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
Ethnographic examples
Case 1:
2 year ethnography of a
karate club
Conflict and
Fragmentation
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.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.
Fig 1. Snapshot of friendships at an early point in
time in a longitudinal study of friendship in a
Karate club, with leaders labeled T and A and
levels of cohesion coded by color.
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. 305359. Blackwell Publishers, Inc., Boston,
USA and Oxford, UK. SFI Posting
Connectivity: Blue=4 Red=3
Green=2 Yellow=1
Ethnography and data source: Wayne Zachary,
1977. An Information Flow Model for Conflict
and Fission in Small Groups. Journal of
Anthropological Research 33:452-73.
Loss of cohesion
T
A
T
T’s side
T and A start to fight: some must choose sides
members of a
group with
cohesion level
k automatically
have at least k
different ways
of being
connected
through (k)
nodeindependent
paths
A
A’s side
Opposing cohesive sides emerge
T = karate teacher
A = club administrator
Block Connectivity:
Blue k=4 (quadricomponent)
Red k=3 (tricomponent)
T
A
Green k=2 (bicomponent)
Yellow k=1 (component)
Figure 1a,b,c Data source: Wayne Zachary, 1977. An Information
Flow Model for Conflict and Fission in Small Groups. Journal of
Anthropological Research 33:452-73.
The sides separate along cohesive fracture
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
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.
1
4
k=2
k=2
3
2
k=1
6
5
k-components may overlap, or be vertically stacked as shown here
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Topology: Overlapping hierarchies (Abstract Model)
A k-ridge supporting structure is a set of n (k+1)-components that are connected,
with intersections containing at least k nodes, where each (k+1)-component has
node-connectivity greater than k.
A k-ridge structure has connectivity k but supports a series of connected (k+1)components, i.e., of connectivity k.
Figure: 3-ridge structure supporting overlapping 4-components
4
3
4
3
5 3
6
4
4
4
3
3
4
3
4
3
3
3 3
3
5
3
3
3
4
4
3
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.
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Topology: Overlapping hierarchies (Empirical Results)
The algorithm for finding social embeddedness in nested
Fig 2. Structural Cohesion of Friendships
cohesive subgroups is applied to high school friendship _______in an American high school
networks (e.g., Fig 2; boundaries of grades are
11-12th grade
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
9th
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
th
(http://www.cpc.unc.edu/addhealth/), Adolescent Risk and 10 grade
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)
8th grade
7th grade
Interpretation: 7th-graders- core/periphery; 8th- two cliques, one hyper-solidary, the other marginalized; 9thcentral transitional; 10th- hang out on margins of seniors; 11th-12th- integrated, but more freedom to marginalize
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Topology: Stacked hierarchies and Dynamics (Empirical Results)
Longitudinal Validation of Structural Cohesion Dynamics in Biotechnology
Fig 3. Biotech Collaborations
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 All ties
1989
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
New ties
subnetworks form that are characterized by multiple, independent
1989
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.
All ties
1989
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.
And so on
Submitted to: American Journal of Sociology.
to 1999
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
New ties, Biotech, 1997
(flip back)
Ethnographic examples
Case 4:
KASS questionnaire
network analysis
e.g., measuring cohesion
in ego networks
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 1: An ego network
under
construction
for
Robert
Corteen
(Hypothetical data) using
the KNQ software of the
KASS project
Pajek
analysis
Fig 3: Cohesive Subgroup Calculation (yellow nodes) Robert Corteen network
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
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
Data and Representation:
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 parental graph
Data and Representation:
Kinship 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
•Treating individuals as lines
•Here: one blue line per
female circle and one red line
per male triangle
•From lines of different type
for different genders we can
read off: a FaSiDa marriage
Data and Representation:
Kinship as Parental Graph Networks
parental graphs link pairs of parents (flexible & culturally defined) to their descendents
FaSi +
FaSiDa
Fa
MaleEgo
parental 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)
Here: one blue line per female and one red line per male: hence
we can visually identify the FaSiDa marriage
Data and Representation:
Relating 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
Further ethnographic examples
Case 5: Carinthian
Farmers
(structural endogamy,
social class, and network
cognition)
Church
Mountains
and Alms
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
The stemline
social class of
farmstead
inheritors,
1510-1980
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.
Pgraph software;
parental graph
representation: these are
the heirs and families that
are maritally relinked
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 25:161-208. Lilyan Brudner and Douglas White
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
Generation
1
2
3
4
5
6
by Ancestral Levels
Present:
Actual
8*
16*
70*
179
257
318
Simulated
0
0
32
183
273
335
by Ancestral Levels
Back 1 gen:
Actual
8*
58*
168
246
308
339
Simulated
0
18
168
255
320
347
by Ancestral Levels
Back 2 gen:
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 25:161208. Lilyan Brudner and Douglas White
Further ethnographic example
Case 6: Pul Eliya, Sri Lanka
(illustrating kinship
structure, networks,
cognition, kin terms)
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 Leach’s 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, L’Homme 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.
parental graph of Pul Eliyan Sidedness
Marriage sides in Pul Eliya, with compound IDs for males,
(this slide was
made with
Pajek, output
for web
viewing)
red lines for females
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.
Frequencies of Actual versus Simulated Consanguineal Marriages for Pul Eliya, Sri Lanka,
Type
Actual Simul
of Mar. Freq. Freq.
Total
(2)Patri-Sided?
Total Fisher|-----Blood Marriage------|
Actual Simul Exact
type
parental graph notation
12:
5
0
40
38 p=.042 MBD(1)GF=FG
2:
1:
3:
4:
5:
6:
7:
8:
9:
10:
11:
13:
14:
15:
16:
17:
18:
19:
20:
21:
22:
23:
24:
25:
26:
3
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
39
56
6
3
5
18
17
18
9
4
6
25
14
7
8
8
9
3
8
3
13
15
11
11
11
40
57
6
1
3
15
12
12
5
5
3
27
10
3
4
2
3
0
2
0
8
13
5
5
4
.317
.508
.538
.800
.444
.558
.433
.661
.399
.600
.400
.528
.600
.727
.692
.818
.769
1.000
.818
1.000
.636
.551
.352
.352
.749
FZD
FZ
FFFZDSD
FFMZDSSD
FFMBDSDD
FMBSD
FMBDD
FMZDD
FMMBSSD
FMMFZSSD
FMMFZDSD
MBSD
MFZDD
MFFZDSSD
MFFZDSD
MFMBDSSD
MFMBDD
MFMBDDDD
MFMFZSSD
MFMFZDDD
MMZSSD
MMBDD
MMZSDD
MMBDDD
MMZDDD
GG=FF
GG=F
GGGG=FGFF
GGGF=FGGFF
GGGF=FFGFG
GGF=FGG
GGF=FFG
GGF=FFF
GGFF=FGGG
GGFFG=FGGF
GGFFG=FGFF
GF=FGG
GFG=FFF
GFGG=FGGFF
GFGG=FGFF
GFGF=FGGFG
GFGF=FFG
GFGF=FFFFG
GFGFG=FGGF
GFGFG=FFFF
GFF=FGGF
GFF=FFG
GFF=FFGF
GFF=FFFG
GFF=FFFF
Actual
yes
yes
no
no
yes
conclusions:
(1) MBD is a
preferred
marriage
(2) All blood
marriages
are patrisided
no
yes
no
yes
no
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
no
no
yes
Correlating Actual versus Simulated non-MBD marriages for Pul Eliya,
showing tendency towards a Patri-Sided (Dravidian) Marriage Rule
Actual
Simulated
Patri-Sided
18
5
Simulation
Unsided
0
7
p=.0004
p=.000004 using the
binomial test of an
expected 50:50 split)
Another ethnographic example
Case 7: Turkish nomads
(kinship, cognition,
semantics, migration)
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.
Applications of Structural Endogamy
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Generations
Data:
parental graph of the conicality of the nomad clan
Coding the data for a Nomadic Clan
– Are we from the same ‘root’? What is our ‘group’?
Johansen’s
genealogical
scroll
4
4
3
2
3
2
to parental
graph (for the
entire society)
1
1
We numbered each person
and gave one line for
each marriage with
number of ego, ego’s
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) !
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 today’s
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
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.
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 picture shows only the
structurally endogamous or
relinked marriages within the
nomad clan (nearly 75% of 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 marital relinking predict staying with the clan, as predicted by PCT?
Results: Yes !
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: 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:
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
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.
Case 8: city networks
and trade, 1175-1500
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
Cohesive nodes (gold and red) in an expanded exchange network and road
identification (red=3-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.
Northern Hanse Trade Organization:
Saintly Brotherhoods
Northeast
Southwest
v
v
v
v
Other Eastern Hanse
German Towns, 1470
END
Case 9: Muslim elites in
Southeastern Java
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 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 “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.
STATUS ENDOGAMY in a Javanese Village (Dukuh Hamlet, Muslim Elites),
Test of Actual versus Simulated Marriage among Consanguineal Kin
key: A
B
TA
TS
=
=
=
=
frequency of actual marriages with a given type of relative
frequency of simulated random marriages with a given type of relative
total of actual relatives of this type
total of simulated relatives of this type
Javanese elites
A S TA TS p=
1: 1 0 4 3 .625
2: 1 2 2 3 .714
3: 2 1 3 2 .714
4: 0 1 6 7 .571
0 0 11 11
0 0 4 4
0 0 2 2
0 0 3 3
0 0 3 3
0 0 4 4
0 0 1 1
0 0 3 3
0 0 3 3
0 0 5 4
0 0 2 2
0 0 4 4
0 0 1 2
0 0 2 3
type
FBD
MBD
FZDD
ZD
Z
BD
ZSD
BDD
ZDD
FZ
FZSD
FZD
FBDD
MZ
MZSD
MZD
MBDD
MZDD
Dukuh Hamlet
A S TA TS p=
0 1 9 12 .591
1 0 11 16 .429
0 0 11 0
0 0 18 24
0 0 36 43
0 0 22 27
0 0
8
8
3-Way Test
type
FBD
MBD
FZDD
ZD
Z
BD
BDD
0 0 21 27
FZ
0 0 13 14
0 0 3 2
0 0 18 23
FZD
FBDD
MZ
0 0 13 14
0 0 6 5
MZD
MBDD
p=1.0
p=1.0
p=1.0
p=1.0
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
Data and Representation:
Relating parental 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
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.
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.
Relational answers to Johansen’s 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):
parental graph of the conical nomad clan
1. An apical ancestor of the 90% of those
down to today’s nomad clan members
2. Structural endogamy of the nomad clan
Each marriage is contained in a cycle of previously linked marriages
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
a)
Slovene Farmers of Feistritz, Austria – How class is counted?
b)
Dukuh Hamlet and Javanese Muslim Village Elites – Are we different?
c)
Pul Eliyan Kinship in Sri Lanka – What ‘side’ are you on?
d)
Aydĭnlĭ Turkish Nomad Clan – What is our ‘group’? Are we from the same
‘root’?
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.
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 Aydĭnlĭ 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
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
Exploratory
 4) book by de Nooy, Batagelj and Mrvar, 2005
Social_Network Analysis
with Pajek
Exploratory Social Network Analysis with Pajek
Cambridge University Press
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.
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 (Multiconnectivity+Robustness=resilience)
• Structurally cohesive groups possess definite lines
of boundedness in social networks.
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
• 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 OwenSmith. 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/issues/v110n4/080171/080171
.html http://www.journals.uchicago.edu/AJS/journal/contents/v110n4.html
Structurally cohesive blocks in social
networks have predictable consequences
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)
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.
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)
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)
Some Findings, 1: general theory
• Cohesive communities with many blood marriages
have preference orderings over the whole series of
marriage types, with implications for selforganizing 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.
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.
II. kinship structure and cognition
This section focuses on
• Kinship Structure: defining and measuring
– structural cohesion / structural endogamy
– cohesive embedding
• Kinship Cognition
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 k=1)
 In each case, every member couple in a block is parentally linked
in two or more ways to every other (ignoring sibling ties)
B. Data and Representation:
How 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)
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
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
Balanced Cycles (Even length) 25
Unbalanced Cycles (Odd Length) 10
Expected
17.5
17.5
p=.008
(all exceptions involve relinkings between nonconsanguineal relatives)
B. Amblilateral-sidedness
(women‘s sidedness adjusted by inheritance rules) - not shown in
figure but shown in final publication (Houseman and White 1997)
Actual
Balanced Cycles (Even length) 35
Unbalanced Cycles (Odd Length) 0
Expected
17.5
17.5
p=.00000000003
C. Relational Thinking: parental
graphs as a relational representation
4
genealogies
3
become
4
2
a parental
graph
2
3
1
1
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 33:454-462.
1996 “Kinship Networks and Discrete Structure Theory: Applications and
Implications.” Social Networks 18:267-314.
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.
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
3
male lines female lines
• parental graphs identify relinkings as cycles
maximal blocks of cycles define limits of structural endogamy1
(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.
2
People Think Relationally in Kinship Practice
o Integrative concepts: e.g., how ‘cognition’ uses
networks in mental operations (‘memory’)
o Network approaches to learn how people think
(preference, cognition) from their behavior
o
Simulation: provides baselines for this purpose
o 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)
Aydĭnlĭ Turkish Nomad Clan – What is our ‘group’? Are we from the same
‘root’?
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 137:107-125.
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
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 don’t 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.
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
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
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)