1. Some Examples of Network Analysis Ethnography of a group undergoing fission Network study of overlapping friendship groups in school Collaborative ties in the biotech industry KASS ethnography, egocentric networks and kinship Social classes in Slovenian Austria, Carinthian farmers Reciprocal exchange and equality in South India Middle Eastern segmented lineage systems, Turkish nomads Medieval city networks and trade, 1175-1500 Doug White Anthropological Seminar Halle MPI in Social Anthropology, June 27, 2005

2. Case 1: 2 year ethnography of a karate club Conflict and Fragmentation Ethnographic examples

3. Longitudinal Network Studies and Predictive Social Cohesion Theory D.R. WHITE, University of California Irvine, BCS-9978282 An operational definition of social cohesion based on network connectivity measures cohesiveness as the minimum number k of actors whose absence would disconnect a group. Two members of a group with cohesion level k automatically have at least k different ways of being connected through independent paths. A test of the measure is exemplified by successful prediction of how a group, studied longitudinally during a period of conflict between leaders, divides into two (Fig 1). 2001 Douglas R. White and Frank Harary, The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density. Sociological Methodology 2001, vol. 31, no. 1, pp. 305- 359. Blackwell Publishers, Inc., Boston, USA and Oxford, UK. SFI Posting The Cohesiveness of Blocks in Social Networks Sociological Methodology 2001SFI Posting Part 1. Development of a Methodology for Network Research on Social Cohesion 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. 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. Connectivity : Blue=4 Red=3 Green=2 Yellow=1

4. 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’s side A’s side A T and A start to fight: some must choose sides Opposing cohesive sides emerge T A 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 T A Loss of cohesion

5. Cases 2,3: overlapping friendship groups where structural cohesion predicts school attachment Evolution of biotech industry where structural cohesion predicts collaborative tie formation Sociological definitions and examples

6. Longitudinal Network Studies and Predictive Social Cohesion Theory D.R. WHITE, University of California Irvine, BCS-9978282 Predictive Social Cohesion Theory: BOUNDEDNESS A k-component of a graph G is a maximal subgraph S with the following equivalent properties: connectivity k, the smallest cutset of S is of size k. multiconnectivity k, the minimal number of node-independent paths in S connecting pairs of nodes in S is k. k-components may overlap, or be vertically stacked as shown here 1 4 k=2 k=2 k=1 3 6 2 5

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

8. 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. 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.AddHealth 2003 James Moody and Douglas R. White, Social Cohesion and Embeddedness: A Hierarchical Conception of Social Groups. American Sociological Review 8(1)Social Cohesion and Embeddedness Longitudinal Network Studies and Predictive Social Cohesion Theory D.R. WHITE, University of California Irvine, BCS-9978282 Fig 2. Structural Cohesion of Friendships _______in an American high school 8 th grade 7 th grade 11-12 th grade 10 th grade 9 th 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

9. 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.Network Dynamics and Field Evolution Interorganizational Collaboration Topology: Stacked hierarchies and Dynamics (Empirical Results) Longitudinal Validation of Structural Cohesion Dynamics in Biotechnology Longitudinal Network Studies and Predictive Social Cohesion Theory D.R. WHITE, University of California Irvine, BCS-9978282 Fig 3. Biotech Collaborations All ties 1989 New ties 1989 All ties 1989 And so on to 1999

10. 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

11. New ties, Biotech, 1997 (flip back)

12. Case 4: KASS questionnaire network analysis e.g., measuring cohesion in ego networks Ethnographic examples

13. Figure 1: An ego network under construction for Robert Corteen (Hypothetical data) using the KNQ software of the KASS project 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 Fig 3: Cohesive Subgroup Calculation (yellow nodes) Robert Corteen network Data transfer to Pajek Pajek analysis KASS (Kinship and Social Security) study at Max Planck-Halle, done with the help of the KNQ (kinship network questionnaire) graphic interface software

14. Object is to show how marriages relink moving on to community level networks Structural endogamy: shifting how we look at the kinship network as a genealogy

15. 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

16. Data and Representation: Kinship Networks parental graphs link pairs of parents (flexible & culturally defined) to their descendants parental graphs are constructed by: 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 Treating couples as nodes, replacing marriage bonds with nodes

17. Data and Representation: Kinship as Parental Graph Networks parental graphs link pairs of parents (flexible & culturally defined) to their descendents parental graphs can be constructed from standard genealogical data files (.GED), using PAJEK and a number of other programs. 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 FaSi + Fa FaSiDa MaleEgo

18. 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

19. Case 5: Carinthian Farmers (structural endogamy, social class, and network cognition) Further ethnographic examples

20. Church Mountains and Alms Farmsteads and Fields 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

21. The stemline social class of farmstead inheritors, 1510-1980

22. 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.

23. Pgraph software; parental graph representation: these are the heirs and families that are maritally relinked TIMETIME

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

25. Number of Structurally Endogamous Marriages Generation123456 Present: by Ancestral Levels Actual8*16*70*179257318 Simulated0032183273335 Back 1 gen: by Ancestral Levels Actual8*58*168246308339 Simulated018168255320347 Back 2 gen: by Ancestral Levels Actual26*115*178243278292 Simulated098194262291310 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) Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161- 208. Lilyan Brudner and Douglas White Statistical conclusion: conscious relinking among families creates structural endogamy

26. Case 6: Pul Eliya, Sri Lanka (illustrating kinship structure, networks, cognition, kin terms) Further ethnographic example

27. 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.

28. parental graph of Pul Eliyan Sidedness

29. Marriage sides in Pul Eliya, with compound IDs for males, red lines for females (this slide was made with Pajek, output for web viewing)

30. 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.

31. 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 yes 1: 0 1 56 57.508 FZ GG=F no 3: 0 1 6 6.538 FFFZDSD GGGG=FGFF no 4: 1 0 3 1.800 FFMZDSSD GGGF=FGGFFyes 5: 0 1 5 3.444 FFMBDSDD GGGF=FFGFGno 6: 1 0 18 15.558 FMBSD GGF=FGG yes 7: 0 1 17 12.433 FMBDD GGF=FFG no 8: 2 1 18 12.661 FMZDD GGF=FFF yes 9: 0 1 9 5.399 FMMBSSD GGFF=FGGG no 10: 0 1 4 5.600 FMMFZSSD GGFFG=FGGFyes 11: 0 1 6 3.400 FMMFZDSD GGFFG=FGFFyes 13: 0 1 25 27.528 MBSD GF=FGG yes 14: 1 0 14 10.600 MFZDD GFG=FFF yes 15: 1 0 7 3.727 MFFZDSSD GFGG=FGGFFyes 16: 1 0 8 4.692 MFFZDSD GFGG=FGFF yes 17: 1 0 8 2.818 MFMBDSSD GFGF=FGGFGyes 18: 1 0 9 3.769 MFMBDD GFGF=FFG yes 19: 1 0 3 0 1.000 MFMBDDDD GFGF=FFFFGyes 20: 1 0 8 2.818 MFMFZSSD GFGFG=FGGFyes 21: 1 0 3 0 1.000 MFMFZDDD GFGFG=FFFFyes 22: 1 0 13 8.636 MMZSSD GFF=FGGF yes 23: 1 0 15 13.551 MMBDD GFF=FFG yes 24: 0 1 11 5.352 MMZSDD GFF=FFGF no 25: 0 1 11 5.352 MMBDDD GFF=FFFG no 26: 1 0 11 4.749 MMZDDD GFF=FFFF yes conclusions: (1) MBD is a preferred marriage (2) All blood marriages are patri- sided Frequencies of Actual versus Simulated Consanguineal Marriages for Pul Eliya, Sri Lanka, Correlating Actual versus Simulated non-MBD marriages for Pul Eliya, showing tendency towards a Patri-Sided (Dravidian) Marriage Rule Patri-Sided Unsided Actual180 Simulated 57 p=.0004 p=.000004 using the binomial test of an expected 50:50 split)

32. Case 7: Turkish nomads (kinship, cognition, semantics, migration) Another ethnographic example

33. 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.

34. parental graph of the conicality of the nomad clan Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Data: Generations

35. Coding the data for a Nomadic Clan – Are we from the same ‘root’? What is our ‘group’? We numbered each person and gave one line for each marriage with number of ego, ego’s mother, father and spouse. 4 1 23 4 2 1 3 Johansen’s genealogical scroll to parental graph (for the entire society) Using Pajek, this gave a graph for the nomadic clan, ready for analysis. Relinking predicts ‘same group’ according to PCT (predictive cohesion theory) !

36. 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 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?

37. 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.

38. 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 Results: Structural Endogamy of the nomad clan

39. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Does marital relinking predict staying with the clan, as predicted by PCT? Results: Yes ! Testing the hypothesis for stayers versus leavers Relinked Non-Relinking Marriages Marriages Totals villagers who became clan members 2** 1** 3 clan Husband and Wife 148 0 148 “ Hu married to tribes with reciprocal exchange 12 14 26 “ Hu left for village life 13 23 36 “ Hu married to village wife (34) or husband (1) 11 24 35 “ Hu married to tribes w/out reciprocal exchange 2 12 5 “ members who left for another tribe 0 8 8 villagers not joined to clan 1 3** 4 * tribes **non-clan by origin Totals 189 85 274 Pearson’s coefficient r=.95 without middle cells

40. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion A power-law decay of marriage frequencies with kinship distance FFZSD FFBSD:10-11 FZD:14 MBD:16 FBD:31 M M =206/x 2 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

41. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: types of marriage are ranked here, reversing axes, to show: numbers of blood marriages follow a power-law (indexical of self-organizing preferential attachments) whereas affinal relinking frequencies follow an exponential distribution that would correspond with randomness

42. –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. Links to Complexity Theory Out of the Turkish Nomad study came hypotheses about preferential attachments Ring Cohesion Theory Results: Summary:

43. Case 8: city networks and trade, 1175-1500

44. Background paper Civilizations as Dynamic Networks: Medieval to Modern, a project with Peter Spufford, assisted by Joseph WehbeCivilizations as Dynamic Networks: Medieval to Modern Civilizations as Dynamic Networks Douglas R. White, Peter Spufford

45. 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. In Northern Europe the Hanseatic port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice. Red 3-components Middle East and its 3-core not sampled

46. Northeast Southwest Northern Hanse Trade Organization: Saintly Brotherhoodsv v Other Eastern Hanse German Towns, 1470

47. END

48. Case 9: Muslim elites in Southeastern Java

49. Example 9: Rural Javanese Elites - Are we elites different than others? Graphic technique: nuclear families as the unit of parental graph analysis, additional arrows for property flows (used in the publication) showed extended family rules for partitioning of mercantile resources and property of groups constituted by relinking. Key concepts: blood marriage as a form of marital relinking, parental graph, structural endogamy, bicomponent of the parental graph, the social biography of things (property flows). Showed (1) apparent differences in marriage patterns of elites and commoners were due to a common cultural practice of status endogamy, which for elites implied a set of potential mates whose smaller size implied marriage among blood relatives within a few generations, (2) given a common rule of division of inheritance, closer marital relinkings among elites facilitated the reconsolid- ation of wealth within extended families, and (3) extended families so constituted operated with a definite set of rules for the division of productive resources so as to distribute access to mercantile as well as landed resources. Douglas White and Thomas Schweizer, 1998 “Kinship, Property and Stratification in Rural Java: A Network Analysis” pp. 36-58 in Schweizer and White, eds. Kinship, Networks, and Exchange. Cambridge Univ. Press.

50. 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 0 0 2 2 ZSD 0 0 3 3 BDD 0 0 8 8 BDD 0 0 3 3 ZDD 0 0 4 4 FZ 0 0 21 27 FZ 0 0 1 1 FZSD 0 0 3 3 FZD 0 0 13 14 FZD 0 0 3 3 FBDD 0 0 3 2 FBDD 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 Statistical conclusion: there are no preferred marriages among elites beyond status endogamy, although blood marriages are common STATUS ENDOGAMY in a Javanese Village (Dukuh Hamlet, Muslim Elites), Test of Actual versus Simulated Marriage among Consanguineal Kin Hence: the same system of marriage rules operates for elites as for commoners

52. Data and Representation: Relating parental graphs to endogamy (Old Testament Men and Women) Male Descent Female Descent Same person (polygamy) Lot marries his daughters Rachel & Jacob & Leah Abraham & Sarah & Hagar Lot Heran ishmael Nahor Isaac Bethel Nahor Terah (Egypt) http://eclectic.ss.uci.edu/~drwhite/pw/White-Jorion1992.pdf

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

55. 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.

57. 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):

58. parental graph of the conical nomad clan

59. 1. An apical ancestor of the 90% of those down to today’s nomad clan members

60. 2. Structural endogamy of the nomad clan Each marriage is contained in a cycle of previously linked marriages

62. 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’?

63. –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. Applications of Structural Endogamy A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems: The Role of Marital Cohesion Results: Summary:

64. Outline of the talk (59 slides) I. network theory of kinship –A. Predictive cohesion theory (PCT) Structural cohesion – 4 slides Applying predictive cohesion theory (PCT) to kinship – 1 slide –B. Marriage Census graph analysis – 1 slide –C. Defining the phenomena of endogamy - 3 slides II. kinship structure and cognition –A. Defining the phenomena of endogamy – 1 slide –B. Data and representation - 3 slides –C. Relational thinking: parental graph as a relational representation - 3 slides –D. Identifying marriage rules and strategies: controlled demographic simulation - 3 slides III. ethnographic examples –1 Slovene Farmers of Feistritz, Austria – How class is counted - 11 slides –2 Dukuh Hamlet Javanese Muslim Village Elites – Are we elites different? - 2 slides –3 Pul Eliyan Kinship in Sri Lanka – What ‘side’ are you on? - 7 slides –4 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

65. Programs & Availability PAJEK  PAJEK reads genealogical datasets (*.ged files) both the usual Ego format and in parental graph format, with dotted female lines (p Dots) and solid male lines.  PAJEK Network/Partition/Components/Bicomponent computes structural endogamy in a parental graph  PAJEK Network/Partition/Depth/Genealogy computes genealogical depth. This enabled 2D or 3D drawings of kinship networks.  Manuals for p-graph kinship analysis and discussions of software programs & multimedia representations are contained in  1) “Analyzing Large Kinship and Marriage Networks with pgraph and Pajek,” Social Science Computer Review 17(3):245-274. 1999. Douglas R. White, Vladimir Batagelj & Andrej Mrvar.  2) http://eclectic.ss.uci.edu/pgraph  3) http://vlado.fmf.uni-lj.si/pub/networks/pajek  4) book by de Nooy, Batagelj and Mrvar, 2005 Exploratory Social Network Analysis with Pajek Cambridge University Press Exploratory Social_Network Analysis with Pajek

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

67. A. Predictive cohesion theory (PCT) The measure of structural cohesion (and structural endogamy) applies from small groups to large communities (scalability) General consequences of structural cohesion: –Internal bonds strong (multiconnectivity) –Resistance to external shock (robustness) –Adaptive (Multiconnectivity+Robustness=resilience) Structurally cohesive groups possess definite lines of boundedness in social networks.

68. A1. Structurally cohesive groups predict: Coherent boundaries of interaction Emergence of shared routines, meanings Greater cultural coherence:- Boundaries of: –Ethnicities –Class (in terms of Social v. Economic ties) –Communities –Kinship groups Conversely, cohesive fissures within more loosely connected groups predict: –Fracturation, splitting of the above –Organizational differentiation

69. Structurally cohesive blocks in social networks have predictable consequences sociological uses of this approach are discussed in –White, Douglas R. and Frank Harary. 2001. "The Cohesiveness of Blocks in Social Networks: Connectivity and Conditional Density." Sociological Methodology 2001, vol. 31(1), pp. 305-359. –Moody, James, and Douglas R. White. 2003. “Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups.” American Sociological Review 68(1):103-127. http://www.asanet.org/journals/ASRFeb03MoodyWhite.pdf Powell, Walter W., Douglas R. White, Kenneth W. Koput and Jason Owen- Smith. 2005. “The Growth of Interorganizational Collaboration in the Life Sciences.” American Journal of Sociology 110(4): 1132-1205. http://www.journals.uchicago.edu/AJS/journal/issues/v110n4/080171/080171.html http://www.journals.uchicago.edu/AJS/journal/contents/v110n4.html

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

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

72. A2. Applying predictive cohesion theory (PCT) to kinship Reknitting kin ties correspond to relinking marriages –Closing a loop between 2-, 3-, 4- families, affines –Between blood kin, 2-, 3- 4- degree consanguines A marriage census –Rank orders the frequencies of relinkings of both types –Examines which types tend to co-occur The results will show either –With blood marriages, a preferential ranking –With affinal marriages, a preferential ranking –Entailments of types (see White 2005, Hamberger et al 2005)

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

74. Some Findings, 1: general theory Cohesive communities with many blood marriages have preference orderings over the whole series of marriage types, with implications for self- organizing or reciprocity based systems Cohesive communities with few blood marriages have preference orderings over the whole series of affinal marriage types In the first case are there no preference orderings on affinal types as in the second case.

75. Some Findings, 2: kinship systems Network findings map onto but vastly increase our sensitivity to the distribution of different types of marriage systems E.g., the frequency of reciprocal dual organization in marriage networks is probably an order of magnitude greater than identified by hereditary moieties. Kinship systems with navigability of strong ties between groups through reciprocal marriage is a possibility not identified previously in the kinship literature. This may also occur in cases like Russia or Baltic states and in Central Asia, and is widespread in Arabized countries.

76. II. kinship structure and cognition This section focuses on Kinship Structure: defining and measuring –structural cohesion / structural endogamy –cohesive embedding Kinship Cognition

77. A. Defining the phenomena of endogamy Endogamy is marriage within the limits of a clan, class, caste, etc., with relative degrees of closure varying inversely with those marrying out. Possible definitons: –By categories/attributes: suffers from problems of specification error –By network relinking: a generalized phenomena of structural endogamy as blocks of generalized relinking (a special case of network cohesion) with:  Subblocks of relinkings of k families, with varying depth in generations  Subblocks of consanguinal (blood) within-family marriage (relinkings for 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)

78. 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)

80. Applications of Structural Endogamy Middle Eastern segmented lineage systems: The Role of Marital Cohesion in a Turkish Nomadic Clan Empirical Setting: An Arabized nomadic clan having the characteristic segmented patrilineages, lineage endogamy, and FBD (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

82. Correlating Balanced vs. Unbalanced cycles in Actual versus Simulated marriage networks for Pul Eliya, showing a perfectly Sided (Dravidian) Marriage Rule A. Viri-sidedness ActualExpected 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) - not shown in figure but shown in final publication (Houseman and White 1997) ActualExpected Balanced Cycles (Even length)35 17.5 Unbalanced Cycles (Odd Length) 0 17.5 p=.00000000003

84. C. Relational Thinking: parental graphs as a relational representation Showing how couples are related, e.g., by sex and rank, makes it easier to see patterns of relations. Conventional genealogical diagrams emphasize the categorical treatment of sibling sets. Douglas R. White and Paul Jorion. 1992 “Representing and Analyzing Kinship: A Network Approach.” Current Anthropology 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. 1 2 3 4 4 2 1 3 a parental graph genealogies become

85. parental graphs identify relinkings as cycles maximal blocks of cycles define limits of structural endogamy (bicomponents: sets of nodes where every pair is linked by two ore more node-independent paths). These are relational patterns of cohesion grouping that people recognize intuitively. 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 2 1 3 male lines female lines

86. People Think Relationally in Kinship Practice oIntegrative concepts: e.g., how ‘cognition’ uses networks in mental operations (‘memory’) oNetwork approaches to learn how people think (preference, cognition) from their behavior oSimulation: provides baselines for this purpose oHow 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’?

87. D. Identifying marriage rules and strategies relationally: controlled demographic simulation in a science of social structure and dynamics that includes marriage and kinship, how to  define and evaluate marriage strategies against random baselines?  separate ‘randomizing’ strategy from ‘preferential’ strategy?  detect atomistic strategies (partial, selective) as well as global or “elementary” marriage-rules or strategies?  detect changes in marriage rules or strategies? D. White. 1997. Structural Endogamy and the graphe de parenté. Mathématique, informatique et sciences humaines 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 http://www.soc.surrey.ac.uk/2/3/5/JASSS.html See: http://eclectic.ss.uci.edu/~drwhite

88. the simulation technique is simple: In each generation of marriages in an actual parental graph – number the set K of marriages 1 to k Reassign each person married into the generation to a random marriage in K, allowing additional rules to prevent incest as defined culturally But 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.

89. applications of the simulation method to study structural endogamy pertain to: Social class, Elite structural endogamy, Wealth consolidation, Community/ethnic integration, Testing alliance, descent, and proscriptive theories and models … in the examples to follow

90. Hypothesis testing We can use various permutation-based procedures to test the observed level of endogamy against a data-realistic random baseline. The substantive marker for endogamic effectiveness is whether the level of endogamy is greater than expected by chance given the genealogical depth of the graph 1997 Structural Endogamy and the graphe de parenté. Mathématique, Informatique et sciences humaines 137:107-125. Paris: Ecole des Hautes Etudes en Sciences Sociales

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