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
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
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
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
Data and Representation:
Building Kinship Networks
P-graphs link pairs of parents (flexible & culturally defined) to their decedents
P-graphs are constructed by:
•Treating couplings as nodes
•Treating individuals as lines
•Usually of different type for
different genders
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)
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 coancestral 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
Case 1
Data and Representation:
Relating p-graphs to endogamy (Old Testament Men and Women)
Nahor
Lot marries
his daughters
Terah
(Egypt)
Heran
Lot
Abraham & Sarah & Hagar
Nahor
ishmael
Bethel
Male Descent
Isaac
Female Descent
Same person
(polygamy)
Rachel & Jacob & Leah
http://eclectic.ss.uci.edu/~drwhite/pw/White-Jorion1992.pdf
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
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
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.
Case 2
Applications of Structural Endogamy
Social Class: Carinthian Farmers
“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.
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161208. Lilyan Brudner and Douglas White
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 25:161208. Lilyan Brudner and Douglas White
Church
Mountains
and Alms
Farmsteads
and Fields
Applications of Structural Endogamy
Social Class: Carinthian Farmers
Data:
•Extensive field work
•Archival: Records of farmstead transfers starting in the 16th 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 25:161208. Lilyan Brudner and Douglas White
Applications of Structural Endogamy
Social Class: Carinthian Farmers
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161208. Lilyan Brudner and Douglas White
Applications of Structural Endogamy
Social Class: Carinthian Farmers
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161208. Lilyan Brudner and Douglas White
Applications of Structural Endogamy
Social Class: Carinthian Farmers
Structural Endogamy w. Ancestors
Generation
1
2
3
4
5
6
Present:
Actual
8*
16*
70*
179
257
318
Simulated
0
0
32
183
273
335
Actual
8*
58*
168
246
308
339
Simulated
0
18
168
255
320
347
Actual
26*
115*
178
243
278
292
Simulated
0
98
194
262
291
310
Back 1 gen:
Back 2 gen:
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161208. Lilyan Brudner and Douglas White
Applications of Structural Endogamy
Social Class: Carinthian Farmers
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161208. Lilyan Brudner and Douglas White
Case 3
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 7th and 8th 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
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.
Applications of Structural Endogamy
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Generations
Data:
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
Results:
•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):
Structural Endogamy 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
Does staying together as a clan depend on marital relinking?
Results: Testing the hypothesis for stayers versus leavers
Relinked
Marriages
Non-Relinking
Marriages
Totals
villagers who became clan members
2**
1**
clan Husband and Wife
148
0
“ Hu married to tribes with reciprocal exchange 12
14
“ Hu left for village life
13
23
“ Hu married to village wife (34) or husband (1) 11
24
“ Hu married to tribes w/out reciprocal exchange 2
12
“ members who left for another tribe
0
8
villagers not joined to clan
1
3**
* tribes
**non-clan by origin
Totals
189
85
Pearson’s coefficient r=.95 without middle cells
3
148
26
36
35
5
8
4
274
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?
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: Rather than treat types of marriage one by one: FBD, MBD etc., we
treat them as an ensemble and plot their frequency distribution
A power-law decay of marriage frequencies with kinship distance
180
160
140
M
Frequency
M =206/x
0 + 156/x^2
2
120
# of Types
100
(power law preferential curve)
80
60
# of Couples
40
FFZSD FFBSD:10-11 FZD:14 MBD:16
FBD:31
20
0
0
Raw
5 frequency 10
15
20
25
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
Applications of Structural Endogamy
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Results: Summary:
– 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.
Links to Complexity Theory
Out of the Turkish Nomad study came hypotheses about preferential attachments
Ring Cohesion Theory
Results: Summary:
– 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.
Case 4
Applications of Structural Endogamy
Social Integration through Marriage Systems: Kandyan Irrigation Farmers in Sri Lanka
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.
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.
P-graph of Pul Eliyan Sidedness
P-graph of Pul Eliyan Sidedness
Curved lines follow
property flows, dashed
lines are gifts.
Property re-connects
across the sided lines.
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.
Correlating Actual versus Simulated non-MBD marriages
for Pul Eliya, showing tendency towards a Viri-Sided
(Dravidian) Marriage Rule
Viri-Sided
Actual
18
Simulated
5
Unsided
0
7
(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.
Correlating Balanced vs. Unbalanced Cycles in Actual
versus Simulated marriage networks for Pul Eliya,
showing a perfectly Sided (Dravidian) Marriage Rule
A. Viri-sidedness
Actual
Expected
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)
Actual
Balanced Cycles (Even length) 35
Unbalanced Cycles (Odd Length) 0
p=.00000000003
Expected
17.5
17.5
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.