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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. 305 359. 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 A 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) node independent paths T = karate teacher A = club administrator

Block Connectivity:

Blue k

=4 (quadricomponent)

Red k

=3 (tricomponent)

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.

T’s side T A A’s side Opposing cohesive sides emerge 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 k=2 3 2 5 4 k=2 6 k=1

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

3 4 3 4 3 5 3 6 4 4 4 3 3 4 3 3 4 3 3 3 3 3 5 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 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.

Fig 2. Structural Cohesion of Friendships _______ in an American high school

11-12 th 9 grade th 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. Editors, 2002, The National Academy Press.

Baruch Fischhoff, Elena O. Nightingale, Joah G. Iannotta, 10 th grade 2003 James Moody and Douglas R. White, Social Cohesion and Embeddedness : A Hierarchical Conception of Social Groups. American Sociological Review 8(1) 7 th grade 8 th grade Interpretation: 7 th -graders- core/periphery; 8 th - two cliques, one hyper-solidary, the other marginalized; 9 th central transitional; 10 th - hang out on margins of seniors; 11 th -12 th - 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 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.

Fig 3. Biotech Collaborations All ties 1989

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

New ties

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.

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. Submitted to: American Journal of Sociology.

All ties 1989 And so on to 1999

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

all ties for a year, Biotech, 1997

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

Figure 1: An ego network under construction for Robert Corteen (Hypothetical data) using the KNQ software of the KASS project

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

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 + Fa

parental graphs can be constructed from standard genealogical data files (.GED), using PAJEK and a number of other programs.

FaSiDa MaleEgo

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 T I M E

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 Present: by Ancestral Levels Actual Simulated 8* 0 16* 0 70* 32 179 183 257 273 Back 1 gen: by Ancestral Levels Actual Simulated 8* 0 58* 18 168 168 246 255 308 320 318 335 339 347 Back 2 gen: by Ancestral Levels Actual Simulated 26* 0 115* 98 178 194 243 262 278 291 292 310

Statistical conclusion: conscious relinking among families creates structural endogamy

Source

: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,”

Theory and Society

25:161 208. 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

sidedness. : 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 • 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 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) GF=FG yes

2:

3

1 39 40 .317 FZD GG=FF 1: 0 1 56 57 .508 FZ GG=F 3: 0 1 6 6 .538 FFFZDSD GGGG=FGFF 4: 1 0 3 1 .800 FFMZDSSD GGGF=FGGFF 5: 0 1 5 3 .444 FFMBDSDD GGGF=FFGFG 6: 1 0 18 15 .558 FMBSD GGF=FGG 7: 0 1 17 12 .433 FMBDD GGF=FFG 8: 2 1 18 12 .661 FMZDD GGF=FFF 9: 0 1 9 5 .399 FMMBSSD GGFF=FGGG 10: 0 1 4 5 .600 FMMFZSSD GGFFG=FGGF 11: 0 1 6 3 .400 FMMFZDSD GGFFG=FGFF 13: 0 1 25 27 .528 MBSD GF=FGG 14: 1 0 14 10 .600 MFZDD GFG=FFF 15: 1 16: 1 0 7 3 .727 MFFZDSSD GFGG=FGGFF 0 8 4 .692 MFFZDSD GFGG=FGFF 17: 1 18: 1 19: 1 20: 1 21: 1 0 8 2 .818 MFMBDSSD GFGF=FGGFG 0 9 3 .769 MFMBDD GFGF=FFG 0 3 0 1.000 MFMBDDDD GFGF=FFFFG 0 8 2 .818 MFMFZSSD GFGFG=FGGF 0 3 0 1.000 MFMFZDDD GFGFG=FFFF 22: 1 0 13 8 .636 MMZSSD GFF=FGGF 23: 1 0 15 13 .551 MMBDD GFF=FFG 24: 0 1 11 5 .352 MMZSDD GFF=FFGF 25: 0 1 11 5 .352 MMBDDD GFF=FFFG 26: 1 0 11 4 .749 MMZDDD GFF=FFFF

conclusions: (1) MBD is a preferred

yes yes yes yes

marriage (2) All blood marriages are patri sided

yes yes yes yes yes yes yes yes yes yes yes no no no no no yes yes yes no no

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 Simulated 5 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

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 3 4 2 3 4 2 to parental graph (for the entire society) 1 We numbered each person and gave one line for each marriage with number of ego, ego’s mother, father and spouse. 1 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 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)

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

“ Hu married to tribes with reciprocal exchange

12

0 148 14 26 “ Hu left for village life 13

23

“ Hu married to village wife (34) or husband (1) 11

24

36 35 5 “ 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 8 4 Totals 189 85 274

Pearson’s coefficient r=.95

without middle cells

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

180 160 140 120 100 80 60 40 20 0

# of Types

Frequency M =206/x 2 0 + 156/x^2

(power law preferential curve) # of Couples

FFZSD FFBSD:10-11 FZD:14 MBD:16 FBD:31 0 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

arrows for

property flows

as the unit of parental graph analysis, additional (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.

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 p=1.0

2: 1 2 2 3 .714 MBD 1 0 11 16 .429 MBD p=1.0

3: 2 1 3 2 .714 FZDD 0 0 11 0 FZDD p=1.0

4: 0 1 6 7 .571 ZD 0 0 18 24 ZD p=1.0

0 0 11 11 Z 0 0 36 43 Z 0 0 4 4 BD 0 0 22 27 BD Statistical 0 0 2 2 ZSD conclusion: there 0 0 3 3 BDD 0 0 8 8 BDD 0 0 3 3 ZDD are no preferred 0 0 4 4 FZ 0 0 21 27 FZ marriages 0 0 1 1 FZSD among elites 0 0 3 3 FZD 0 0 13 14 FZD 0 0 3 3 FBDD 0 0 3 2 FBDD beyond status 0 0 5 4 MZ 0 0 18 23 MZ 0 0 2 2 MZSD 0 0 4 4 MZD 0 0 13 14 MZD 0 0 1 2 MBDD 0 0 6 5 MBDD 0 0 2 3 MZDD 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) Abraham & Sarah & Hagar Heran Lot Nahor ishmael Bethel

Male Descent

Isaac

Female Descent

Rachel & Jacob & Leah

Same person (polygamy)

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

genealogies measure of the extent to which marriages take place among descendents of a limited set of ancestors. For the nomad clan

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) b) c) d) Slovene Farmers of Feistritz, Austria – How class is counted?

Dukuh Hamlet and Javanese Muslim Village Elites – Are we different?

Pul Eliyan Kinship in Sri Lanka – What ‘side’ are you on?

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

endogamy in a parental graph computes structural PAJEK

Network/Partition/Depth/Genealogy

computes genealogical depth. This enabled 2D or 3D drawings of kinship networks.

Manuals for p-graph kinship analysis

multimedia representations are contained in  1) “Analyzing Large Kinship and Marriage Networks with pgraph and Pajek,”

Social Science Computer Review

and discussions of software programs & 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

Exploratory Social Network Analysis with Pajek

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 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/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 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.

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  Subblocks of relinkings of

structural endogamy as blocks of generalized relinking (a special case of network cohesion) with: 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 7 th and 8 th century?

Data: Genealogies on two thousand clan members and their ancestors, from

1800 to the present, a long-term ethnography by Professor Ulla C. Johansen, University of Cologne

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

Balanced Cycles (Even length) Actual 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)

Balanced Cycles (Even length) Unbalanced Cycles (Odd Length) Actual 35 0 Expected 17.5

17.5 p=.00000000003

C. Relational Thinking: parental graphs as a relational representation

4 genealogies 3 2 become 4 a parental 2 graph 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 endogamy (

bicomponents

: sets of nodes where every pair is linked by two 1 ore more node-independent paths). These are relational patterns of cohesion grouping that people recognize intuitively.

2

o

People Think Relationally in Kinship Practice Integrative concepts: e.g., how ‘cognition’ uses networks in mental operations (‘memory’)

o o

Network approaches to learn how people think (preference, cognition) from their behavior

o

Simulation: provides baselines for this purpose

How people ‘count’ on each other - examples

1) 2) 3) 4) Slovene Farmers of Feistritz, Austria – How class is counted Dukuh Hamlet and Javanese Muslim Village Elites – Are we different?

Pul Eliyan Kinship in Sri Lanka – What ‘side’ are you on?

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

http://www.soc.surrey.ac.uk/2/3/5/JASSS.html

3(2). 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)