# Pul Eliya

Pul Eliya Its the men who are more mobile, sometimes the origin of their fathers is ignored, especially if the father is from a different village. So the sons of these distant-village fathers are free to marry where they will, and so do not belong to an inherited agnatic compound. These brothers are free to marry women from various compounds, without regard for marital sidedness. This part of what accounts for the black solid lines that do not correspond to the viri- sides but rather cross over from side to side relative to their fathers. Nonetheless, all marriages among blood relatives who are four or fewer generational links distant follow the rule of virisidedness. This is what accounts for the majority of dotted red lines (for wives) who marry side-to-side, connecting the two "sociocentric" sides of males.

There are eight generations here, as in the original publication, where generations were calculated by a fortran program. 1998. **Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya** Michael Houseman & Douglas R. White. pp. 59-89 In, Kinship, Networks and Exchange, eds. Thomas Schweizer and Douglas R. White. Cambridge University Press.

Until 2009 the Pajek program did not compute generations correctly, and would yield nine generations.

http://eclectic.ss.uci.edu/~drwhite/pub/PUL-CAMB1a.pdf http://tinyurl.com/2lb2gu http://www.ivry.cnrs.fr/spafrican/chercheurs/articles/Network%20Mediation.pdf

White established that sidedness was perfectly realized in behavior for blood relatives within four generations and continued that study in 1999 Controlled Simulation of Marriage Systems. **Journal of Artificial Societies and Social Simulation** 2(3). http://jasss.soc.surrey.ac.uk/2/3/5.html.

It is also possible to prove mathematically that when two individuals with two or more common ancestors with inconsistent sidedness at 4 or fewer generations remove, their intermediate relatives will have inconsistent sidedness in their parental or grandparental relations, which is strongly avoided societies with sided kinship terminologies (a parent or grandparents is never classified as an "affine").

These findings provide one resolution to the arguments about the relationship between egocentric sidedness and sociocentric sidedness, so long argued in social anthropology.

It is common for societies to have named moieties where sidedness is inherited in the male or female line, but this does not occur in many societies like Pul Eliya, where sidedness in the kinship terminology does not automatically determine sociocentric sides. How this occurs, then, is a solved problem for the Pul Eliya and illustrates a more general network principle of balance where local network structure entails a more general sociocentric outcome, with exceptions.

The probability that the sidedness of a graph is random is computed from its largest bicomponent, which includes all nodes with 2 or more links and has no cutnode. With n nodes and e edges, the number of independent cycles k is k = e - n + 1. Counting the number v of edges that violate sidedness, then the expected value of v = k/2, i.e., half the k independent cycles will be sided, half nonsided, and the deviation from randomness is computed by the binomial theorem.

## Repast and Pajek

This Pul Eliya graph emphasizes male links that violate sidedness, which is a more global network structure with local realizations. Once Repast generates random networks, the more usual step is to compute the frequencies of all the more local motifs, as in the JASSS paper, and compare them with their simulated random frequencies. Those counts are done in Pajek with the fragment-in-graph finder.