# P-graph

- Breitling Lutz P. Breitling. <lutz.breitling@gmail.com> <l.breitling@dkfz-heidelberg.de> 2010. dagR: a suite of R functions for directed acyclic graphs. Epidemiology 21(4):586-587. Lutz P Breitling <lutz.breitling@gmail.com> dagR: A Suite of R Functions for Directed Acyclic Graphs[http://journals.lww.com/epidem/Fulltext/2010/07000/dagR__A_Suite_of_R_Functions_for_Directed_Acyclic.26.aspx
- Breitling LP (submitted). Understanding confounding and data analytical strategies through DAG-based data simulations.
- Greenland S, Pearl J, Robins JM (1999). Causal diagrams for epidemiologic research. Epidemiol- ogy 10(1):37-48.

- [http://cran.r-project.org/web/packages/dagR/dagR.pdf Package(dagR.pdf)
- [http://artax.karlin.mff.cuni.cz/r-help/library/dagR/html/summary_dagRdag.html
- Kn\"uppel S, Stang A (2010). DAG Program: identifying minimal sufficient adjustment sets. Epidemiology 21(1):159.
- http://rgm3.lab.nig.ac.jp/RGM/R_rdfile?f=dagR/man/dagR-package.Rd&d=R_CC

Response to David_M._Schneider#Debate_over_Kinship

see also: http://www.kintip.net/content/view/74/#Tip_format The paj files currently on Kinsources are in the all-arcs (5 relation numbers) format. But this is just a coincidence. The Tip4Pajek macros allow transforming them into Ore-graph format, and Puck can transform them into P-graph format.

## Contents

## formats for ego2cpl

http://eclectic.ss.uci.edu/~drwhite/pgraph/ego2cpl.html#data

## P-graph

The p-graph is so named for parental graphs (French parenté). In the expanded version of White and Jorion (1992). as opposed to P for Paul-graphs which were marriage rule models, the nodes in the p-graph are nodes defined by the parents or offspring in nuclear families. A node may represent either (1) a couple or parental couple or single parent or (2) an unmarried child. A node of either type may have a directed tie to a parental node. A node of the second type will transform to one of the first type upon becoming a parent, or married, or coupled.

1992 Representing and Computing Kinship: A New Approach. Douglas R. White, Paul Jorion. Current Anthropology 33(4): 454-463. http://eclectic.ss.uci.edu/~drwhite/pw/White-Jorion1992.pdf

1996 Kinship networks and discrete structure theory: Applications and implications. Douglas R. White, Paul Jorion. Special Issue on Social Network and Discrete Structure Analysis. Social Networks 18(3): 267-314. doi:10.1016/0378-8733(95)00277-4 http://eclectic.ss.uci.edu/~drwhite/pub/KinNetsDiscStr1996.pdf

## Pgraph software

The White and Jorion (1992, 1996) articles used the Pgraph FORTRAN program written by White to analyze canonical kinship networks where a child has only a single parental node. The key data storage is a pair of vectors for a daughter's F(i) link and a son's G(i) link to the parent.

## Pajek software

The Pajek program adopted the p-graph as a formal structure for representing kinship networks as defined by genealogical relationships and read from GEDcom or GEnealogical Data COMmunication files in which most of the world's genealogical files have been encoded, along with dates of birth, marriage, death, as well as occupation, residence and life events. All the basic data in GED files are automatically transcribed into Pajek files for further analysis. One of the nice properties of the p-graph is that it defines maximal sets of kin who are connected by structural endogamy, or what are called by collaborator Michael Houseman the **matrimonial core** of a kinship community, a concept related to **structural cohesion**.
See also Petri net

### Pajek p-graph format example

This is an illustrative Pajek *.net file for a couple (node 1), their son (2) and their daughter (node 3). You can open an empty file with notebook or any ASCII editor, copy and past, and save with a *.net extension.

*Vertices 3 1 "Michiel Mence + Anucla Gondola" box 2 "Raduo Mence " triangle 3 "daughter" ellipse *Arcs :1 "Son's Parent" 2 1 1 c Black *Arcs :2 "Daughter's Parent" 3 1 2 c Red p Dots

Black lines are to parents of a male, Red dotted lines are to parents of a female. The square box is a couple, the triangle an unmarried male, the circle an unmarried female. Those shapes can be altered to suit your objective.

*This is an expansion of the p-graph format *Vertices 6 1 "James + Janinea" box 2 "Colin M" triangle 3 "Hannah" ellipse 4 "Richard + Winifred" box 5 "Vicky" 6 "Orville + Bonnie" box *Arcs :1 "Son's Parent" 2 1 1 c Black 1 4 1 c Black *Arcs :2 "Daughter's Parent" 3 1 2 c Red p Dots 1 6 2 c Red p Dots 5 6 2 c Red p Dots

### P-graph fragment census

Pgraph_Notation_Test.xls can be downloaded and used as input for creation the P-Frag.for program which makes small Pajek cycles that represent types of marriages. Pajek will search for these and census them, picking out the segments of the larger network in which they occur. See: The P-graph/Pajek marriage census

## P-system

Frank Harary and Doug White defined the P-system as a formal mathematical model that supports the p-graph construction.

2001 Frank Harary and Douglas R. White P-Systems: A Structural Model for Kinship Studies. Connections 24(2):35-46. Click the article title at that site for the PDF.

Abstract: Several mathematical models have been proposed for kinship studies. We propose an alternate structural model designed to be so simple logically and intuitively that it can be understood and used by anyone, with a minimum of complication. It is called a P-system, which is short for parental system. The P-system incorporates the best features of each of the previous models of kinship: a single relation of parentage, graphs embedded within the nodes of other graphs, and segregation of higher level descent and marriage structure from nuclear family structure. The latter is also the key conceptual distinction used by Lévi-Strauss (1969) in the theory of marriage alliance. While a P-system is used to represent a concrete network of kinship and marriage relationships, this network also constitutes a system in the sense that it contains multiple levels where each level is a graph in which each node contains another graph structure. In sum, the connections between the nodes at the outer level in a P-system are especially useful in the analysis of marriage and descent, while at inner level we can describe how individuals are embedded in the kinship structure.

## Summaries

The early exemplars and definitions for Pajek reading, representation, and analysis of genealogical networks are described in the following article:

1999 Douglas R. White, Vladimir Batagelj and Andrej Mrvar, Analyzing Large Kinship and Marriage Networks with Pgraph and Pajek, Social Science Computer Review 17(3):245-274. For the Sage Article pdf see: http://eclectic.ss.uci.edu/~drwhite/pw/AnalyzingLargeKinshipNetworks1999.pdf

Abstract: The p-graph approach that has proven an invaluable aid to the study of kinship, marriage and genealogical network analysis is explicated here in terms of solving five key conceptual problems of network studies, including that of identifying subgroup boundaries -- and combined with a computer package for sparse-network algorithmic analysis and visual representation of large (up to 90,000 node) networks. The results of this new marriage between graph-theoretical analysis, computer science, network anthropology and network-visualized social history are illustrated for a 1600- person social system consisting of an entire Turkish nomad society, with a relinking density of 75%, the highest density of structural endogamy yet recorded. It is shown how the algorithmic, analytic and graph-editing technology of this new concatenation of elements for network analysis leads to striking new understandings of social structure and social processes, and how to prepare visualizations of discoverable emergent properties of structure in such a large and dense network. This article reviews the developments and contributions of the authors to the evolution of these tools and methods for large-scale network analysis, and provides a complete series of guides and illustrations for the reader to utilize the two software packages discussed.