st: identifying extended families (or clusters) from parent-child (or arcs/edges) relationships.

[Lucas Ferreira Mation <lucasmation@gmail.com>]

Dear Statalisters,

Simplified version of the question: from a list of "parent" "child"
relationships, How to find the "extended families"(or "clusters"),
i.e. groups of people that are somehow connected?
In the example:

	input str1 parent str1 child extended_family_ID
		A T 1
		B T 1
		C Y 2
		C U 2
		D W 3
		E W 3
		E Z 3
		F Z 3
end

suppose I did not have the column "extended_family_ID" (which I
included manually). How could i create it automatically?
Note that extended families 1 and 2 are "normal". In family 1, parents
A and B have child T. In family 2, parent C has children Y and U.
Family 3 is more complicated. Parents parents D and F are only related
because their children (W and Z) share the same parent E.


I've searched Stata manuals and Statalist but could not find a
solution for this, so I appreciate any ideas. I´ve found a hint of a
solution using Social Network Analysis
(http://www.rensecorten.dds.nl/files/netplot_120410.pdf) which would
require converting the relationship data to a adjacency matrix and its
powers do define connected "vertices" (=extended families) > convert
back to parent-child format including the family information. But I
wanted to know if there is a less convoluted solution.

The above question is a pedagogic version. In reality, I´m trying to
map the minimal geographical areas of the Brazilian Census (called
"Setores Censitários", which is equivalent to a few blocks) through
time. The difficulty is that, from one Census to the next, some of
areas divide up while others are aggregated in complex ways.

regards
Lucas Mation
IPEA

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