






By categories/attributes: 

suffers from problems of specification error 

By network relinking: 

structural endogamy consists of blocks of
relinkings: 

blocks of blood marriage as samefamily
relinking 

blocks of kfamily relinkings, with depth g
generations 

network cohesion is the more general concept 





sociological uses of this approach are discussed
in 

White, Douglas R. and Frank Harary. 2001.
"The Cohesiveness of Blocks in Social Networks: Connectivity and
Conditional Density." To appear in Sociological Methodology 2001. 

White, Douglas R. and Mark E. J. Newman. 2001.
ìFast approximation algorithms for finding nodeindependent paths.î
Submitted to Sociological Methodology 2002. 

Moody, James, and Douglas R. White. 2001.
ìStructural Cohesion and Embeddedness:A hierarchical conception of social
groups.î Santa Fe Institute Working Paper 0008049, submitted to the
American Journal of Sociology. 

example (from plenary session): 

Powell, Walter W., Douglas R. White, Kenneth W.
Koput and Jason OwenSmith. 2001. ìEvolution of a ScienceBased Industry:
Dynamic Analyses and Network Visualization of Biotechnology.îİ Informal working paper: Santa Fe
Institute. 







PAJEK is a program for large network analysis
(Batagelj and Mrvar 1999).İ In
Decemberí97 PAJEK 0.23 implemented the pgraph format of White and Jorion
(1992) as the default for genealogical datasets (*.GED files), the drawing
of dotted (p Dots) versus solid lines (p Solid) for the different sexes,
and a fast version of bicomponents (for the study of structural endogamy).
There is also a genealogical representation using triangles or circles as
nodes for individuals, and a representation that combines the two systems
of representation. 



Network/Partition/Depth/Genealogy command 
implemented to compute genealogical depth. This enabled 2D or 3D drawings
of kinship networks.İ Illustrations
will be given. 



Manuals for pgraph kinship analysis and
discussions of software programs and multimedia representations are found
at 

1) http://eclectic.ss.uci.edu/~drwhite (has
links to articles) 

2) http://eclectic.ss.uci.edu/~drwhite/pgraph 

3) http://vlado.fmf.unilj.si/pub/networks/pajek 

İİİ (each
of these sites has a link to the other) 





Pajek keeps evolving.İ In SeptemberOctoberí98, Pajek 0.3336 added Vectors (*.vec)
whose values can be real numbers, including: 

Editing vectors, making vectors from a
partition, and vector transformations (multiplying by a constant, absolute,
sqrt, normalizations), reordering and binary operations on vectors (sum,
difference, product, division, min, max) and additional operations
according to neighbors. 

Retrieving and putting coordinates of network to
vector and vice versa. 

In Novemberí99, Pajek 0.50 added automatic demographic
vectors for birth, marriage, and death dates, when GEDCOM files are read. 

AprilMay 2000, Pajek 0.5455 implemented: 

Network/Generate in Time to produce timeseries
graphs. 

DrawVector and DrawPartitionVector with Options/Previous/Next
that uses vector values to modify size of nodes in timeseries graphs. 

File/TimeEventsNetwork/Read and /Save for
reading and saving a time network in time events format to control every
feature of the graphs. 




PGRAPH  graphs and simulations, sidedness,
segmentary dual organization, etc. 

ParCalc  frequencies for marriages of blood
relatives 

ParLink  frequencies for twofamily relinkings 

ParComp (incorporates Fisher tests)  for
outcomes based on types (blood or relinking) 

ParBloc  for global analysis of relinkings 

ParSide (binomial test)  computes likelihood
of sidedness 

ParCoef  computes inbreeding coefficients and
relatedness 

Ego2Cpl UTILITY  converts *.txt files to
pgraph/pgraph formats. 

See http://eclectic.ss.uci.edu/~drwhite/pgraph
for guides as to website availability with documentation (and multimedia
representations) 






in a science of social structure and dynamics
that includes marriage and kinship, how to 

define and evaluate marriage strategies against
random baselines? 

separate ërandomizingí strategy from
ëpreferentialí strategy? 

detect atomistic strategies (partial, selective)
as well as global or ìelementaryî marriagerules or strategies? 

detect changes in marriage rules or strategies? 



D. White. 1997. Structural Endogamy and the
graphe de parentÈ.İ MathÈmatique,
informatique et sciences humaines 137:107125. Paris: Ecole des Hautes
Etudes en Sciences Sociales 

İİİİİ D.
White. 1999. ìControlled Simulation of Marriage Systems.î Journal of
Artificial Societies and Social Simulation 3(2). http://www.soc.surrey.ac.uk/2/3/5/JASSS.html 

İİİİİ
See: http://eclectic.ss.uci.edu/~drwhite 




In each generation of marriages in an actual
pgraph ñ 

number the set K of marriages 1 to k 



Reassign each person married into the generation
to a random marriage in K, allowing additional rules to prevent incest as
defined culturally 



But donít change the parents: that keeps each
sibling set intact 

İİİİ (all
this is done automatically by the Pgraph software) 



This gives a simulated dataset that has the same
numbers of people and of marriages, the same distribution of sibling sets,
hence the same sex ratio in each generation, etc. 






Social class, 

Elite structural endogamy, 

Wealth consolidation, 

Community/ethnic integration, 

Testing alliance, descent, and proscriptive
theories and models 






Social Class and Structural Endogamy in the
Austrian village of Feistritz:İ
Strategic Relinking (w/ Lilyan Brudner) 



Status Endogamy in a Javanese village (Dukuh
hamlet and Muslim) Elites: Marriages frequencies governed by demographic
constraints, not by different consanguineal marriage preferences (w/ Thomas
Schweizer) 



Dual Organization in Sri Lanka: Preferred
Marriages and Sidedness in Pul Eliya Village (w/ Michael Houseman) 



Tzintzuntzan (w/ Eric Widmer and Robert van
Kemper) 



Clan Organization among Nomadic Herders (w/ Ulla
Johansen 2001) 






Graphic technique: showed households as a
macrounit of analysis, containing successive nuclear or stem families as
nodes in the graph. 



Key concepts: marital relinking, pgraph (where
nodes are marriages and lines are filiation), structural endogamy, bicomponent
of the pgraph defines endogamous boundary (in those case, of social
class). 



Predicted social class and heirship among
farmers from the cohesive set of marriages in the farming valley (non heirs
did not enter in the kinship bicomponent) 



1997 ìClass, Property and Structural Endogamy:
Visualizing Networked Histories,î Theory and Society 25:161208. Lilyan
Brudner and Douglas White. http://eclectic.ss.uci.edu/~drwhite/T&S/T&Spage1.htm 






SOCIAL CLASS in Feistritz:İ Comparison of Relinking Frequencies for
Actual and Simulated Data 

(*=actual frequencies greater than chance as
determined by simulation) 







Graphic technique: nuclear families as the unit
of pgraph analysis, additional arrows for property flows (used in the
publication) showed extended family rules for partitioning of mercantile
resources and property of groups constituted by relinking. 



Key concepts: blood marriage as a form of marital
relinking, pgraph, structural endogamy, bicomponent of the pgraph, the social
biography of things (property flows). 



Showedİ
(1) apparent differences in marriage patterns of elites and
commoners were due to a common cultural practice of status endogamy, which
for elites implied a set of potential mates whose smaller size implied marriage
among blood relatives within a few generations, (2) given a common rule of
division of inheritance, closer marital relinkings among elites facilitated
the reconsolidation of wealth within extended families, and (3) extended
families so constituted operated with a definite set of rules for the
division of productive resources so as to distribute access to mercantile
as well as landed resources. 



Douglas White and Thomas Schweizer, 1998
ìKinship, Property and Stratification in Rural Java: A Network Analysisî
pp. 3658 in Schweizer and White, eds. Kinship, Networks, and Exchange.
Cambridge Univ. Press. 




key: A = frequency of actual marriages with a
given type of relative 

İİİİ B =
frequency of simulated random marriages with a given type of relative 

İİİ TA =
total of actual relatives of this type 

İİİ TS =
total of simulated relatives of this type 



İJavanese
elitesİİİİİİİİİİİ Dukuh Hamletİİİİİİİİİİİİİİ 3Way Test 

İİİ A S
TA TS p=İİ typeİİİİ A S TA TS p=İİ type 

İ1: 1
0İ 4İ 3 .625 FBDİİİİİ 0
1İ 9 12 .591 FBDİİİİİİİİİİ p=1.0 

İ2: 1
2İ 2İ 3 .714 MBDİİİİİ 1 0 11
16 .429 MBDİİİİİİİİİİ p=1.0 

İ3: 2
1İ 3İ 2 .714 FZDDİİİİ 0 0
11İ 0İİİİİ FZDDİİİİİİİİİ
p=1.0 

İ4: 0
1İ 6İ 7 .571 ZDİİİİİİ 0 0 18
24İİİİİ ZDİİİİİİİİİİİ p=1.0 

İİİ 0 0
11 11İİİİİ Zİİİİİİİ 0 0 36 43İİİİİ Z 

İİİ 0
0İ 4İ 4İİİİİ BDİİİİİİ 0 0 22 27İİİİİ BD 

İİİ 0
0İ 2İ 2İİİİİ ZSD 

İİİ 0
0İ 3İ 3İİİİİ BDDİİİİİ 0 0İ
8İ 8İİİİİ BDD 

İİİ 0
0İ 3İ 3İİİİİ ZDD 

İİİ 0
0İ 4İ 4İİİİİ FZİİİİİİ 0 0 21 27İİİİİ FZ 

İİİ 0
0İ 1İ 1İİİİİ FZSD 

İİİ 0
0İ 3İ 3İİİİİ FZDİİİİİ 0 0 13 14İİİİİ FZD 

İİİ 0
0İ 3İ 3İİİİİ FBDDİİİİ 0 0İ
3İ 2İİİİİ FBDD 

İİİ 0
0İ 5İ 4İİİİİ MZİİİİİİ 0 0 18 23İİİİİ MZ 

İİİ 0
0İ 2İ 2İİİİİ MZSD 

İİİ 0
0İ 4İ 4İİİİİ MZDİİİİİ 0 0 13 14İİİİİ MZD 

İİİ 0
0İ 1İ 2İİİİİ MBDDİİİİ 0 0İ
6İ 5İİİİİ MBDD 

İİİ 0
0İ 2İ 3İİİİİ MZDD 




Graphic technique: nuclear families as the unit
of pgraph analysis, analysis of blood marriages, sibling sets and of
inheritance or bequests revealed an underlying logic of marital sidedness. 



Key concepts: bipartite graph and sidedness (empirical
bipartition of a matrimonial network, reiterated from one generation to
another following a sexual criterion). 



ìThis remarkable work, among other merits, has
that of reconstituting the neartotality of the data of Leachís study of
Pul Eliya, reexamined by means of the PGRAPH program.İ It 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 that the authors call dividedness and in another
form sidedness:İ invisible to the
untrained eye, 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)î (review by Georg
Augustins, LíHomme 2000) 



Michael Houseman and Douglas White. 1998
ìNetwork Mediation of Exchange Structures: Ambilateral Sidedness and
Property Flows in Pul Eliya, Sri Lankaî pp. 5989 in Schweizer and White,
eds. Kinship, Networks, and Exchange. Cambridge Univ. Press. 




İTypeİ Actual Simulİ Totalİ
Total FisherBlood Marriageİİİİİİ (2)PatriSided? 

of Mar. Freq. Freq.İ Actual Simul Exactİ
typeİİ Pgraph notationİİİİİİİİİİ Actualİİİİ Simul 

İİ 12:İİ 5İİ
0İ 40İ 38 p=.042 MBD(1)GF=FGİİİİ yes 

İİİ
2:İİİ 3İİİ 1İİ
39İİ 40İİ .317 FZDİİİİİ GG=FFİİİİ
yes 

İİİ
1:İİİ 0İİİ 1İİ
56İİ 57İİ .508 FZİİİİİİ GG=Fİİİİİ
no 

İİİ
3:İİİ 0İİİ 1İİİ
6İİİ 6İİ .538 FFFZDSDİ GGGG=FGFF no 

İİİ
4:İİİ 1İİİ 0İİİ
3İİİ 1İİ .800 FFMZDSSD GGGF=FGGFF yes 

İİİ
5:İİİ 0İİİ 1İİİ
5İİİ 3İİ .444 FFMBDSDD GGGF=FFGFG no 

İİİ
6:İİİ 1İİİ 0İİ
18İİ 15İİ .558 FMBSDİİİ GGF=FGGİİ
yes 

İİİ
7:İİİ 0İİİ 1İİ
17İİ 12İİ .433 FMBDDİİİ GGF=FFGİİ
no 

İİİ
8:İİİ 2İİİ 1İİ
18İİ 12İİ .661 FMZDDİİİ GGF=FFFİİ
yes 

İİİ
9:İİİ 0İİİ 1İİİ
9İİİ 5İİ .399 FMMBSSDİ GGFF=FGGG no 

İİ
10:İİİ 0İİİ 1İİİ
4İİİ 5İİ .600 FMMFZSSD GGFFG=FGGF yes 

İİ
11:İİİ 0İİİ 1İİİ
6İİİ 3İİ .400 FMMFZDSD GGFFG=FGFF yes 

İİ
13:İİİ 0İİİ 1İİ
25İİ 27İİ .528 MBSDİİİİ GF=FGGİİİ
yes 

İİ
14:İİİ 1İİİ 0İİ
14İİ 10İİ .600 MFZDDİİİ GFG=FFFİİ
yes 

İİ
15:İİİ 1İİİ 0İİİ
7İİİ 3İİ .727 MFFZDSSD GFGG=FGGFF yes 

İİ
16:İİİ 1İİİ 0İİİ
8İİİ 4İİ .692 MFFZDSDİ GFGG=FGFF yes 

İİ
17:İİİ 1İİİ 0İİİ
8İİİ 2İİ .818 MFMBDSSD GFGF=FGGFG yes 

İİ
18:İİİ 1İİİ 0İİİ
9İİİ 3İİ .769 MFMBDDİİ GFGF=FFGİ yes 

İİ
19:İİİ 1İİİ 0İİİ
3İİİ 0İ 1.000 MFMBDDDD GFGF=FFFFG yes 

İİ
20:İİİ 1İİİ 0İİİ
8İİİ 2İİ .818 MFMFZSSD GFGFG=FGGF yes 

İİ
21:İİİ 1İİİ 0İİİ
3İİİ 0İ 1.000 MFMFZDDD GFGFG=FFFF yes 

İİ
22:İİİ 1İİİ 0İİ
13İİİ 8İİ .636 MMZSSDİİ GFF=FGGFİ yes 

İİ
23:İİİ 1İİİ 0İİ
15İİ 13İİ .551 MMBDDİİİ GFF=FFGİİ
yes 

İİ
24:İİİ 0İİİ 1İİ
11İİİ 5İİ .352 MMZSDDİİ GFF=FFGFİ
no 

İİ
25:İİİ 0İİİ 1İİ
11İİİ 5İİ .352 MMBDDDİİ GFF=FFFGİ
no 

İİ
26:İİİ 1İİİ 0İİ
11İİİ 4İİ .749 MMZDDDİİ GFF=FFFFİ yes 





Correlating Balanced vs. Unbalanced cycles in
Actual versus Simulated marriage networks for Pul Eliya, showing a
perfectly Sided (Dravidian) Marriage Rule 





A. Virisidedness 

Actual Expected 

Balanced Cycles (Even length) 25 İİ 17.5 

Unbalanced Cycles (Odd
Length) 10 İİ 17.5 

p=.008 

(all exceptions involve relinkings between
nonconsanguineal relatives) 





B. Amblilateralsidednessİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİİ
(womenës sidedness adjusted by inheritance rules)  not shown in
figure but shown in final publication (Houseman and White 1997) 



Actual Expected 

Balanced Cycles (Even length) 35 İİ 17.5 

Unbalanced Cycles (Odd Length)
0 İİ 17.5 

p=.00000000003 










1999 ìControlled Simulation of Marriage
Systems.îİ Journal of Artificial
Societies and Social Simulation 2(3). Douglas R. White. http://www.soc.surrey.ac.uk/2/3/5/JASSS.html
software and statistical methodology for comparing systems of
marriagerules to random baseline models with controls for demographic
variability. 



For the Austrian study, random baseline models
established the preference for relinking with relatives within 3
generations. 



For the Javanese study, the lack of difference
between commoner and elite marriages is supported, in spite of differences
in frequency of different marriage types. 



For the Pul Eliya study, random baseline models
established the patrisided marriage rule for blood marriages, and the
absence of a genealogical rule for determining the marriageability of
distant affines. 



Tzintzuntzan, a 4^{th} example, is in
process. 



If time allows, Iíll give a more extended 5^{th}
example, or just show on Pajek slide and stop 







We numbered each person and gave one line for
each marriage with number of ego, egoís mother, father and spouse. 



Using Pgraph and Pajek, this gave a graph for
the nomadic clan, ready for analysis: 





