1. Kinship Networks and Structural Endogamy: Women in the Old Testament; Rural Classes in Slovenian Austria; Middle Eastern segmented lineage systems; Reciprocal Exchange and Equality in South India Lilyan Brudner- White University of California – Irvine and Doug White Anthropological Seminar University of Ljubljana, May 20, 2005

2. Defining the phenomena of endogamy: Endogamy is marriage within the limits of a clan, class, caste, etc., with relative degrees of closure. Possible definitons: –By categories/attributes: suffers from problems of specification error –By network relinking: a generalized phenomena of structural endogamy as blocks of generalized relinking (a special case of network cohesion) with:  Subblocks of k-relinkings of k families, with varying depth in generations  Subblocks of consanguinal (blood) marriage as within-family relinkings

3. Data and Representation: Building Kinship Networks To analyze large-scale kinship networks, we need a generalizable graph representation of kinship networks. Problems: Cultural definitions of “kin” lead to cross-cultural ambiguity Forced to pick ‘primary’ relations (marriage, descent) against ‘implied’ relations (siblings, cousins, etc.) or include a complete graph with multiple labeling

4. Data and Representation: Building Kinship Networks The traditional representation is a genealogical kinship graph Individuals are nodes Males and females have different shapes Edges are of two forms: Marriage (usually a horizontal, double line) Descent (vertical single line) Has a western bias toward individuals as the key actor Not a valid network, since edges emerge from dyads Better solution is the P-graph

5. Data and Representation: Building Kinship Networks P-graphs link pairs of parents (flexible & culturally defined) to their decedents P-graphs are constructed by: Treating individuals as lines Usually of different type for different genders Treating couplings as nodes

6. Data and Representation: Building Kinship Networks P-graphs link pairs of parents (flexible & culturally defined) to their descendents P-graphs can be constructed from standard genealogical data files (.GED), using PAJEK and a number of other programs. See: http://eclectic.ss.uci.edu/~drwhite for guides as to web-site availability with documentation (& multimedia representations)

7. Data and Representation: Relating p-graphs to endogamy Cycles in p-graphs are direct markers for endogamy, and satisfy the elementary requirements for theories of kinship-based alliances (Levi-Strauss 1969, Bourdieu 1976): Circuits in the p-graph are isomorphic with one or more of: Blood Marriages, where two persons of common ancestry from a new union Redoublement d’alliance, where unions linking two co- ancestral lines are redoubled Renchainement, where two or more intermarried co-ancestral lines are relinked by a new union These can be subsumed as subtypes of marital relinking

8. Case 1

9. Data and Representation: Relating p-graphs to endogamy (Old Testament Men and Women) Male Descent Female Descent Same person (polygamy) Lot marries his daughters Rachel & Jacob & Leah Abraham & Sarah & Hagar Lot Heran ishmael Nahor Isaac Bethel Nahor Terah (Egypt) http://eclectic.ss.uci.edu/~drwhite/pw/White-Jorion1992.pdf

10. Programs & Availability PAJEK  PAJEK reads genealogical datasets (*.ged files) both the usual Ego format and in p-graph format, with dotted female lines (p Dots) and solid male lines.  PAJEK Network/Partition/Components/Bicomponent computes structural endogamy in a p-graph  PAJEK Network/Partition/Depth/Genealogy computes genealogical depth. This enabled 2D or 3D drawings of kinship networks.  Manuals for p-graph kinship analysis and discussions of software programs & multimedia representations are contained in  1) “Analyzing Large Kinship and Marriage Networks with pgraph and Pajek,” Social Science Computer Review 17(3):245-274. 1999. Douglas R. White, Vladimir Batagelj & Andrej Mrvar.  2) http://eclectic.ss.uci.edu/pgraph  3) http://vlado.fmf.uni-lj.si/pub/networks/pajek  4) book by de Nooy, Batagelj and Mrvar

11. Programs & Availability Hypothesis testing We can use various permutation-based procedures to test the observed level of endogamy against a data-realistic random baseline. The substantive marker for endogamic effectiveness is whether the level of endogamy is greater than expected by chance given the genealogical depth of the graph 1997 Structural Endogamy and the graphe de parenté. Mathématique, Informatique et sciences humaines 137:107-125. Paris: Ecole des Hautes Etudes en Sciences Sociales

12. Applications of Structural Endogamy Social Class Social class as “a general way of life, a sub-culture, tends to be hereditary because (a) individuals from the same sub-culture tend to intermarry, and (b) parents bring up their children to imitate themselves.” (Leach, 1970). If we were to examine the extent to which particular social class formations were concomitant with structural endogamy, we would expect that: Families involved would know "good families“ and "suitable matches,” not all children of the class would be "required" to marry within the class, but social class inscription would take place through the diffuse agency of relinking by marriage, which could both validate the social standing of the individual and constitute the diffuse but relinked social unit -- endogamic block -- of class formation.

13. Case 2

14. Applications of Structural Endogamy Social Class: Carinthian Farmers Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White “Class is rooted in relations to property, but the holding of property is particularistic, bound by social relations that channel its inheritance within particular sets of personal biographies, such as those linked by kinship and marriage. As property flows through a social network, its biography unfolds as a history of the transfer from person to person or group to group.” (p.162) Institutions (such as class), emerge out of the networked actions and choices devolving in turn in specific and changing historical context. A duality of persons and property, each linked through the others, characterizes the class system.

15. Applications of Structural Endogamy Social Class: Carinthian Farmers Empirical setting: Inheritance of property among families in an Austrian Village Background: In the Austrian farming valleys of southern Carinthia, the perpetuation of Slovenian ethnicities and Windisch dialects has been associated with heirship of farmsteads. Unlike many rural areas (and as predicted by Weber and others), farms tended to be inherited complete, without the kind of splitting that fractures property and reduces average class wealth. Main hypothesis: That two social classes emerged historically in this village and have long remained distinct as a product of differential marriage strategies. The mechanism for keeping land intact is that a structurally endogamous farmstead-owner social class emerged from marriages that relinked stem family or heirship lines that were already intermarried. The relinked couples inheriting farmsteads recombined primary heirships with secondary quitclaim land parcels allowing stability in reconstituting “impartible-core” farmsteads. Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White

16. Church Mountains and Alms Farmsteads and Fields

17. Applications of Structural Endogamy Social Class: Carinthian Farmers Data: Extensive field work Archival: Records of farmstead transfers starting in the 16 th century Genealogical histories on families collected by Brudner Supplemented from data collected by White from gravestones and church records Facts about the setting: Village population has been (relatively) stable from 1759 – 1961, fluctuating between 618 (1923) to 720 (1821) Most transfers are through inheritance, but the data includes purchases as well. Daughters tend to move to their husbands house of residence Purchase of farmsteads for sons is common, but rare for daughters Daughters tend to bring a land dowry to a marriage Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White

18. Applications of Structural Endogamy Social Class: Carinthian Farmers Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White

19. Applications of Structural Endogamy Social Class: Carinthian Farmers Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White

20. Structural Endogamy w. Ancestors Generation123456 Present: Actual8*16*70*179257318 Simulated0032183273335 Back 1 gen: Actual8*58*168246308339 Simulated018168255320347 Back 2 gen: Actual26*115*178243278292 Simulated098194262291310 Applications of Structural Endogamy Social Class: Carinthian Farmers Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White

21. Applications of Structural Endogamy Social Class: Carinthian Farmers

22. Case 3

23. Applications of Structural Endogamy Middle Eastern segmented lineage systems: The Role of Marital Cohesion in a Turkish Nomadic Clan Empirical Setting: An Arabized nomadic clan having the characteristic segmented patrilineages, lineage endogamy, and FBD (father’s brother’s daughter) marriages Key questions: Is this a prototype of a widespread variety of decentralized self-organizing lineage system stemming Arab societies or societies Arabized along with the spread of Islam in 7 th and 8 th century? Data: Genealogies on two thousand clan members and their ancestors, from 1800 to the present, a long-term ethnography by Professor Ulla C. Johansen, University of Cologne

24. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Sources: 2002 Ulla Johansen and Douglas R. White, Collaborative Long-Term Ethnography and Longitudinal Social Analysis of a Nomadic Clan In Southeastern Turkey, pp. 81-99, Chronicling Cultures: Long-Term Field Research in Anthropology, eds. R. van Kemper and A. Royce. AltaMira Press. 2003 Douglas R. White and Michael Houseman The Navigability of Strong Ties: Small Worlds, Tie Strength and Network Topology, Complexity 8(1):72-81. 2003 Douglas R. White and Ulla Johansen. 2004. Network Analysis and Ethnographic Problems: Process Models of a Turkish Nomad Clan. Lexington Press.

25. p-graph of the conicality of the nomad clan Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Data: Generations

26. The index of relinking of a kinship graph is a measure of the extent to which marriages take place among descendents of a limited set of ancestors. For the nomad clan the index of relinking is 75%, which is extremely high by world standards. This is a picture of the structurally endogamous or relinked marriages within the nomad clan (nearly 75% or all marriages): Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: Structural Endogamy of the nomad clan

27. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Does staying together as a clan depend on marital relinking? Results: Testing the hypothesis for stayers versus leavers Relinked Non-Relinking Marriages Marriages Totals villagers who became clan members 2** 1** 3 clan Husband and Wife 148 0 148 “ Hu married to tribes with reciprocal exchange 12 14 26 “ Hu left for village life 13 23 36 “ Hu married to village wife (34) or husband (1) 11 24 35 “ Hu married to tribes w/out reciprocal exchange 2 12 5 “ members who left for another tribe 0 8 8 villagers not joined to clan 1 3** 4 * tribes **non-clan by origin Totals 189 85 274 Pearson’s coefficient r=.95 without middle cells

28. An apical (circled) ancestor of the 90% of those down to today’s nomad clan members. Attributing common unilineal descent because of common roots is a common feature of Middle Eastern lineages Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: Does the high degree of structural endogamy create a single root to the nomadic clan?

29. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion A power-law decay of marriage frequencies with kinship distance FFZSD FFBSD:10-11 FZD:14 MBD:16 FBD:31 M M =206/x 2 Raw frequency (power law preferential curve) # of Couples # of Types Results: Rather than treat types of marriage one by one: FBD, MBD etc., we treat them as an ensemble and plot their frequency distribution

30. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: reversing axes, types of marriage are ranked here to show that numbers of blood marriages follow a power-law (indexical of self-organizing preferential attachments) while affinal relinking frequencies follow an exponential distribution

31. –Who stays and who returns to village life is predicted from kinship bicomponent membership. –Bicomponent relinking also plays a role in the emergence of a root ancestor, and of more localized root ancestors for different levels of kinship groupings. –Dynamic reconfigurations of political factions and their leaders are predicted from ensembles with different levels of edge-independent connectivity. –An index of the decline of cohesion of the clan would be the fragmentation of cohesive components in later generations... Key concepts: bicomponent, edge-independent paths, connectivity. Graphic technique: nuclear families as the unit of p-graph analysis. An explanation of methods will be found in a book ms. : Social Dynamics of a Nomadic Clan in Southeastern Turkey: An Introduction to Networked Histories. Douglas White and Ulla Johansen. Submitted: Lexington and Altamira Press. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: Summary:

32. –The frequency distributions of different kinds of affinal relinkings were tested in two societies, and a separate test was done for consanguineal relinkings. –The societies with high rates of blood marriages had preferential attachment power-law distributions for different types of consanguineal relinkings, but exponential decay distributions for different types of affinal relinkings –Most societies with low rates of blood marriage had exactly the reverse. –The approach was generalized to the study of short-cycle frequencies in any kind of network with multiple types or nodes and/or edges. Key concepts: power-law, exponential rank frequency distributions. Graphic theoretic techniques: independent cycle theorem, cycle generation concept An explanation of methods will be found in a book ms. : Social Dynamics of a Nomadic Clan in Southeastern Turkey: An Introduction to Networked Histories. Douglas White and Ulla Johansen. Submitted: Lexington and Altamira Press. Links to Complexity Theory Out of the Turkish Nomad study came hypotheses about preferential attachments Ring Cohesion Theory Results: Summary:

33. Case 4

34. Results: Reveals that Leach had not seen, and could not for lack of requisite tools of analysis, that marriages were organized in response to a logic called dividedness and (in another form) sidedness. the matrimonial network is bipartite, the marriages of the parents and those of the children divide themselves into two distinct ensembles (which have nothing to do with moieties). Graphic technique: Nuclear families as the unit of p-graph analysis, analysis of blood marriages, sibling sets and of inheritance or bequests revealed the underlying logic of marital sidedness. Key concepts: bipartite graph and sidedness: sidedness is an empirical bipartition of a matrimonial network, reiterated from one generation to another following a sexual criterion. The next slide shows sidedness in the Pul Eliyan networks operating through the male line, with some female heirs acting as agnatic channels for inheritance where there are no male heirs (i.e., they lack brothers) and they marry outsiders from distant villages. Applications of Structural Endogamy Social Integration through Marriage Systems: Kandyan Irrigation Farmers in Sri Lanka Source: 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” (Houseman and White). pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.

35. P-graph of Pul Eliyan Sidedness

36. Curved lines follow property flows, dashed lines are gifts. Property re-connects across the sided lines.

37. Frequencies of Actual versus Simulated Consanguineal Marriages for Pul Eliya, Sri Lanka. Conclusions: All blood marriages are patri-sided, and secondarily, only MBD is a marriage that is especially preferred Type Actual Simul Total Total Fisher|-----Blood Marriage------| (2)Viri-Sided? of Mar. Freq. Freq. Actual Simul Exact type P-graph notation Actual Simul 12: 5 0 40 38 p=.042 MBD(1) GF=FG yes 2: 3 1 39 40.317 FZD GG=FF yes 1: 0 1 56 57.508 FZ GG=F no 3: 0 1 6 6.538 FFFZDSD GGGG=FGFF no 4: 1 0 3 1.800 FFMZDSSD GGGF=FGGFFyes 5: 0 1 5 3.444 FFMBDSDD GGGF=FFGFGno 6: 1 0 18 15.558 FMBSD GGF=FGG yes 7: 0 1 17 12.433 FMBDD GGF=FFG no 8: 2 1 18 12.661 FMZDD GGF=FFF yes 9: 0 1 9 5.399 FMMBSSD GGFF=FGGG no 10: 0 1 4 5.600 FMMFZSSD GGFFG=FGGFyes 11: 0 1 6 3.400 FMMFZDSD GGFFG=FGFFyes 13: 0 1 25 27.528 MBSD GF=FGG yes 14: 1 0 14 10.600 MFZDD GFG=FFF yes 15: 1 0 7 3.727 MFFZDSSD GFGG=FGGFFyes 16: 1 0 8 4.692 MFFZDSD GFGG=FGFF yes 17: 1 0 8 2.818 MFMBDSSD GFGF=FGGFGyes 18: 1 0 9 3.769 MFMBDD GFGF=FFG yes 19: 1 0 3 0 1.000 MFMBDDDD GFGF=FFFFGyes 20: 1 0 8 2.818 MFMFZSSD GFGFG=FGGFyes 21: 1 0 3 0 1.000 MFMFZDDD GFGFG=FFFFyes 22: 1 0 13 8.636 MMZSSD GFF=FGGF yes 23: 1 0 15 13.551 MMBDD GFF=FFG yes 24: 0 1 11 5.352 MMZSDD GFF=FFGF no 25: 0 1 11 5.352 MMBDDD GFF=FFFG no 26: 1 0 11 4.749 MMZDDD GFF=FFFF yes Source: 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” (Houseman and White). pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.

38. Applications of Structural Endogamy Social Integration through Marriage Systems: Kandyan Irrigation Farmers in Sri Lanka Empirical Setting: An immensely detailed network ethnography by Sir Edmund Leach demonstrates how kinship relations are strategically constructed through matrimonial alliances that alter the flow of inheritance of land and water rights by deviating from normal agnatic (father’s-side) rights to property and emphasizing the secondary rights of daughters, with expectation that property alienated through marriage will flow back to the agnatic group through the completion of elaborate marriage exchanges between the two “sides” of the kindred. Key question: Is there a hidden order of marital practices that links to the two-sidedness of kinship terminology and Leach’s earlier findings about balanced and reciprocated exchanges? Data: genealogies, inheritances, classifications of normal and exceptional residence practices and of normal and exceptional types of marriage. Source: 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” (Houseman and White). pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.

39. Correlating Actual versus Simulated non-MBD marriages for Pul Eliya, showing tendency towards a Viri-Sided (Dravidian) Marriage Rule Viri-SidedUnsided Actual180 Simulated 57 (p=.0004; p=.000004 using the binomial test of 50%:50% expected) Source: 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” (Houseman and White). pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.

40. Correlating Balanced vs. Unbalanced Cycles in Actual versus Simulated marriage networks for Pul Eliya, showing a perfectly Sided (Dravidian) Marriage Rule A. Viri-sidedness ActualExpected Balanced Cycles (Even length)25 17.5 Unbalanced Cycles (Odd Length)10 17.5 p=.008 (all exceptions involve relinkings between nonconsanguineal relatives) B. Amblilateral-sidedness (women‘s sidedness adjusted by inheritance rules) ActualExpected Balanced Cycles (Even length)35 17.5 Unbalanced Cycles (Odd Length) 0 17.5 p=.00000000003 Source: 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” (Houseman and White). pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.