Some Examples of Network Analysis

1
Some Examples of Network Analysis Ethnography of
a group undergoing fission Network study of
overlapping friendship groups in
school Collaborative ties in the biotech
industry KASS ethnography, egocentric networks
and kinship Social classes in Slovenian Austria,
Carinthian farmers Reciprocal exchange and
equality in South India Middle Eastern segmented
lineage systems, Turkish nomads Medieval city
networks and trade, 1175-1500
Doug White
Anthropological Seminar Halle MPI in Social
Anthropology, June 27, 2005
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Ethnographic examples
Case 1 2 year ethnography of a karate
club Conflict and Fragmentation
3
Longitudinal Network Studies and Predictive
Social Cohesion TheoryD.R. WHITE, University of
California Irvine, BCS-9978282
Part 1. Development of a Methodology for Network
Research on Social Cohesion

• An operational definition of social cohesion
  based on network connectivity measures
  cohesiveness as the minimum number k of actors
  whose absence would disconnect a group. Two
  members of a group with cohesion level k
  automatically have at least k different ways of
  being connected through independent paths.
• A test of the measure is exemplified by
  successful prediction of how a group, studied
  longitudinally during a period of conflict
  between leaders, divides into two (Fig 1).
• 2001 Douglas R. White and Frank Harary, The
  Cohesiveness of Blocks in Social Networks Node
  Connectivity and Conditional Density.
  Sociological Methodology 2001, vol. 31, no. 1,
  pp. 305-359. Blackwell Publishers, Inc., Boston,
  USA and Oxford, UK. SFI Posting

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Loss of cohesion
A
T
 

•  

   
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Sociological definitions and examples
Cases 2,3 overlapping friendship groups where
structural cohesion predicts school
attachment Evolution of biotech industry where
structural cohesion predicts collaborative tie
formation
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Longitudinal Network Studies and Predictive
Social Cohesion Theory D.R. WHITE, University of
California Irvine, BCS-9978282
Predictive Social Cohesion Theory BOUNDEDNESS A
k-component of a graph G is a maximal subgraph S
with the following equivalent properties
connectivity k, the smallest cutset of S is of
size k. multiconnectivity k, the minimal number
of node-independent paths in S connecting pairs
of nodes in S is k. k-components may
overlap, or be vertically stacked as shown here
 

•  

1
4 k2 k2 k1 3
6 2
5
   
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Topology Overlapping hierarchies (Abstract
Model) A k-ridge supporting structure is a set
of n (k1)-components that are connected, with
intersections containing at least k nodes, where
each (k1)-component has node-connectivity
greater than k. A k-ridge structure has
connectivity k but supports a series of connected
(k1)-components, i.e., of connectivity k.
Figure 3-ridge structure supporting
overlapping 4-components
Longitudinal Network Studies and Predictive
Social Cohesion Theory D.R. WHITE, University of
California Irvine, BCS-9978282
2003 Douglas R. White, Walter W. Powell, and
Jason Owen-Smith, Embeddedness in Multiple
Networks, Organization Theory and Structural
Cohesion Theory. In preparation for
Computational and Mathematical Organization
Theory special issue on Mathematical
Representations for the Analysis of Social
Networks within and between Organizations, guest
edited by Alessandro Lomi and Phillipa Pattison.
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Topology Overlapping hierarchies (Empirical
Results)
Longitudinal Network Studies and Predictive
Social Cohesion Theory D.R. WHITE, University of
California Irvine, BCS-9978282

• The algorithm for finding social embeddedness
  in nested cohesive subgroups is applied to high
  school friendship networks (e.g., Fig 2
  boundaries of grades are approximate) and to
  interlocking corporate directorates. The
  usefulness of the measures of cohesion and
  embeddedness are tested against outcome variables
  of school attachment in the friendship study and
  similarity in corporate donations to political
  parties in the corporate interlock study. The
  cohesion variables outperform other network and
  attribute variables in predicting the outcome
  variables using multiple regression.
• Nearly identical findings are replicated for
  school attachment measures and friendship
  networks in 12 American high schools from the
  AddHealth Study (http//www.cpc.unc.edu/addhealth/
  ), Adolescent Risk and Vulnerability Concepts
  and Measurement. Baruch Fischhoff, Elena O.
  Nightingale, Joah G. Iannotta, Editors, 2002, The
  National Academy Press.
• 2003 James Moody and Douglas R. White, Social
  Cohesion and Embeddedness A Hierarchical
  Conception of Social Groups. American
  Sociological Review 8(1)

Interpretation 7th-graders- core/periphery 8th-
two cliques, one hyper-solidary, the other
marginalized 9th- central transitional 10th-
hang out on margins of seniors 11th-12th-
integrated, but more freedom to marginalize
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Topology Stacked hierarchies and Dynamics
(Empirical Results) Longitudinal Validation of
Structural Cohesion Dynamics in Biotechnology
Longitudinal Network Studies and Predictive
Social Cohesion Theory D.R. WHITE, University of
California Irvine, BCS-9978282

• To account for the development of
  collaboration among organizations in the field of
  biotechnology, four logics of attachment are
  identified and tested accumulative advantage,
  homophily, follow-the-trend, and
  multiconnectivity. We map the network dynamics of
  the field over the period 1988-99 (Fig 3 ?1999).
  Using multiple novel methods, including analysis
  of network degree distributions, network
  visualizations, and multi-probability models to
  estimate dyadic attachments, we demonstrate how a
  preference for diversity and multiconnectivity in
  choice of collaborative partnerships shapes
  network evolution. Cohesion variables outperform
  scores of other independent variables.
• Collaborative strategies pursued by early
  commercial entrants are supplanted by strategies
  influenced more by universities, research
  institutes, venture capital, and small firms. As
  organizations increase both the number of
  activities around which they collaborate and the
  diversity of organizations with which they are
  linked, cohesive subnetworks form that are
  characterized by multiple, independent pathways.
  These structural components, in turn, condition
  the choices and opportunities available to
  members of a field, thereby reinforcing an
  attachment logic based on connection to partners
  that are diversely and differently linked. The
  dual analysis of network and institutional
  evolution offers a compelling explanation for the
  decentralized structure of this science-based
  field.
• 2003 Walter W. Powell, Douglas R. White,
  Kenneth W. Koput and Jason Owen-Smith. Network
  Dynamics and Field Evolution The Growth of
  Interorganizational Collaboration in the Life
  Sciences, 1988-99. Submitted to American
  Journal of Sociology.

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all ties for a year, Biotech, 1997

• Flip forward and back for a sense of
  dynamic alternation of consolidation and reaching
  out for innovation
• all ties / new ties

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New ties, Biotech, 1997
(flip back)
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Ethnographic examples
Case 4 KASS questionnaire network
analysis e.g., measuring cohesion in ego networks
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KASS (Kinship and Social Security) study at Max
Planck-Halle, done with the help of the KNQ
(kinship network questionnaire) graphic interface
software
Data transfer to Pajek
Figure 2 An ego network for Robert Corteen
Individuals, Couples (squares), kinship links
(arcs up to parents), Generations (colors), and
two support links (downward arcs). This is called
a bipartite parental (p-) graph
Pajek analysis
Fig 3 Cohesive Subgroup Calculation (yellow
nodes) Robert Corteen network
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Structural endogamy shifting how we look at the
kinship network as a genealogy
Object is to show how marriages relink moving on
to community level networks
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Data and RepresentationKinship 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 parental graph

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Data and RepresentationKinship Networks
parental graphs link pairs of parents (flexible
culturally defined) to their descendants
parental graphs are constructed by

• Treating couples as nodes, replacing
• marriage bonds with nodes

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Data and RepresentationKinship as Parental
Graph Networks
parental graphs link pairs of parents (flexible
culturally defined) to their descendents
parental graphs can be constructed from standard
genealogical data files (.GED), using PAJEK and a
number of other programs. Seehttp//eclectic.ss.
uci.edu/drwhite for guides as to web-site
availability with documentation ( multimedia
representations)
FaSi Fa FaSiDa
MaleEgo
Here one blue line per female and one red line
per male hence we can visually identify the
FaSiDa marriage
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Data and RepresentationRelating parental graphs
to endogamy

• Cycles in parental 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 parental graph are isomorphic
  with one or more of
• Blood Marriage Relinking, where two persons of
  common ancestry from a new union
• Redoubling, where unions linking two co-ancestral
  lines are redoubled
• Affinal Relinking, where two or more intermarried
  co-ancestral lines are relinked by a new union
• These can be subsumed as subtypes of marital
  relinking

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Further ethnographic examples
Case 5 Carinthian Farmers (structural endogamy,
social class, and network cognition)
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Mountains and Alms
Church
Our idea here was to follow the kinship and
marriage links not only between people but the
stemline households with impartible inheritance
of farmsteads and fields
Farmsteads and Fields
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The stemline social class of farmstead
inheritors, 1510-1980
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Applications of Structural Endogamy Social Class
Carinthian Farmers
Within the red circles are bicomponents with
2-family relinkings, the simplest affinal
relinking. The bicomponents are connected into a
single kinship core.
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Applications of Structural Endogamy Social Class
Carinthian Farmers
Here the relinking couples are correlated with
the social class of farmstead heirs (r.54,
p.000000001) if adjusted for types of missing
data, the correlation is much higher
Ethnography and Data Source 1997 Class,
Property and Structural Endogamy Visualizing
Networked Histories, Theory and Society
25161-208. Lilyan Brudner and Douglas White
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Structural Endogamy among known relatives Social
Class Carinthian Farmers of Feistritz
Comparison of Relinking Frequencies for Actual
and Simulated Data (actual frequencies greater
than chance as determined by simulation)
Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages Number of Structurally Endogamous Marriages
Generation 1 2 3 4 5 6
Present by Ancestral Levels Present by Ancestral Levels Present by Ancestral Levels Present by Ancestral Levels Present by Ancestral Levels Present by Ancestral Levels Present by Ancestral Levels
Actual 8 16 70 179 257 318
Simulated 0 0 32 183 273 335
Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels Back 1 gen by Ancestral Levels
Actual 8 58 168 246 308 339
Simulated 0 18 168 255 320 347
Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels Back 2 gen by Ancestral Levels
Actual 26 115 178 243 278 292
Simulated 0 98 194 262 291 310
Statistical conclusion conscious relinking among
families creates structural endogamy
Source 1997 Class, Property and Structural
Endogamy Visualizing Networked Histories,
Theory and Society 25161-208. Lilyan Brudner and
Douglas White
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Further ethnographic example
Case 6 Pul Eliya, Sri Lanka (illustrating
kinship structure, networks, cognition, kin terms)
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Example 3 Kandyan Irrigation Farmers in Sri
Lanka What side are you on?

• Graphic technique nuclear families as the unit
  of parental graph 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).
• This remarkable work, among other merits, has
  that of reconstituting the near-totality of the
  data of Leachs study of Pul Eliya, reexamined by
  means of the PGRAPH program. 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
  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) (review by
  Georg Augustins, LHomme 2000)
• Michael Houseman and Douglas White. 1998 Network
  Mediation of Exchange Structures Ambilateral
  Sidedness and Property Flows in Pul Eliya, Sri
  Lanka pp. 59-89 in Schweizer and White, eds.
  Kinship, Networks, and Exchange. Cambridge Univ.
  Press.

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parental graph of Pul Eliyan Sidedness
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Marriage sides in Pul Eliya, with compound IDs
for males,
(this slide was made with Pajek, output for web
viewing)
red lines for females
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parental graph of Pul Eliyan Sidedness, also
showing inheritance and property devolution
Curved lines follow property flows, dashed lines
are gifts. Property re-connects across the
sided lines.
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Frequencies of Actual versus Simulated
Consanguineal Marriages for Pul Eliya, Sri Lanka,

• Type Actual Simul Total Total
  Fisher-----Blood Marriage------
  (2)Patri-Sided?
• of Mar. Freq. Freq. Actual Simul Exact type
  parental graph notation Actual
  Simulation
• 12 5 0 40 38 p.042 MBD(1)GFFG
  yes
• 2 3 1 39 40 .317 FZD GGFF
  yes
• 1 0 1 56 57 .508 FZ GGF
  no
• 3 0 1 6 6 .538 FFFZDSD
  GGGGFGFF no
• 4 1 0 3 1 .800 FFMZDSSD
  GGGFFGGFF yes
• 5 0 1 5 3 .444 FFMBDSDD
  GGGFFFGFG no
• 6 1 0 18 15 .558 FMBSD
  GGFFGG yes
• 7 0 1 17 12 .433 FMBDD
  GGFFFG no
• 8 2 1 18 12 .661 FMZDD
  GGFFFF yes
• 9 0 1 9 5 .399 FMMBSSD
  GGFFFGGG no
• 10 0 1 4 5 .600 FMMFZSSD
  GGFFGFGGF yes
• 11 0 1 6 3 .400 FMMFZDSD
  GGFFGFGFF yes
• 13 0 1 25 27 .528 MBSD GFFGG
  yes
• 14 1 0 14 10 .600 MFZDD
  GFGFFF yes
• 15 1 0 7 3 .727 MFFZDSSD
  GFGGFGGFF yes
• 16 1 0 8 4 .692 MFFZDSD
  GFGGFGFF yes
• 17 1 0 8 2 .818 MFMBDSSD
  GFGFFGGFG yes

conclusions (1) MBD is a preferred marriage
(2) All blood marriages are
patri-sided
Correlating Actual versus Simulated non-MBD
marriages for Pul Eliya, showing tendency towards
a Patri-Sided (Dravidian) Marriage Rule
Patri-Sided Unsided Actual 18 0 Simulate
d 5 7 p.0004
p.000004 using the binomial test of an expected
5050 split)
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Another ethnographic example
Case 7 Turkish nomads (kinship, cognition,
semantics, migration)
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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. 2005 Douglas R. White and Ulla
Johansen. Network Analysis and Ethnographic
Problems Process Models of a Turkish Nomad Clan.
Lexington Press. See also 2003 Douglas R.
White and Michael Houseman The Navigability of
Strong Ties Small Worlds, Tie Strength and
Network Topology, Complexity 8(1)72-81.
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parental 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
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Coding the data for a Nomadic Clan Are we from
the same root? What is our group?
Johansens genealogical scroll
to parental graph (for the entire society)

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

Using Pajek, this gave a graph for the
nomadic clan, ready for analysis. Relinking
predicts same group according to PCT
(predictive cohesion theory) !
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Applications of Structural Endogamy Are we from
the same root? What is our group? (cognition
and kinship)
Does the high degree of structural endogamy
create a single root to the nomadic clan?
Results yes ! An apical (circled) ancestor of
the 90 of those down to todays nomad clan
members. A product of structural cohesion early
on. Attributing common unilineal descent because
of common roots is a common feature of Middle
Eastern lineages
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The polysemy of aile and kabile as embedded
units of shifting scale

• It is through selection by relinking that a
  single root ancestor emerges as a statistical
  tendency, although there are original seven
  independent lineage founders.
• By the same token, smaller subsets of kinsmen
  come to have cohesive units defined by the
  intersection of blood kinship (often patrilineal)
  plus intramarriage.
• This is also the key to how preferences for
  close marriages (FaBrDa or FaFaBrSoDa) and
  distant marriages coexist families establish
  cohesive relations at all levels, from the
  minimal lineage to the other lineages of the
  clan, as will also be seen in questions of
  support for leadership.

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Applications of Structural Endogamy A Turkish
Nomadic Clan as prototype of Middle Eastern
segmented lineage systems The Role of Marital
Cohesion
Structural Endogamy of the nomad clan
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 picture shows only the structurally
  endogamous or relinked marriages within the nomad
  clan (nearly 75 of all marriages)

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Applications of Structural Endogamy A Turkish
Nomadic Clan as prototype of Middle Eastern
segmented lineage systems The Role of Marital
Cohesion
Does marital relinking predict staying with the
clan, as predicted by PCT? Results Yes
! 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
Pearsons coefficient r.95 without middle cells
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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
41
Applications of Structural Endogamy A Turkish
Nomadic Clan as prototype of Middle Eastern
segmented lineage systems The Role of Marital
Cohesion

• Results
• types of marriage are ranked here, reversing
  axes, to show
• numbers of blood marriages follow a power-law
  (indexical of self-organizing preferential
  attachments)
• whereas affinal relinking frequencies follow
  an exponential distribution that would correspond
  with randomness

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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.
• An explanation of methods and concepts is found
  in the Glossary of 2005, Network Analysis and
  Ethnographic Problems Process Models of a
  Turkish Nomad Clan. Douglas White and Ulla
  Johansen. Boston Lexington Press.

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Case 8 city networks and trade, 1175-1500
44
Civilizations as Dynamic Networks Douglas R.
White, Peter Spufford
Background paper Civilizations as Dynamic
Networks Medieval to Modern, a project with
Peter Spufford, assisted by Joseph Wehbe
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Cohesive nodes (gold and red) in an expanded
exchange network and road identification
(red3-cohesive) shows two cohesive accumulation
regions -- such cohesion supported the creation
of wealth among merchants and merchant cities,
with states supported by indirect taxation and
loans.
Red 3-components
Middle East and its 3-core not sampled
In Northern Europe the Hanseatic port of Lubeck
had about 1/6th the trade of Genoa, 1/5th that of
Venice.
46
    
Northern Hanse Trade Organization Saintly
Brotherhoods
       
vv
vv
Other Eastern Hanse German Towns, 1470
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END

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Case 9 Muslim elites in Southeastern Java
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Example 9 Rural Javanese Elites - Are we elites
different than others?

• Graphic technique nuclear families as the unit
  of parental graph 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, parental graph, structural endogamy,
  bicomponent of the parental graph, the social
  biography of things (property flows).
• Showed (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
  reconsolid-ation 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
  Kinship, Property and Stratification in Rural
  Java A Network Analysis pp. 36-58 in Schweizer
  and White, eds. Kinship, Networks, and Exchange.
  Cambridge Univ. Press.

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STATUS ENDOGAMY in a Javanese Village (Dukuh
Hamlet, Muslim Elites), Test of Actual versus
Simulated Marriage among Consanguineal Kin

• key A frequency of actual marriages with a
  given type of relative
• B frequency of simulated random marriages
  with a given type of relative
• TA total of actual relatives of this type
• TS total of simulated relatives of this
  type
• Javanese elites Dukuh Hamlet
  3-Way Test
• A S TA TS p type A S TA TS p type
• 1 1 0 4 3 .625 FBD 0 1 9 12 .591 FBD
  p1.0
• 2 1 2 2 3 .714 MBD 1 0 11 16 .429 MBD
  p1.0
• 3 2 1 3 2 .714 FZDD 0 0 11 0 FZDD
  p1.0
• 4 0 1 6 7 .571 ZD 0 0 18 24 ZD
  p1.0
• 0 0 11 11 Z 0 0 36 43 Z
• 0 0 4 4 BD 0 0 22 27 BD
• 0 0 2 2 ZSD
• 0 0 3 3 BDD 0 0 8 8 BDD
• 0 0 3 3 ZDD
• 0 0 4 4 FZ 0 0 21 27 FZ
• 0 0 1 1 FZSD
• 0 0 3 3 FZD 0 0 13 14 FZD

Statistical conclusion there are no preferred
marriages among elites beyond status endogamy,
although blood marriages are common
Hence the same system of marriage rules operates
for elites as for commoners
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Data and RepresentationRelating parental graphs
to endogamy (Old Testament Men and Women)
Nahor
Terah
(Egypt)
Abraham Sarah Hagar
Heran
Lot
Nahor
ishmael
Bethel
Isaac
Rachel Jacob Leah
http//eclectic.ss.uci.edu/drwhite/pw/White-Jorio
n1992.pdf
53
Conclusion

• It is possible to construct a field of conceptual
  ethnography where cognition, social structure,
  and culture are integrated.
• Cognition counts upon the social network,
  relationally
• Culture and cohesive integration can be defined
  relationally, utilizing networks.

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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 (fathers-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
Leachs 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.
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Relational answers to Johansens ethnographic
questions 1 Was there a single root to the
nomadic clan? 2 How are kinship units formed
and why do units of different scale bear the same
name (such as aile for family, minimal lineages,
and larger joint families kabile for tribes or
smaller lineages). Are such kinship groupings the
result of marriages?

• To the extent that marriages relink different
  families into socially cohesive sets or
  bicomponents (in which each node is connected by
  at least two independent paths to other nodes),
  patterns of structural endogamy defined by
  relinking reinforce and redefine the effective
  units and subunits formed by consanguineal
  kinship links among families.
• The index of relinking of a kinship graph is
  measure of the extent to which marriages take
  place among descendents of a limited set of
  ancestors. For the nomad clan genealogies index
  of relinking is 75, which is extremely high by
  world standards.
• Here is a picture of the structurally endogamous
  or relinked marriages within the nomad clan
  (nearly 75 or all marriages)

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parental graph of the conical nomad clan
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1. An apical ancestor of the 90 of those down
to todays nomad clan members
60
2. Structural endogamy of the nomad clan
Each marriage is contained in a cycle of
previously linked marriages
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Thinking Relationally

1. Categorical thinking e.g., groups as a
   classificatory partition or hierarchy of mutually
   exclusive classes
2. Relational thinking e.g., who is linked to whom?
   What is linked to what? On whom do people
   count?
3. Simulation baselines and relational biases

1. Slovene Farmers of Feistritz, Austria How class
   is counted?
2. Dukuh Hamlet and Javanese Muslim Village Elites
   Are we different?
3. Pul Eliyan Kinship in Sri Lanka What side are
   you on?
4. Aydinli Turkish Nomad Clan What is our group?
   Are we from the same root?

63
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 parental 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.

64
Outline of the talk (59 slides)

• I. network theory of kinship
• A. Predictive cohesion theory (PCT)
• Structural cohesion 4 slides
• Applying predictive cohesion theory (PCT) to
  kinship 1 slide
• B. Marriage Census graph analysis 1 slide
• C. Defining the phenomena of endogamy - 3 slides
• II. kinship structure and cognition
• A. Defining the phenomena of endogamy 1 slide
• B. Data and representation - 3 slides
• C. Relational thinking parental graph as a
  relational representation - 3 slides
• D. Identifying marriage rules and strategies
  controlled demographic simulation - 3 slides
• III. ethnographic examples
• 1 Slovene Farmers of Feistritz, Austria How
  class is counted - 11 slides
• 2 Dukuh Hamlet Javanese Muslim Village Elites
  Are we elites different? - 2 slides
• 3 Pul Eliyan Kinship in Sri Lanka What side
  are you on? - 7 slides
• 4 Aydinli Turkish Nomad Clan What is our
  group? Are we from the same root? - 10
  slides ? and one on links to complexity theory /
  one on historical continuity

65
Programs Availability PAJEK

• PAJEK reads genealogical datasets (.ged files)
  both the usual Ego format and in parental graph
  format, with dotted female lines (p Dots) and
  solid male lines.
• PAJEK Network/Partition/Components/Bicomponent
  computes structural endogamy in a parental 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, 2005
• Exploratory Social Network Analysis with Pajek
• Cambridge University Press

66
I. Network Theory of Kinship

• Cohesion in human groups is built up through
  social ties.
• There is a specific network measure of structural
  cohesion.
• For kinship this measure takes the form of
  structural endogamy.
• Predictive cohesion theory (PCT) predicts that
  structural cohesion (and structural endogamy as a
  special case) has similar consequences across
  different historical and ethnographic contexts.

67
A. Predictive cohesion theory (PCT)

• The measure of structural cohesion (and
  structural endogamy) applies from small groups to
  large communities (scalability)
• General consequences of structural cohesion
• Internal bonds strong (multiconnectivity)
• Resistance to external shock (robustness)
• Adaptive (MulticonnectivityRobustnessresilience)
  
• Structurally cohesive groups possess definite
  lines of boundedness in social networks.

68
A1. Structurally cohesive groups predict

• Coherent boundaries of interaction
• Emergence of shared routines, meanings
• Greater cultural coherence- Boundaries of
• Ethnicities
• Class (in terms of Social v. Economic ties)
• Communities
• Kinship groups
• Conversely, cohesive fissures within more loosely
  connected groups predict
• Fracturation, splitting of the above
• Organizational differentiation

69
Structurally cohesive blocks in social networks
have predictable consequences

• 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."
  Sociological Methodology 2001, vol. 31(1), pp.
  305-359.
• Moody, James, and Douglas R. White. 2003.
  Structural Cohesion and Embeddedness A
  Hierarchical Concept of Social Groups. American
  Sociological Review 68(1)103-127.
• http//www.asanet.org/journals/ASRFeb03MoodyWhite.
  pdf
• Powell, Walter W., Douglas R. White, Kenneth W.
  Koput and Jason Owen-Smith. 2005. The Growth of
  Interorganizational Collaboration in the Life
  Sciences. American Journal of Sociology
  110(4)1132-1205.
• http//www.journals.uchicago.edu/AJS/journal/issue
  s/v110n4/080171/080171.html http//www.journals.uc
  hicago.edu/AJS/journal/contents/v110n4.html

70
Aging effects in structurally cohesive groups

• Newly emergent cohesion generates solidarity
• Political and military esprit-de-corps
• Ability to wage battles, fight empires, expand
• Mobilization of political parties
• Institutional aging of cohesion atrophies
• Organizational differentiation, splitting
• Conflict among differentiated interests groups
• Lowered popular support for governing
  institutions
• (see Peter Turchin 2003, Historical Dynamics, CUP)

71
Organizational features of structurally cohesive
groups

• Cohesion is generated by local action of
  reknitting ties.
• Once reknitting occurs, people have
  multiconnectivity.
• This means they have multiple paths connecting
  them.
• A reknitting action is one that creates multiple
  paths.
• Thus it creates one or more identifiable cycles.
• Such cycles differ by the types of relation
  forming them
• The study of cohesive actions thus focuses on
• A census of types of cycles.
• An analysis of rules, preferences, or simulated
  randomness that would predict the cycles that
  account for cohesion.

72
A2. Applying predictive cohesion theory (PCT) to
kinship

• Reknitting kin ties correspond to relinking
  marriages
• Closing a loop between 2-, 3-, 4- families,
  affines
• Between blood kin, 2-, 3- 4- degree consanguines
• A marriage census
• Rank orders the frequencies of relinkings of both
  types
• Examines which types tend to co-occur
• The results will show either
• With blood marriages, a preferential ranking
• With affinal marriages, a preferential ranking
• Entailments of types
• (see White 2005, Hamberger et al 2005)

73
B. Marriage Census Graph Analysis

• All the types of relinking marriages are shown
• Closing a loop between 2-, 3-, 4- families,
  affines
• Between blood kin, 2-, 3- 4- degree consanguines
• Census graphs show
• frequencies of each type (nodes, their sizes)
• frequencies of overlaps of types (thickness of
  edges)
• The second-order organization of marriages
• Entailments of types
• Something of the logic and redundancies of
  kinship
• And a third-order analysis includes individuals
  and so can be related to spatial distribution,
  occupation, etc.
• (see White 2005, Hamberger et al 2005)

74
Some Findings, 1 general theory

• Cohesive communities with many blood marriages
  have preference orderings over the whole series
  of marriage types, with implications for
  self-organizing or reciprocity based systems
• Cohesive communities with few blood marriages
  have preference orderings over the whole series
  of affinal marriage types
• In the first case are there no preference
  orderings on affinal types as in the second case.

75
Some Findings, 2 kinship systems

• Network findings map onto but vastly increase our
  sensitivity to the distribution of different
  types of marriage systems
• E.g., the frequency of reciprocal dual
  organization in marriage networks is probably an
  order of magnitude greater than identified by
  hereditary moieties.
• Kinship systems with navigability of strong ties
  between groups through reciprocal marriage is a
  possibility not identified previously in the
  kinship literature. This may also occur in cases
  like Russia or Baltic states and in Central Asia,
  and is widespread in Arabized countries.

76
II. kinship structure and cognition

• This section focuses on
• Kinship Structure defining and measuring
• structural cohesion / structural endogamy
• cohesive embedding
• Kinship Cognition

77
A. Defining the phenomena of endogamy

• Endogamy is marriage within the limits of a clan,
  class, caste, etc., with relative degrees of
  closure varying inversely with those marrying
  out.
• 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 relinkings of k families, with
  varying depth in generations
• Subblocks of consanguinal (blood) within-family
  marriage (relinkings for k1)
• In each case, every member couple in a block is
  parentally linked in two or more ways to every
  other (ignoring sibling ties)

78
B. Data and RepresentationHow to construct
kinship networks for analysis

• 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
• Therefor to study how cohesion is created, take
  only primary relations (marriage, descent)
  against those implied (siblings, cousins, etc.)
  by parental networks
• (the implied relations may differ in their
  cultural meanings, appropriate terminology and
  behavior)

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80
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 (fathers brothers
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
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82

• 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
  (womens 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 17.5
• Unbalanced Cycles (Odd Length) 0 17.5
• p.00000000003

83
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84
C. Relational Thinking parental graphs as a
relational representation
Showing how couples are related, e.g., by sex and
rank, makes it easier to see patterns of
relations. Conventional genealogical diagrams
emphasize the categorical treatment of sibling
sets.
Douglas R. White and Paul Jorion. 1992
Representing and Analyzing Kinship A Network
Approach. Current Anthropology
33454-462. 1996 Kinship Networks and Discrete
Structure Theory Applications and Implications.
Social Networks 18267-314. Douglas R. White,
Vladimir Batagelj and Andrej Mrvar. 1999.
Analyzing Large Kinship and Marriage Networks
with Pgraph and Pajek, Social Science Computer
Review 17(3)245-274.
85
Defining endogamy relationally

• Categorical attributes for endogamy
• suffer from problems of specification error
  
• Structural endogamy is relational
• It consists of blocks of relinkings
• blocks of blood marriage as same-family relinking
• blocks of k-family relinkings, with depth g
  generations
• network cohesion is the more general concept

4
male lines female lines
2
3

• parental graphs identify relinkings as cycles
• maximal blocks of cycles define limits of
  structural endogamy (bicomponents sets of nodes
  where every pair is linked by two ore more
  node-independent paths). These are relational
  patterns of cohesion grouping that people
  recognize intuitively.

1
86

People Think Relationally in Kinship Practice

• Integrative concepts e.g., how cognition uses
  networks in mental operations (memory)
• Network approaches to learn how people think
  (preference, cognition) from their behavior
• Simulation provides baselines for this purpose
• How people count on each other - examples

1. Slovene Farmers of Feistritz, Austria How class
   is counted
2. Dukuh Hamlet and Javanese Muslim Village Elites
   Are we different?
3. Pul Eliyan Kinship in Sri Lanka What side are
   you on?
4. Aydinli Turkish Nomad Clan What is our group?
   Are we from the same root?

87
D. Identifying marriage rules and strategies
relationally controlled demographic simulation

• in a science of social structure and dynamics
  that includes marriage and kinship, how to
• define and evaluate marriage strategies against
  random baselines?
• separate randomizing strategy from
  preferential strategy?
• detect atomistic strategies (partial, selective)
  as well as global or elementary marriage-rules
  or strategies?
• detect changes in marriage rules or strategies?
• D. White. 1997. Structural Endogamy and the
  graphe de parenté. Mathématique, informatique et
  sciences humaines 137107-125. Paris Ecole des
  Hautes Etudes en Sciences Sociales
• D. White. 1999. Controlled Simulation of
  Marriage Systems. Journal of Artificial
  Societies and Social Simulation 3(2).
  http//www.soc.surrey.ac.uk/2/3/5/JASSS.html
• See http//eclectic.ss.uci.edu/drwhite

88
the simulation technique is simple

• In each generation of marriages in an actual
  parental graph
• 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 dont change the parents that keeps each
  sibling set intact
• (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.

89
applications of the simulation method to study
structural endogamy pertain to

• Social class,
• Elite structural endogamy,
• Wealth consolidation,
• Community/ethnic integration,
• Testing alliance, descent, and proscriptive
  theories and models

in the examples to follow
90
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 137107-125. Paris Ecole des
Hautes Etudes en Sciences Sociales
91
E. How people count on each other - Case Study
examples

• Social class and structural endogamy in the
  Austrian village of Feistritz Strategic
  counting of relinked kin (w/ Lilyan Brudner
  1997)
• Status endogamy in a Javanese village (Dukuh
  hamlet and Muslim) elites (w/ Thomas Schweizer
  1998) discounting differences in marriage
  frequencies (they are governed by demographic
  constraints, not by different consanguineal
  marriage preferences)
• Dual organization in Sri Lanka Preferred
  marriages and sidedness in Pul Eliya counting
  sides (w/ Michael Houseman 1998)
• Clan Organization among Turkish Nomads
  counting on shifting and groups with sliding
  scales of integration (w/ Ulla Johansen 2005)