, Company A would have 1
first degree connection and 2 second degree connections.

My goal is to create something similar to a shortest path measurement
whereby a first degree connection is equal to 1, a second degree
connection 1/2, a third degree connection 1/3, and so forth. In the
above example, Company A's score would be (1/1)+(2/2) or 2. I believe
this is a closeness/shortest path centrality approach, but I may be
mistaken (and would love to be corrected!).

After making the connections symmetric (i.e. all pairs are present as
both inbound and outbound connections), I've attempted three
approaches, all without success:

1. Use netsis and netsummarize. Neither the adjacency nor closeness
calculations seems to get me to the right answer. I don't have
experience using mata, but it appears that the matrix generate by
netsis doesn't reflect the appropriate connections (i.e. a connection
in the original edge list is not represented by a 1 in the matrix)

netsis Source Target, measure(adjacency) name(A, replace);
netsummarize A/(rows(A)-1), generate(degree) statistic(rowsum);

netsis Source Target, measure(distance) name(D, replace)
netsummarize (rows(D)-1):/rowsum(D), generate(closeness) statistic(rowsum)

2. Create a matrix data structure in Stata and use centpow. I keep
receiving an error noting that the matrix is not symmetrical. I've
checked and made sure that the dataset is a perfect square (it has 707
observations and 707 variables) and that a connection between Company
A and Company B is also represented by a connection between Company B
and Company A. Does centpow require the data to actually be in a mata
matrix?

use ".\dta\\${connection}_connectionIDSymmetric${typeInt}.dta";
contract targetID sourceID;
reshape wide _freq , i(targetID) j(sourceID);
qui foreach v of var _freq* {;
replace `v' = 0 if mi(`v');
};
drop targetID;
save ".\dta\\${connection}_adjacencyMatrix${typeInt}.dta", replace;
centpow ".\dta\\${connection}_adjacencyMatrix${typeInt}.dta";

3. Start with the edgelist, and merge it with itself, changing the
Target and Source variable names such that Target becomes Source for
the second degree connection and so forth (I think this is
demonstrably not the solution, so I won't elaborate further).

I think this either has a simple solution that I can't think of
involving the edge list, or will involve a more intensive solution
using mata. If anyone has experience or could point me in the
direction of content (Statalist has limited SNA resources), that would
be a huge help.

Here are some of the resources I've already reviewed:
http://www.rensecorten.org/index.php/research/social-network-analysis-with-stata/
https://sites.google.com/site/statagraphlibrary/netgen111
http://www.ats.ucla.edu/stat/sna/sna_stata.htm

Thanks in advance.

Best,

Mike
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