The P-graph/Pajek marriage census

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Doug 08:00, 7 February 2009 (PST)Douglas R. White P-graph#P-graph_fragment_census

Example: Alyawarra

If you edit the kin-type graph generator labels file to include

ZHZHZHZ that would be distant ZHZ would be close

run the *.exe to get the fragment graphs then find the fragments

How to run the fragment detector / counter

  • Read a kinship P-graph fragment file, e.g., MBD.net, into the network window of Pajek.
  • Read a kinship P-graph *net file, e.g., P-Aly.net, into the network window of Pajek.
  • Click at the right of the lower network window of Pajek, select the P-graph *net file, e.g., P-Aly.net
  • Choose /Nets/Fragment (First in Second)/find
  • A results window will open thats gives the frequency of marriages with a mother's brother's daughter, i.e., of graph fragments for this Kin-type found in the larger network that match the network for a MBD marriage.

Fragment generator

P-FRAG.FOR is a Fortran program (executable: P-frag.exe) that reads a file named KinTypes with entries for Marriage-type Pajek graph fragments such as

BWZ
ZHZ
FZD
MBD
FBD
MZD
MMBDD

and produces the appropriate *.net files. These seven files are stored in Fragments.paj. Other marriage-types may be added by typing their symbols into the KinTypes file. A rather complete set of *.net fragment files is in the zip file P-KinTypes.zip. Pgraph_Notation_Test.xls Has the labels for kin types that can be read by software to create fragments.

Finding marriage-type fragments in the P-graph

Open Pajek, load your *.net file, and then Read the Fragments.paj. Place one of the fragments in the upper "net" window and your *.net file in the lower "net" window. To count the number of fragments of this type:

/Nets/Fragments/(First in Second)/Find

or

/Nets/Fragments/(First in Second)/Options

to change from the Induced [x] to the [ ] (noninduced) fragment search.

Half siblings

If your p-graph *.net file has N nodes, this requires two vectors of length N: one for the personal ID numbers of the male in each node, if any, and one for the female personal ID.

If you want a fragment search of your kinship network that includes half-sibling relationships, the small letters p for paternal and m for maternal are used, e.g.,

FmZD - father's maternal half-sisther's daughter
MMpBDD - mother's mother's father's paternal half-brother's daughter's daughter

This requires a vector ID.vec (ASCII file) of length N with two blank-separated columns, the first for male personal ID, the second for female. 0 is used for no data.

Relative age

If you want a fragment search that distinguishes elder/younger sibling relationships, the small letters e for elder, y for younger and ? for unknown are used, e.g.,

FyZD - father's maternal younger sister's daughter
MMeBDD - mother's mother's father's elder half-brother's daughter 
M?BD - mother's brothers daughter, relative age unknown

This requires a vector AgeRel.vec (ASCII file) of length N with two blank-separated columns, the first for male personal age indicators, the second for female. 0 is used for no data. Nonzero entries are required only for sets of siblings, and birth orders may be represented by 1, 2, 3, ... or by birthdates.

Relative age and half siblings

If you want a fragment search that distinguishes elder/younger AND maternal-paternal half-sibling relationships, both sets of small letters are used, e.g.,

FymZD - father's maternal younger half-sister's daughter
MMepBDD - mother's mother's father's elder paternal half-brother's daughter's

Par-Calc to Pajek

The White and Jorion (1992:458) article that initiated P-graph and kinship network analysis discussed a Fortran program, Par-Calc(.exe), that calculates marriage types for consanguineal kin like FZD, MBD, FBD, MZD, and MMBDD:

"The heart of the P graph algorithm (PAR-CALC), given G and F as input vectors, consists of tracing convergences by vectorial genealogy: BEGIN trace husbands' genealogical trees to a nonempty vector; BEGIN trace wives' genealogical trees to a nonempty vector; save convergences; continue wives' trees until done (no nonempty vectors); END; continue husbands' trees until done (no nonempty vectors); END." (1992:457).

It does not calculate affinal marriage types like BWZ, ZHZ and others. The file structure read by Par-Calc is a *.vec vector file with six vectors and entries for each of N node:

  1. Male's Parents for ith node
  2. Female's Parents for ith node
  3. Male's Sibling order for ith node
  4. Femle's Sibling order for ith node
  5. Male's Personal ID for ith node
  6. Female's Personal ID for ith node

A conversion program is now available from *.vec to *.net format for Pajek.

Once Pajek adopted the P-graph format as the default for conversion of kinship *.Ged files, further program development proceeded in Pajek.

Policy for P-graph/Pajek development