(Structural) Cohesion in Organizations

(Structural) Cohesion in Organizations

Douglas R. WhiteUniversity of California – Irvine

With

James MoodyThe Ohio State University

Séminaire " Réseaux et régulation " Lasmas, IRESCO, Paris, June 2003

Structural Cohesion for Organizations

• Part One – Predictive Cohesion Theory for Cohesive Blocks and Ridges in Organizations

• Theory and Dynamical Networks; Case Study Examples using Pajek– k-ridges of Structural Cohesion (an extension of Friedkin’s

work on cohesion in formal organizations)– Cohesive Blocks in High School Friendships (w Moody)– Cohesive Dynamics: the splitting of blocks in organizations

(with Harary)– Cohesion Dynamics in Biotechnology (with Powell…)

• Part Two – Predictive Cohesion Theory for Marriage, Class, Community and Ethnicity

Longitudinal Network Studies and Predictive Social Cohesion Theory D.R. WHITE, University of California Irvine, BCS-9978282

Predictive Social Cohesion Theory

Paper in preparation for MISH, 2004, special issue on Social Networks, edited by Degenne

• “Traversal” and “structural” cohesion are two graph theoretic properties of multiconnectivity in networks that are proven by Menger Theorem (1927) to be isomorphic .

• The isomorphism suggests that multiconnectivity will have strong predictive effects in networks.

• Organization theory suggests that alternate topologies of multiconnectivity will vary with types of organizations.


Predictive Social Cohesion Theory: Basic Measures

Multiconnectivity in networks has two aspects

• Maximum (pairwise, graphwise) “traversal” cohesion Number of node-independent paths – redundant transmissibility

• Minimum (pairwise, graphwise) “structural” cohesion Number of nodes in a cutset – resistance to disconnection

Strong predictive effects because by Menger’s Theorem (1927)

• These two multiconnectivity measures are identical

• They are identical both for pairwise and graphwise measures


Predictive Social Cohesion Theory: graph theoretical distinction for a graph or a pair of nodes in a graph, following Harary (1969) between:

Multiconnectivity -- the maximum number of node-independent paths between {each pair; a pair} of nodes in the graph. Following Menger (1927) it is equivalent to Node connectivity: The minimum number of nodes whose removal is needed to disconnect the {graph; pair of nodes}. Multiconnectivity is a measure of cohesion (Harary et al 1965).

Edge connectivity -- the minimum number of edges whose removal is needed to disconnect the {graph; pair of nodes}. Menger (1927) theorem was extended by Ford and Fulkerson to the measure of Flow as the maximum number of edge-independent paths between {each pair; a pair} of nodes in the graph. Flow is equivalent to edge connectivity and is not a measure of cohesion (White and Harary 2001).


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.

A k-edge component of a graph is similarly defined using edge cutsets and edge-independent paths.

1 4

3

2 5


Predictive Social Cohesion Theory -- concerns Node Connectivity or Multiconnectivity only:

The bow tie graph. The lowest order of graph (n = 5) at which edge and node connectivities differ (node connectivity = 1, while edge connectivity = 2). Sets {1,2,3} and {3,4,5} are cohesive 2-components that overlap in node 3, while the 2-edge-component {1,2,3,4,5} is noncohesive. The flow from 1 to 4 is 2, but the maximum number of node-independent paths is 1.

1 4

3

2 5

Arrows show flows, which may pass through the same intermediate nodes but must be edge-independent


Predictive Social Cohesion Theory: Organizational Structure

Multiconnectivity in networks has two logically possible topologies

•Stacking: component, bicomponent, tricomponent, k-component

•Overlap: at most k-1 nodes in common for k-components

These may occur exclusively or combine in three topologies

•Overlapping hierarchies (k-ridge)

•Pure hierarchical stacking (n-cone)

•Pure overlap of cohesion in its simplest form (bicomponents)


Predictive Social Cohesion Theory: Organizational Structure

Organization Theory suggests the three typologies have the following associations

• Pure hierarchical stacking – informal unrestrained cooperative with decentralized control

• Overlapping hierarchies – constrained by formal organization and competitive with decentralized control

• Pure overlap of cohesion in its simplest form (bicomponents): social class, ethnicity and community as formed by intermarriage and kinship (structural endogamy), auto-reproductive

Topology 1: 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 3 4 3 3 3 3 3 5 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.

Topology 1: Overlapping hierarchies (Empirical Study 1)

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)


Fig 2. Friendship Cohesion in an American high school

8th grade

7th grade

11-12th grade

10th grade

9th

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


ATTACHMENT INFLUENCE

Source of network diagrams: Friedkin (1998: 156 and 175).

K-ridge model applied to an example from Friedkin 1998: Columbia University sciences faculty: cohesive attachments predict reported flows of interpersonal influence

Topology 1: Overlapping hierarchies (Empirical Study 2)


Overlapping hierarchies (Empirical Study 2)

Prediction from Ridge Attachment to Interpersonal Influence; Gamma = .714, tau-b = .55, Somer’s D=.5, p < .02.

N=15 Positions

INFLUENCE

Reciprocal

Directional orReciprocal

None

ATTACHMENT

High 2 1

Directional 2

Edge Bridge only

4

None 2 4


Topology 2: Stacked hierarchies (Abstract Model)

An n-cone is a stack of k-components for k=1 to n, where each k-component is nested in a k-1 component. Each k-component of an n-cone has connectivity k and contains a series of (k+m)-components for m=1 to n-k.

Figure: An 8-cone supporting nested k-components for k=1 to 8.

3 4 7 8 6 5


Topology 2: Stacked hierarchies splitting into Overlapping (Study 2)

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), based on cohesion and distance.

Reference:

2001 Douglas R. White and Frank Harary, The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density, vol. 31, no. 1 in Sociological Methodology 2001: 305-359. Blackwell Publishers, Inc., Boston, USA.

Fig 1. Snapshot of friendships at successive points 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. When members with ties to both leaders T and A are forced to choose between them, removing the red lines, two cohesive hierarchies form that bifurcate the club.

Data source: Wayne Zachary, 1977. An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research 33:452-73.

Connectivity: Blue=4 Red=3 Green=2 Yellow=1

TA

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 = karate teacher

A = club administrator

Block Connectivity:

Blue k=4 (quadricomponent)

Red k=3 (tricomponent)

Green k=2 (bicomponent)

Yellow k=1 (component)

T

T A

A

T and A start to fight: some must choose sides Opposing cohesive sides emerge

TA

The sides separate along cohesive fracture

members of a group with cohesion level k automatically have at least k different ways of being connected through (k) node-independent paths

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.

Topology 2: Stacked hierarchies and Dynamics (Empirical Study 2) Longitudinal Validation of Structural Cohesion Dynamics in Biotechnology


Fig 3. Biotech Collaborations

All ties 1989

New ties 1989

All ties 1989

And so on to 1999


Predictive Social Cohesion Theory: Topology 2 (Single Hierarchy). An article on the biotech industry under review by Powell, White, Koput and Owen-Smith can be found at the ~drwhite home page athttp://eclectic.ss.uci.edu/~drwhite/links2pdf.htmAnd is reviewed at the Barabási site athttp://www.nd.edu/~networks/linked/newfile18.htm

The rest of this talk will consider Topology 3 (overlap of bicomponents of structural endogamy for social class, ethnicity and community as formed by auto-reproductive intermarriage and kinship networks.These slides were prepared with James Moody.

Structural Cohesion for Organizations,

Kinship Networks and Demography

Outline: Part Two• Introduction: Concepts for Network Cohesion in

Marriage, Class, Community and Ethnicity• A Network Approach to Marriage Rules and

Strategies via Controlled Demographic Simulation• Representing Kinship as A Network: P-graphs• Case Study Examples

– Emergence and Fission of Groups in Social Networks– Elite and Class Cohesion via Structural Endogamy– Community/Ethnic Cohesion via Structural Endogamy

Introduction: some questions of interest

1 What is the influence of demography on social structure and the reverse?

2 How does one measure the demography of marriage and network behaviors in human populations?

3 What is the influence of social structure on such behaviors?

• For this purpose “social structure” is the network of social bonds among people and with things to which people have significant links (property, ideas, material and ecological items).

• Some aspects of social institutions are implied or included in this definition insofar as they are an emergent result of social/legal/political bonds and of responses to demographic pressures.

Structural demography might include:

• The social field of kinship as the place of (social) reproduction in which structural endogamies define the reproductive boundaries of social class, ethnic identities, kinship groups, and so forth.

• The social field of groups, in which cohesion and coordinated social action emerges within social networks and connectivities define the limits of cooperation and competition

• The social field of stratification in which groups (or individuals) are situated (i.e. occupy structural positions) and centralities define inequalities among individuals and groups within social networks.

The importance of measurement concepts in structural demography

• Network-based concepts such as structural endogamy, multiconnectivity, and centrality, when applied to large scale (community/nation) networks allows the possibility of a social network approach to questions about:

– longitudinal and historical studies of entire large populations

– social studies on norms and behavior

– studies of the relation between the structural positions of individuals and their behavior

– relationships between social structure and demographic variables

Applications of Structural Cohesion• Emergence and Fission of Groups in Social Networks

• Elite and Class Cohesion

• Community/Ethnic Cohesion– “The Cohesiveness of Blocks in Social Networks: Node

Connectivity and Conditional Density” (drw and Frank Harary). 2001. Sociological Methodology 2001, vol. 31, no. 1, pp. 305-359

– “Social Cohesion and Embeddedness: A hierarchical conception of social groups” (Moody and White). 2003. American Sociological Review 68(1):101-24.

Controlled Demographic Simulation: A Network Approach to Discovering Marriage Rules and Strategies

• In a quantitative science of social structure that includes marriage and kinship, how does one:

define and evaluate marriage strategies relative to random baselines?

separate ‘randomizing’ strategy from ‘preferential’ strategy? detect atomistic strategies (partial, selective) as well as global

or “elementary” marriage-rules or strategies?

“Controlled Simulation of Marriage Systems,” 1999. Journal of Artificial Societies and Social Simulation 3(2). White

A Network Approach to Marriage Rules and Strategies via Controlled Demographic Simulation

Categorical attribute models for marriage mixing are problematic, due to ambiguities in the categories and questions about how to nest various attributes.

A relational approach builds random baselines by comparing against randomized elements of the observed data. This allows one to hold constant many elements of the kinship system (for example, matrimonial decent), while testing for random mixing in other elements (‘flow’ of husbands through the system).

Defining the phenomena of endogamy:

• Endogamy is the custom of marrying only within the limits of a clan or tribe.

• Practical Strategies:– By categories/attributes:

• suffers from problems of specification error

– By network relinking: • the generalized phenomena of structural endogamy as blocks of

generalized relinking, (a special case of network cohesion) with: Subblocks of k-relinkings of k families, with g-depth in generations Subblocks of consanguinal (blood) marriage as within-family relinkings

Data and Representation:Building Kinship Networks

To analyze large-scale kinship networks, we need a generalizable graph representation of kinship networks.

Problems:•Cultural definitions of “kin” lead to cross-cultural ambiguity

•Forced to pick ‘primary’ relations (marriage, descent) against ‘implied’ relations (siblings, cousins, etc.) or include a complete graph with multiple labeling


The traditional representation is a genealogical kinship graph

•Individuals are nodes•Males and females have different shapes

•Edges are of two forms:•Marriage (usually a horizontal, double line)•Descent (vertical single line)

•Has a western bias toward individuals as the key actor

•Not a valid network, since edges emerge from dyads

•Better solution is the P-graph


P-graphs link pairs of parents (flexible & culturally defined) to their decedents

P-graphs are constructed by:

•Treating individuals as lines

•Usually of different type for different genders

•Treating couplings as nodes


P-graphs link pairs of parents (flexible & culturally defined) to their decedents

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

See:http://eclectic.ss.uci.edu/~drwhite for guides as to web-site availability with documentation (& multimedia representations)

Data and Representation:Relating p-graphs to endogamy

Cycles in p-graphs are direct markers for endogamy, and satisfy the elementary requirements for theories of kinship-based alliances (Levi-Strauss (1969, Bourdieu 1976):

Circuits in the p-graph are isomorphic with one or more of:•Blood Marriages, where two persons of common ancestry from a new union

•Redoublement d’alliance, where unions linking two co-ancestral lines are redoubled

•Renchainement, where two or more intermarried co-ancestral lines are relinked by a new union

Data and Representation:Relating p-graphs to endogamy

Male Decent

Female Decent

Same person (polygamy)

Lot & his Wives

Programs & Availability PAJEK

PAJEK reads genealogical datasets (*.ged files) both the usual Ego format and in Pgraph format, with dotted female lines (p Dots) and solid male lines.

PAJEK Network/Partition/Components/Bicomponent computes structural endogamy

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

Programs & Availability Hypothesis testing

We can use various permutation-based procedures to test the observed level of endogamy against a data-realistic random baseline.

The substantive marker for endogamic effectiveness is whether the level of endogamy is (a) greater than expected by chance given (b) the genealogical depth of the graph

1997 Structural Endogamy and the graphe de parenté. Mathématique, Informatique et sciences humaines 137:107-125. Paris: Ecole des Hautes Etudes en Sciences Sociales

Applications of Structural EndogamySocial Class

Social class as “a general way of life, a sub-culture, tends to be hereditary because (a) individuals from the same sub-culture tend to intermarry, and (b) parents bring up their children to imitate themselves.” (Leach, 1970).

If we were to examine the extent to which particular social class formations were concomitant with structural endogamy, we would expect that:

•Families involved would know "good families“ and "suitable matches,”

•not all children of the class would be "required" to marry within the class, but social class inscription would take place through the diffuse agency of relinking by marriage,

•which could both validate the social standing of the individual and constitute the diffuse but relinked social unit -- endogamic block -- of class formation.

Organizational Applications of Structural EndogamySocial Class: Carinthian Farmers

Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161-208. Lilyan Brudner and Douglas White

“Class is rooted in relations to property, but the holding of property is particularistic, bound by social relations that channel its inheritance within particular sets of personal biographies, such as those linked by kinship and marriage. As property flows through a social network, its biography unfolds as a history of the transfer from person to person or group to group.” (p.162)

Institutions (such as class), emerge out of the networked actions and choices devolving in turn in specific and changing historical context. A duality of persons and property, each linked through the others, thus characterizes the class system.


Empirical setting: Inheritance of property among families in an Austrian Village

Background: In the Austrian farming valleys of southern Carinthia, the perpetuation of Slovenian ethnicities and Windisch dialects has been associated with heirship of farmsteads. Unlike many rural areas (and as predicted by Weber and others), farms tended to be inherited complete, without the kind of splitting that fractures classes.

Main hypothesis: That two social classes emerged historically in this village and have long remained distinct as a product of differential marriage strategies.

•The mechanism for keeping land intact is that a structurally endogamous farmstead-owner social class emerged from marriages that relinked stem family or heirship lines that were already intermarried. The relinked couples inheriting farmsteads recombined primary heirships with secondary quitclaim land parcels allowing stability in reconstituting “impartible-core” farmsteads.



Data: •Extensive field work•Archival: Records of farmstead transfers starting in the 16th century•Genealogical histories on families collected by Brudner•Supplemented from data collected by White from gravestones and church records

Facts about the setting:•Village population has been (relatively) stable from 1759 – 1961, fluctuating between 618 (1923) to 720 (1821)•Most transfers are through inheritance, but the data includes purchases as well.•Daughters tend to move to their husbands house of residence•Purchase of farmsteads for sons is common, but rare for daughters•Daughters tend to bring a land dowry to a marriage


Organizational Applications of Structural Endogamy Social Class: Carinthian Farmers




Structural Endogamy w. AncestorsGeneration 1 2 3 4 5 6

Present:

Actual 8* 16* 70* 179 257 318

Simulated 0 0 32 183 273 335

Back 1 gen:

Actual 8* 58* 168 246 308 339

Simulated 0 18 168 255 320 347

Back 2 gen:

Actual 26* 115* 178 243 278 292

Simulated 0 98 194 262 291 310





Organizational Applications of Structural EndogamyElite Structural Endogamy: Rural Javanese Elites

Empirical Setting: Muslim village elites have their own compounds and extensive landholdings that qualify them for village leadership. They often marry blood relatives, while commoners do not.

Key questions: Javanese peasant villages are often characterized as a ‘loose’ social structure. Is the blood-marriage endogamy we see among village elites simply due to the demographic constraints imposed by very restricted size of the elite group, with the elites and commoners sharing the same ‘loose’ rules of marriage?

Data: Extensive field work, genealogies and ethnography by Thomas Schweizer

Organizational Applications of Structural EndogamyElite Structural Endogamy: Rural Javanese Elites

• Results:

• 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.

• Given a common rule of division of inheritance, closer marital relinkings among elites facilitated the reconsolidation of wealth within extended families

• 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.

• Graphic technique: Nuclear families as the unit of p-graph analysis, additional arrows for property flows, and extended family as constituted by marital relinking and the repartitioning of mercantile and properties resources.

•Source: 1998 “Kinship, Property and Stratification in Rural Java: A Network Analysis” (White and Schweizer). pp. 36-58, In, Thomas Schweizer and Douglas White, eds. Kinship, Networks, and Exchange. Cambridge University Press.

Organizational Applications of Structural EndogamySocial 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.

Results: Reveals that Leach had not seen, and could not for lack of requisite tools of analysis, that marriages were organized in response to a logic called dividedness and (in another form) sidedness.

the matrimonial network is bipartite, the marriages of the parents and those of the children divide themselves into two distinct ensembles (which have nothing to do with moieties).

•Graphic technique: Nuclear families as the unit of p-graph analysis, analysis of blood marriages, sibling sets and of inheritance or bequests revealed the underlying logic of marital sidedness.

•Key concepts: bipartite graph and sidedness: sidedness is an empirical bipartition of a matrimonial network, reiterated from one generation to another following a sexual criterion. The next slide the sidedness of the Pul Eliyan networks operating through the male line, with some female heirs acting as agnatic channels for inheritance where there are no male heirs (I.e., they lack brothers).

Organizational Applications of Structural EndogamySocial Integration through Marriage Systems: Kandyan Irrigation Farmers in Sri Lanka


P-graph of Pul Eliyan Sidedness

P-graph of Pul Eliyan Sidedness and Property Transactions

Curved lines follow property flows, dashed lines are gifts.

Property re-connects across the sided lines.

Correlating Actual versus Simulated non-MBD marriages for Pul Eliya, showing tendency towards a Viri-Sided (Dravidian) Marriage Rule

Viri-Sided Unsided

Actual 18 0

Simulated 5 7

(p=.0004; p=.000004 using the binomial test of 50%:50%

expected)


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

A. Viri-sidedness

Actual Expected

Balanced Cycles (Even length) 25 17.5

Unbalanced Cycles (Odd Length) 10 17.5

p=.008

(all exceptions involve relinkings between nonconsanguineal relatives)

B. Amblilateral-sidedness (women‘s sidedness adjusted by inheritance rules)

Actual Expected

Balanced Cycles (Even length) 35 17.5

Unbalanced Cycles (Odd Length) 0 17.5

p=.00000000003


Organizational Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:

The Role of Marital Cohesion

Empirical Setting: An Arabized nomadic clan having the characteristic segmentedpatrilineages, 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



Sources: 2002 Ulla Johansen and Douglas R. White, Collaborative Long-Term Ethnography And Longitudinal Social Analysis of a Nomadic Clan In Southeastern Turkey, pp. 81-99, Chronicling Cultures: Long-Term Field Research in Anthropology, eds. R. van Kemper and A. Royce. AltaMira Press.

2003 Douglas R. White and Michael Houseman The Navigability of Strong Ties: Small Worlds, Tie Strength and Network Topology, Complexity 8(1).

2003 Douglas R. White and Ulla Johansen. Network Analysis and Ethnographic Problems: Process Models of a Turkish Nomad Clan. Lexington and AltaMira. In Press.

p-graph of the conicality of the nomad clan

Organizational Applications of Structural EndogamyA Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:


Data:

Gen

erat

ion

s

•The index of relinking of a kinship graph is a measure of the extent to which marriages take place among descendents of a limited set of ancestors.

• For the nomad clan the index of relinking is 75%, which is extremely high by world standards.

•This is a picture of the structurally endogamous or relinked marriages within the nomad clan (nearly 75% or all marriages):



Results: Structural Endogamy of the nomad clan



Does staying together as a clan depend on marital relinking?Results: 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

Pearson’s coefficient r=.95 without middle cells



A power-law decay of marriage frequencies with kinship distance

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25

Frequency

0 + 156/x 2̂

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

MM =206/x2

Raw frequency

(power law preferential curve)

# of Couples

# of Types

Results: Rather than treat types of marriage one by one: FBD, MBD etc., we treat them as an ensemble and plot their frequency distribution



Results:

reversing axes, types of marriage are ranked here to show that

numbers of blood marriages follow a power-law (indexical of self-organizing preferential attachments) while affinal relinking frequencies follow an exponential distribution

An apical (circled) ancestor of the 90% of those down to today’s nomad clan members.

Attributing common unilineal descent because of common roots is a common feature of Middle Eastern lineages



Results: Does the high degree of structural endogamy create a single root to the nomadic clan?

– Who stays and who returns to village life is predicted from kinship bicomponent membership.

– Bicomponent relinking also plays a role in the emergence of a root ancestor, and of more localized root ancestors for different levels of kinship groupings.

– Dynamic reconfigurations of political factions and their leaders are predicted from ensembles with different levels of edge-independent connectivity.

– An index of the decline of cohesion of the clan would be the fragmentation of cohesive components in later generations...

• Key concepts: bicomponent, edge-independent paths, connectivity.

• Graphic technique: nuclear families as the unit of p-graph analysis.

• An explanation of methods will be found in a book ms. : Social Dynamics of a Nomadic Clan in Southeastern Turkey: An Introduction to Networked Histories. Douglas White and Ulla Johansen. For submission to Westview or Altamira Press.


The Role of Marital CohesionResults: Summary:

Conclusion?

• Predictive Cohesion Theory has broad applications and empirical support in a variety of studies

Bibliography:

Brudner and White. 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161-208.

Houseman and White. 1998 “Network Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lanka” pp. 59-89, In, Thomas Schweizer and drw, eds. Kinship, Networks, and Exchange. CUP.

Moody and White. 2003. “Social Cohesion and Embeddedness: A hierarchical conception of social groups” American Sociological Review 68:101-24.

White. 1997. “Structural Endogamy and the graphe de parenté” Mathématique, Informatique et sciences humaines 137:107-125.

White. 1999. “Controlled Simulation of Marriage Systems” Journal of Artificial Societies and Social Simulation 3(2).

White, Batagelj and Mrvar. 1999. “Analyzing Large Kinship and Marriage Networks with pgraph and Pajek,” Social Science Computer Review 17:245-274.

White and Harary. 2001. “The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density” Sociological Methodology 31:305-359

White and Jorion. 1996. “Kinship Networks and Discrete Structure Theory: Applications and Implications.” Social Networks 18:267-314

White and Schweizer 1998. “Kinship, Property and Stratification in Rural Java: A Network Analysis” pp. 36-58, In, Thomas Schweizer and Douglas White, eds. Kinship, Networks, and Exchange. Cambridge University Press.


Predictive Social Cohesion Theory

Summary and ExtensionsWhere would the concept of structural endogamy connect to current population concerns?

Social reproduction of ethnicity through differential fertility

Differences in reproductive rates by social groups mean that genealogical distance is shorter in some groups than others, likely implying very different relinking patterns.

For example, if one race/ethnic group tends to (a) couple younger, (b) have children younger, and/or (c) re-marry/couple more often than another race/ethnic group, then social divisions between those groups will likely expand, and we would likely see a stronger social reproduction of class within the more strongly re-linked group.

Current (historical) work w. Padgett on Florentine families (N~98,000) works through some of these ideas.

There is a direct link between questions of structural endogamy and inter-group marriage, that is ripe for an extension.

•Classical models in this area fit log-linear models to husband_race by wife_race mixing tables. We can broaden our view of inter-mixing, by tracking the salience of race/ethnicity as the degree to which race and ethnicity reflect real communities through re-linking.

•If ethnically-based endogamy decreases over time, for example, then we can argue for a decreasing salience of that ethnicity.

•Looking forward, the re-linked community of today can become the ethnicity of tomorrow in a processual sense

•An interesting extension will be to the demarcations between ethnicities within relinked communities. Is the pattern really one of total group mixing, or is contact at the peripheries of communities?

Summary and ExtensionsWhere would the concept of structural endogamy connect to current population concerns?

Ethnic Intermarriage and the identification of ethnicity

We can make a similar line of argument for national/ regional elite structures.

Historically, white elites sent their children to a very small subset of all schools (boarding and college), where they mixed within a very small set of potential marriage partners.

•This would emerge as an endogamous class of elites (We can show, for example, that almost all US Presidents can be relinked to a common elite US ancestor).

• If recent attempts at affirmative action and universal education have been successful, then we would expect greater out-marriage and lower re-linking

Summary and Extensions (from paa talk) Where would the concept of structural endogamy connect to current population concerns?

Class Mobility

Documents

(Structural) Cohesion in Organizations