Kinship, Class, and Community

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Response to David_M._Schneider#Debate_over_Kinship

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White, Douglas R. 2011. Kinship, Class, and Community. Chapter 10: In, J. C. Scott and P. Carrington, (Eds.), Sage Handbook of Social Networks. http://intersci.ss.uci.edu/wiki/pub/SubstantiveKinshipShortDbl13.pdf

Contents

Commentary

---------------------------- Original Message ----------------------------
Subject: Re: Kinship networks chapter
From:    "Peter Carrington" <pjc@uwaterloo.ca>
Date:    Tue, January 26, 2010 11:59 am
To:      "Robert A. Hanneman" <robert.hanneman@ucr.edu>
Cc:      Douglas.White@uci.edu

       I agree, it really is a knockout chapter! Peter

Robert A. Hanneman wrote: Hello Peter and Doug, Thanks, both, for the efforts! A very quick scan suggests that this is going to be a very stimulating read, indeed. The cohesion and linking core ideas, the multiplicity of diverse examples, and the clarity and precision are wonderful. I'll have to use this carefully for undergraduates, I think. But, I can't imagine a more valuable introduction to the core ideas of kinship structure and societal integration, and exposure to cultural/historical diversity. Thanks much! Bob H. Robert A. Hanneman Professor of Sociology University of California Riverside, CA 92521 voice: 951-827-3638 web: http://faculty.ucr.edu/~hanneman ---- Original message ---- Date: Mon, 25 Jan 2010 20:56:07 -0500 From: Peter Carrington Subject: Re: Kinship networks chapter To: Douglas.White@uci.edu, "Robert A. Hanneman"

Background

Kinship, Class, and Communities (possible title Kinship Computing: Communities, Class, and Complexity): see Chapter 10: Sage Handbook of Social Networks, eds. Peter Carrington and John Scott. Hypothesis: Cohesive blocks in kinship networks are predictive of {class formation, leadership, etc} when there are resources to transmit. The 9000 word chapter limit is based on the overall limit in our editors' contract with Sage. The 9000 words includes everything in the chapter, e.g. notes and references. Our contract with Sage says that "non-text" material e.g. tables, illustrations, is "deemed equivalent to words at the rate of 425 words per book page and pro rata for part pages." So, the "cost" in words of a figure or table depends on how much of a page it will take up. See 2000 Handbook: http://www.sagepub.com/booksProdDesc.nav?prodId=Book209124

draft (not for citation): by Douglas R. White, Editors, John Scott and Peter Carrington phone: +1 519 888 4567 ext. 33961 Sage Handbook of Social Network Analysis. Due fall 2008 Two Articles for Carrington volume. UC Videoconference talk: Kinship Computing, Communities, Class, and Complexity October 10, 2008, 1:30-3PM. Paris Musée Branly (Anthropology) Kinship and computing Videoconference talk: October 24, 2008, 3-5PM (UCSD time: 6-9AM). Kinship and Complexity undergraduate class.

The companion article for the Sage volume is Kinship analytic methods by Klaus Hamberger, Douglas R. White, and Michael Houseman. It will likely center on (1) some of the more technical material (moved there from this article), current Pajek stuff of DRW and the Pajek macros of Hamberger and Houseman, (2) the new Java kinship network analysis program Puck, written by Klaus, from the Tipp project, and (3) the controlled simulation in R that is so important for inferential statistics and substantive model testing. Klaus's email is klaus_hamberger@yahoo.fr

Abstract and Introduction

Abstract

This chapter focuses on substantive findings and network methods resulting from the weaving together of anglophone and the francophone social science traditions dealing with kinship. The merger of these two traditions has dealt with kinship networks as research objects using P-systems. P-systems include graph theoretic network approaches as formal methods for analyzing relations of parentage and the larger units (marriages, kin groups, cohesive groups) in which individuals are embedded. Harary and White (2001) provide a summary formulation, just as White and Harary (2001) provide new foundations for the study of cohesion, which apply also to kinship networks. The first of these approaches trace back to the field of kinship computing, partly inspired by the works of mathematicians André Weil (1949) and Oystein Ore (1960), as established by P-graph analysis of kinship networks (White and Jorion 1992) and then incorporated into Pajek (Batagelj and Mrvar 1998, White, Batagelj, and Mrvar 1999) and other software, most recently, Hamberger and Houseman (2008), Hamberger, Houseman and Grange( 2008), Hamberger and Daillant (2009). P-systems incorporate models of kinship through relations of coupling and parentage, with graphs embedded within the nodes of other graphs, and segregation of higher level descent and marriage structure from nuclear family structure. White and Johansen (2006) view these contrasting perspectives as embodying the key conceptual distinction used by Lévi-Strauss (1949) in the theory of marriage alliance and by Murdock (1949) in a theory that views kinship as an extension of the family. P-systems endorse neither theory, and are generally neutral with respect to favored theories. Rather, they allow a synthesis of key elements of many different theoretical approaches, including those of complex systems. "While a P-system is used to represent a concrete network of kinship and marriage relationships, this network also constitutes a system in the sense that it contains multiple levels where each level is a graph in which each node contains another graph structure. In sum, the connections between the nodes at the outer level in a P-system are especially useful in the analysis of marriage and descent, while at inner level we can describe how individuals are embedded in the kinship structure" (Harary and White 2001:1). Kinship computing has contributed a wide range of substantive contributions that are reviewed here. These approaches have produced new substantive results in sociology, history, ethnography, and SNA with its development of the new field of kinship computing inaugurated in White and Jorion (1992)

Introduction

Lloyd Warner (5 vols. 1941-1959), one of the great ethnographers of America (also 1949, 1960a, 1960b), viewed church and voluntary associations as the two great institutional organizations of the U.S., one religiously divisive, the other integrative. Warner's (1949) Yankee City study, however, focusing on Newburyport, was seen by Newburyport's novelist and Warner's satirist John Phillips Marquand as imbued with an academic social determinism that, in portraying Newburyport as a "beautiful, static, organized community" (the words of his "Lloyd Warner" character, Malcolm Bryant, in the novel, Point of No Return) failed to to grasp the ironies of "the confining nature of life in America's upper class and among those who aspired to join it" (Wikipedia 7/10/2008) and of mixed views on the importance of descent in claims to elite status.

Against this sociological backdrop, introducing a more horizontal view of kinship ties, one of the recently invented concepts about kinship structures in democracies was the idea of relinking or renchaînement, presented by Jola, Verdier, and Zonabend (1970) as a form of social integration in peasant villages in France and elsewhere in Europe, where two or more intermarried ancestral lines are newly relinked by marriage. First demonstrated by Brudner and White (1997), one of the substantive contributions of P-systems analysis was to move from a local view of relinking to network analyses that could show how the social construction of class is partly constituted by cohesive ties of relinking at larger scales, including those of social strata within communities.

Often said in some form is that what constitutes the social tissues of our lives is invisible to us, and that our ideologies blind us to social actuality. Yankee elites are not alone in their obsession with pedigree and lineage or lines of vertical descent. Relinkings, however, are horizontal circles of intermarriages, circles that overlap many times to form larger cohesive units that go far beyond several families to form large and cohesive social formations.

Max Weber, of course, like most theorists of social class, was not blind to relinking: his two basic characteristics of class were endogamy (social class; often confused with prestige hierarchies) and differential access to life chances or access to productive wealth (economic class, acquired through inheritance or achievement). Analyzing systemic relinking among Guatemalan colonial elites, Casasola (2003; Casasola and Alcantara 2003) show both network aspects of class elites, social and economic, were recognized family by family by experts in this historical period and as identified through network analyses of relinking. Like Brudner and White (1997), these collaborations showed conformity between the social (endogamously bounded) and economic (weaith and property transmission) aspects of Weberian class.

When sociologists speak of endogamy, however, they think of intermarriage within a community, a territory, an occupational group, a level of wealth, or, in short, within social units as defined by attributes that might specify the loci of intermarriages. Endogamy has rarely been defined in terms of networks although it is always assumed that endogamous marriages do constitute themselves in this way as networks. Rather than play the game of finding which attributes of individuals or partitions of networks (see Girvin and Newman 2003, for example, on "community detection"), White (1997) asked instead: What "kinds" or aspects of networks actually define endogamy rather than merely correlate with its varying subgroup densities? By answering this question, Brudner and White (1997) and others could go ahead and find the properties intrinsic to endogamy as a structural unit of cohesion in a kinship network. Fitzgerald (2004 ), analyzing cohesive relinkings in the Bevis Marks Synagogue of the Sephardim in London, even found distinct strata of structural endogamies at the levels of office workers, crafts people, and elites. Widmer, Sutter Widmer, Sigris and Fitzgerald (1999), in contrast, found deep ancestral (vertical) relinking and relinking between family lines in among the Geneva Sciences of the 17th-19th centuries. Kuper's (2006) P-system study of the families of Bloomsbury and finds relinking and blood marriages forming cohesive groupings that mounted some of the great English scientific and political projects (the Darwin-Wedgewood families, ...) of the 19th and early 20th centuries.

Once relinkings are analyzed to show the extent of interfamily cohesion at different class levels, the pluralistic theory of interest groups can be challenged by ones that explore how different levels of interfamily cohesion intersect with office holding, directorships, leadership roles, and the like. Systematic use of kinship network data, in the manner of analyzing horizontal social cohesion, can provide a basis for the study of power elites, for example, such as the study of the Mexican power elites by Narda Alcantara (2003) and Schmidt and Gil Mendieta (2002). Cohesion was so dense in the latter study that clique overlaps (Adamcsek, et al 2006) provided a sufficient basis for study of network cohesion. The advantage of relinkage analysis and structural endogamy or structural cohesion is that effective social linkage concentrations can be found in large and sparse networks. Rather than footnotes to history, the identification of cohesive groups provide a basis for causal modeling of historical contingencies.

What defines endogamy structurally? This was not recognized as a valid sociological question until it was defined under the name of structural endogamy in the French journal, Mathématiques et Sciences Humaines(White 1997), Structural endogamy is a network concept that provides a formal means of finding the boundaries of endogamy in a community using only genealogical and marriage links (See Wikipedia:Structural endogamy, originally written by me). In France "endogamie structurale" has been on people's lips since 1997. In francophone "anthropologie mathématique," however, the idea was originally given in obscure form by Bourbaki algebraist André Weil (1949) as an appendix to Lévi-Strauss (1949). Here again the weaving together of anglophone and francophone social science traditions in dealing with kinship networks as research objects has produced new substantive results, as I will show. ((Harrison White...))

Batagelj and Mrvar (2008) summarize the mathematics of P-system and related formalisms for kinship networks. One of the advantages of directed arcs pointing to parental nodes is that semicycles of P-graphs form bicomponents which are maximally large subgraphs with the significant attribute that every one of its arcs and nodes must be connected to every other by two or more independent paths. Each bicomponent defines a unit of structural endogamy. Menger's theorem proves that no bicomponent can be disconnected without removal of two or more of its nodes. Because the processing time for finding all the bicomponents in a graph is linear with the number of edges (Gibbons 1985), all the bicomponents and hence all the structurally endogamous units are easily found in a large graph of any finite size. Where only two parents are specified, and c is the average number of children, roughly only 2c computational steps are needed to find all bicomponents.

Discovery of the the Menger theorem's importance for finding meaningful emergent units of endogamy in kinship networks led naturally to consider the importance of structural k-cohesion (k-components) as the units of social cohesion in networks generally. This work was undertaken first by White and Harary (2001), then generalized by Moody and White (2003) and implemented by algorithms in SAS (James Moody) and R (Peter McMahan).

Substance

I will show the contributions of kinship network analysis and theory to social theory generally, in the areas of:

  1. Class formation, Community, Ethnicity, Segregation (considered in terms of Structural endogamy, Relinking, and causal effects of cohesive groups in networks)
  2. Wealth consolidation, Families as historical actors, Merchants and trade, Trade diaspora (considered in terms of economic flows and network process)
  3. Heritable and reconfigurable social exchange (the implications of network structure in relation to modes of exchange), Balanced exchange, Generalized exchange, and Mobility)
  4. Power elites, Stratification, Leadership, Trust, Navigability (considered in terms of Strategic behavior in networks)
  5. Organizations, Organizational dynamics and change, Families as historical actors, Corporations, Social conflict and competition (considered in terms of the local-extralocal organization and power of competing cohesive groups in networks).
  6. Praxis theory in social dynamics and change (considered in terms of Decision theory, Scaling behavioral outcomes as probability distributions, and how macro-micro network dynamics, including how behavioral choices alter network structure with consequences for altering social choice).

Continued below under #Social Theory, Networks and Controlled simulation

See the chapter Kinship analytic methods for more technical analytic methods.

These findings contrast with the all-too-common stereotypes that studies of kinship and kinship networks are concerned only with descriptive typologies of kinship systems or that kinship networks are merely the incidental ties between nuclear families, simply the genealogies and pedigrees of families or individuals.

Form

What makes important substantive findings possible in all of these areas of social theory are the different scales at which kinship is constructed. For Murdock (1949), the basic unit of kinship is the "nuclear" family of parents and children: the smallest local units that are glued together in endless forms and combinations. Lévi-Strauss (1949), in contrast, focuses on a more global scale of the building-block principles of how families are connected in different geometries of marriage and reproductive links that enable families, individuals, and societies to exist and coexist. The gap between these two, in networks and complexity theory, is the micro-macro linkage problem, consisting of theorems, simulation results, and the study of dynamics (White and Johansen 2006).

The first debates that we had in our anglophone-francophone collaborations were about the concept of structure. André Weil (1949) had helped Lévi-Strauss formulate his ideas about structure algebraically, as recurrent patterns. Australian kinship had a certain number of types of marriage, four, for example, in a Kariera section system with two sets of paired marriage types connected by father-son relations, two by mother-daughter relations, and two by husband-wife relations. These formed an algebraic group (each pair overlapping once with every other). Marriage exchanges in the French tradition are viewed as reciprocal or delayed reciprocal ("restrained") exchange or as generalized exchange through paths of unreciprocated marriages. These connect to different ways of addressing and naming kin, local principles of residence, descent, succession, and inheritance, to form kinship "systems" or "structures." This form of research on kinship, inherited from Morgan (1871) was concerned with typologies and loose or speculative theorizing about general principles.

The breakthrough in our collaborations was twofold. One was to see both local and global patterns of kinship in terms of networks, and to see networks of kin as a new object of study. Two was to make the causal temporal precedence relation between parents and children a central component of the kinship network: Parents precede their children in time, and cause their birth. Although modern technology has intervened, this was both a material fact of biological kinship and the basis for the universality of the idea of kinship in different societies and in different cultural idioms. A third element, no less important, was that kinship networks constructed culturally as genealogies consisted in attributions of parentage consistent with the notions of causality (your child cannot be your parent; I'm not my own GrandPa no matter what the song says). Temporally-ordered parental relations are the generators of the genealogical network, and further work or data can be integrated with this scaffolding. White and Johansen's (2006) book is in fact an experiment on the extent to which a whole ethnography can be constructed with the aid of this scaffolding and the experiment worked through network and other ethnographic data (and stories) overlaid on networks, with networks and complexity and micro-macro linkages as the explanatory theoretical framework.

When we asked, in our earliest collaborations, What is the geometry of kinship? -- in the sense of how we draw the network of kinship from attributed relations of parentage (White and Jorion 1992) and how to simulate kinship networks (White 1999), we took as an axiom that parents precede their children in time, and thus the network of kinship consists of directed arcs that go from parents to children. At the local level this network has two dimensions, one up-down between generations, and one side-side between those who connect through marriage or parental bonding to produce children.

Time and causality

The decision to represent kinship networks as ordered in time meant that every such network had a given number G of implicit generations that could be determined independently of the birth and death dates of individuals. The result of an order relation, the G-minimum equals one plus the length of the longest directed chain of child-to-parent links. I asked Andrej Mrvar, programmer of Pajek (de Nooy, Batagelj, and Mrvar 2005), to program a "genealogical" generation (putting parents and children close together in a partial order depth partition) and later to program a "generational" partition that did so within the depth G for a given kinship network. Simulations can then be done that permute marriages within a generation according to a specified probability model of marriage biases. The major advantages of this method (controlling for the existing demography and also for how "generation" is constructed) is discussed below.

Although people in a given ordered generation might be of different ages, and marriages might or might not always take places between those whose parents are of the same generation order, we had the possibility to study how kinship network structure changed through time. This allows the study of causality if we can determine how changes at one time affect changes at another. Some types of marriage, for example, might result from types of marriages made in earlier generations. Laurent Barry (1998, 2000) was the first to show such effects statistically. Because generations are a product of temporal ordering, causal effects can be explored for networks where dates of birth were not known, provided that the genealogical data were correct. With estimates of how generational order roughly corresponds to historical periods, event data from those periods could also be explored for causal effects.

Quantum kinship

The notion of causality with which our collaborations began is fundamental to kinship-network analysis. Analogies, myth, laws and precedents may be reversed, but causality cannot, and the arrow of time as the scaffold on which kinship is built is an invaluable step in modeling. In modeling the indeterminacies of quantum theory, this step in introducing time into the generation of structure turns out to be a key self-organizing principle of the quantum universe as modeled by Ambjørn, Jurkiewicz and Loll (2008) in a way that resolves many of the quantum paradoxes. The outcome is that geometry at the smallest scale is fractal, of dimension two (unlike string theory with many dimensions and microstructures), increasing to 4-dimensional at the largest physical scale, but with one dimension, time, not "imaginary" as Hawking would have it, but "causal," meaning that every quantum unit that composes the universe has a temporal orienting dimension, and these line up to create the universe "correctly" as we know it. This is not to say that stories are not important, or not an important part of network theory, identity, and control, as argued beautifully by Harrison White (2009). But stories need to be seen against a temporal backdrop: if Ambjørn et al. are correct, there are no wormholes or reverse time travelers except in another universe whose laws we can only imagine.

Formal Behavioral Modeling

Kinships, classes, and communities

The modest revolution in kinship analysis described here was brought on by the concepts of network, relational structures, math and computation (kinship computing), and the tension between realism and abstraction. As Ulla Johansen and I describe (2006: Chapter 4), and I repeat myself, this tension was present in the contrast between Lévi-Strauss (1949) and Weil (1949), on the one hand, to raise the level of theory, generality, and abstraction in the social sciences and, on the other, Murdock's (1949) attempt to ground the scientific concepts of anthropology in a theory of diverse cultural phenomena that might have their comparative basis in core human experiences in the nuclear family and their "extensions" to broader networks. Our approach is synthetic as between these two poles. In the first of these conceptions, social networks were conceived as taking a broad form ("generalized exchange" versus "restricted exchange") or global structure that shapes more localized oppositions. In the second social networks were conceived as growing out of universals in human psychology, operating locally through families, to shape the more global structures of society. In complexity theory today this dichotomous tension would situate itself in models of local-global interactions, networked interactions that shape one another at different levels. Johansen and I describe (Chapter 1) some of these interactions in terms of complexity and network theory, and note how the conception of social networks in anthropology in the 1960s (e.g., the edited book by Mitchell 1969), dominated by an exclusively local conception of interpersonal networks, has been amplified by an entirely distinct approach to network methodologies. These methodologies take on something of the flavor of the kind of realism sought and exemplified by Malinowski's view of kinship and interactive network dynamics as enacted in flesh and blood rather than the more sociologically sterile conception of Radcliffe-Brown as systems of abstracted roles.

In 1968, a period of theoretical turmoil in anthropology, I was to meet François Lorrain, whose work with Lévi-Strauss and Guilbaud at the EHESS in Paris and his passage to Harvard with Harrison White was to embolden the sociological side of the search for structure in realistic settings that kept alive the flavor both of ethnographically observable behavior and of the cognitive-emotional processes that enlivened social interaction: a blend of anthropology, sociology and psychology. Adding also history, network analysis in the social sciences today is a blend of all these disciplines and many more as well with the entrance of diverse fields into the network sciences. Lorrain's concept of blockmodeling was conceived to apply to cognition and emotion (as found today in conceptual blending theory in cognitive science) and to the identification of social roles through observed regularities in interpersonal interactions. In my encounter with Lorrain at a Mathematical Social Science Board planning meeting at Irvine, I brought to the table the completion of a thesis that showed for 90 indigenous societies in a contiguous region of North America how the cooperative complexity of productive tasks in different societies was coterminous with the complexity of overlapping and integrative social networks, and how both coevolved with historical processes that changed economies and social formations synchronously.

Kinship is not universal in that there are many ways that parentage, marriage, and kinship relations are culturally defined. We can speak of kinships as differing from culture to culture. Culturally defined kinships reflect the enormous varieties of ways that parentage, marriage, and diverse kinship relations are culturally defined, in their overlays on the factual or attributed relations generated by parental relations in genealogical networks.

There is a universal way of coding kinship in terms of how parental and marriage ties are attributed, in some form, often variable, in each community or culture. These attributions (which may depend on the speaker) may be multiple and contested, but are often high-consensus, or if not, contested for reasons worth looking into. What an individual will be called in the kinship lexicons of a group or culture (terms of address, terms of reference; depending on the individual using the term) may take into account one or some subset or all of the genealogical positions occupied by the referent, but may also depend on context and variant lexical usage.

Schneider (1980) critiques what amounts to the anglophone tradition for its reliance on concepts such as descent, which are often taken as links defined by biology rather than culture. Cultural attributions of parentage or kinship, in the French tradition, are not based on biological attribution.

Languages of behavior as a critique of the "everything comes out of mind" fallacy

Genealogical relationships, independently of kinship lexicons, once they are constituted as a network within a community, can be read as a language of behavior in the same way that linguists build units of meaning and intelligibility from their study of recorded or transcribed speech in an unknown language or dialect. Analysis begins with phonetics, finds allophones to define morphemes, identifies how morphemes are combined to form words and boundaries of sentences. Understanding the language of behavior expressed in kinship networks start from the "etic" grid of genealogy and can derive intelligibility in behavioral choices (like word and sentence choices) in "emic" terms. From observation of behaviors in the social context of a community, individuals in that community can "read" or parse the meanings of different relations and the components of the social contexts in which they live without having to express these components, relations, and units of meaningful behavior in named categories, i.e., in spoken language. The study of kinship networks, then, does not have to begin with the welter of kinships as embodied in speech and text. It is sufficient to begin with analysis of the genealogical grid, and compare findings derived from analysis of behavior with the overlay of social idioms and stories in speech and written documents.

The "etics" of genealogy describe attributions of marriage and/or parentage from a set of primitives, namely, S,D,M,F,H,W for son, daughter, mother, father, husband and wife (and whatever additional modifies one wishes to add, such as e/y for elder/younger, m/f for the male/female distinctions implied in these terms). A set of genealogical positions derive from these primitives, such as o/s for opposite/same sex, SS for a particular type of grandson, WH for a wife's husband, distinct from ego. Generated relationships include relative products such as B/Z (brother/sister as son/daughter of F or M) and finer distinctions like pB for paternal brothers who do not share the same mother.

It is within communities and organizations (concrete social institutions) where people interact more intensively that "cultures" of shared meanings are formed in beliefs, cognition, the reading of expression, behaviors, and components of structure and dynamics in social and kinship networks. No less important is the question of how language and behavior are interpreted and acted upon across boundaries: with insiders, outsiders, or between communities, for example. In looking for the language of behavior in a sociocultural context, the most useful place to start is with concrete organizations: they “are not only found here and there in culture; they are the basis of it. They are what generate and support many of the more ordinary stereotypes, beliefs, and the rest, just as the premises of geometry generate and support the specific figures of geometry. They are the basis of the distinctively expansive nature of human communicative abilities, compared to those of other species and what make cultural and organizational consensus possible“ (Leaf 2007:18). Further: “All organizations must have a form in the sense described. There must be some most basic set of logically consistent and generative relationships among its parts. Without this, people could not imagine themselves as “in” them, just as we could not imagine ourselves within space and time if space and time did not rest on formal concepts of a similar sort but with a different logic. Although the character of formal systems in culture has been obscured by the application of theory and metatheory that made it impossible for them to be uncovered in their own terms, they are not mysterious when approached without such an intellectual overburden.”

False starts and Discoveries

It is worth noting that the "ethnoscience" and "componential analysis" movements of the 1960s used kinship as a major domain of study, relying on the emic/etic linguistic analogy that grounded the cultural meanings of kin terms on attribute-based components which combine to give meaning (like the "emes" of phonemes, morphemes and lexemes). Boyd (1969) attempted a proof of isomorphism between the composition of kinship relations (English: "brother" OF "father"="uncle") and meaning component "emes" but he withdrew the 1969 proof after finding a flaw (Boyd 1972) and went on to try an algebraic reduction approach to empirical networks as models yielding roles that composed to form regular algebraic structures (Boyd, Haehl, and Sailer 1972). The problem here is that kinship symmetries and compositions include those yet unborn, and those ancestors forgotten, so kinship "algebra" is unrealistic for actual networks, either in "closed" or "open" forms, and they suffer from misplaced concreteness.

"Algebras," however, have been discovered (first by A.F.C. Wallace and John Atkins 1960, then by Murray Leaf 1971, 2007) in kinship cognition, in terms of how relative products are formed among not only kin types (e.g., FaBr as a descriptive kin type) but among kin terms (e.g., in English "Brother" of "Father"="Uncle"). Dwight Read (2006, 2008) has shown the likely universality of generative principles of kinship terminology using a kinship algebra of cognitive operations.

Networks, math, and realism

Kinship is comprised of extended networks that alter and are altered by local circumstances. Lévi-Strauss (1965:125, cited in White and Johansen 2006:67), however, drew on his older departmental colleague Goldenweiser's (1913) observation about the "impossible complexity" of kinship networks to justify treating kinship through models of norms and strategies as abstracted systems of rules. Game theory offered one metaphor among many for an integrated approach to modeling. The arbitrariness of choices in modeling also generalizes to the situation of members of a given culture because they necessarily – Lévi-Strauss’s view – have to rely on cognitive models to reduce the impossible complexity of networks. The analogy that underlay his thinking was that between culture and linguistics, where modeling of meanings relies on finding "emic" units used to construct meaning from the "etic" variability of sounds taken in their context of utterance. "Emics" as model constructions in mind is still sometimes used today to justify the priority of cognition over behavior as they key to understanding culture (White and Denham 2008). Like White and Johansen, they take the view that there are also interpretable “languages” of behavior. If emics exist at both cognitive and behavioral levels, then neither one is the “privileged” starting point or paradigm for explanation of human culture and social patterning. There is no empirical validity to the view that humans lack heuristic capabilities for perceiving complex patterns in behavior (e.g., Gigerenzer et al. 1999) or that behavioral regularities lack emic interpretability. I hold the view that there are patterns of behavior evident in networks that have equal validity to the view that cognition imposes patterns on behavior in the form of instantiated rules (Read 2008).

In this chapter I consider kinships of different peoples and their situated consequences in social networks as a primary domain of anthropology, and of ethnography in particular. The interest in realism with which ethnographers approach their studies has been very useful in the revolution that has occurred in the last 40 years in studying networks. Sociologists have added vastly to the psychological (sociometric) and anthropology (social networks) toolkit as it had developed up through the 1960s, but as we shall see, the sociological methods of network analysis did not equip ethnographers with a new or even useful approach. Instead, some of the core insights of Weil (1949), working with Lévi-Strauss, did so.

From algebra to networks

Weil's (1949) core insight about kinship, although highly idealized. is that the cultural conception of kinship begins and rests with couples and offsping and the ways that they fit together to form networks. That is, it is not simply individuals who link to form social relations, some of which may arbitrarily be recognized as sex, marriage, or reproduction, the duality of relational forms – individuals in marriages, marriages that link individuals – that are equally important. Breiger (1974) was later to reflect on duality as between individuals linked by their membership in groups and groups linked by their common members and the necessary basis of multilevel P-systems as recognized by Harary and White (2001). Marriage as a unit formed in culturally acknowledged reproduction, however, takes a special form. It always takes recognition of two or more persons (for the Trio for example, two men and a wife) that are necessary to "father" and "mother" a child.

Social Theory, Networks and Controlled simulation

  1. Class formation, Community, Ethnicity, Segregation (considered in terms of Structural endogamy, Relinking, and causal effects of cohesive groups in networks)
  2. Wealth consolidation, Families as historical actors, Merchants and trade, Trade diaspora (considered in terms of economic flows and network process)
  3. Heritable and reconfigurable social exchange (the implications of network structure in relation to Balanced exchange, Generalized exchange, and Mobility)
  4. Power elites, Stratification, Leadership, Trust, Navigability (considered in terms of Strategic behavior in networks)
  5. Organizations, Organizational dynamics and change, Families as historical actors, Corporations, Social conflict and competition (considered in terms of the local-extralocal organization and power of competing cohesive groups in networks).
  6. Praxis theory in social dynamics and change (considered in terms of Decision theory, Scaling behavioral outcomes as probability distributions, and how macro-micro network dynamics, including how behavioral choices alter network structure with consequences for altering social choice).

See above #Introduction

http://eclectic.ss.uci.edu/~drwhite/cases/table2.htm

  1. Class formation (Feistritz, Colonial Guatemala, Mexican political elites, London Bevis Marks Synagogue, Wealthy Parisian Jewish Bourgeoisie) #Structural endogamy, Relinking (France, America), Structural k-cohesion, Generative cohesion /// Community (Warren County) Ethnicity (Wealthy Parisian Jewish Bourgoisie--Grange, Cyril) Segregation (Belen (Tlaxcala, Mexico)) Mobility (e.g., Renaissance Florence, Feistritz(Austria))
  2. Wealth consolidation. through structural endogamy (Brudner and White, 1997; Merchants, trade and trade diaspora (Berkowitz) Families as historical actors (Bloomsbury: Darwins and Wedgewoods, Nathan Rothschilds)
  3. Heritable and reconfigurable social exchange (Kariera, Alyawarra, Dravidian, Pul Eliya, Amazonia) Balanced exchange (Anuta) Generalized exchange (Bearman)
  4. Power elites (Spain, Mexican political elites) Stratification (Colonial Guatemala, Leadership (Turkish nomads) Trust (Turkish nomads) Navigability (Turkish nomads)
  5. Organizations (Bevis Marks Synagogue) Organizational Dynamics and change ( ) Social dynamics (Turkish nomads, Renaissance Florence) #Social conflict and competition (Zachary karate club?)
  6. Praxis and Decision theory (Pul Eliya Chuukese residence controversy??)


MOVE TO BIBLIOGRAPHY

Warner, W. Lloyd. 1941-1959. Five Volume series ("Yankee City" study of Newburyport).

1941, The Social Life of a Modern Community. 
1942. The Status System of a Modern Community. 
1945, The Social Systems of American Ethnic Groups). 
1947. The Social System of a Modern Factory.
1959. The Living and the Dead: A Study in the Symbolic Life of Americans.
  1. Warner, W. Lloyd. 1949. Democracy in Jonesville: A Study of Quality and Inequality. (a Midwestern community study)
  2. Warner, W. Lloyd, with Marchia Meeker and Kenneth Eells. 1960a. Social Class. in America: A Manual of Procedure for the Measurement of Social Status. New York:
  3. Warner, W. Lloyd. 1960b. The Family of God: A Symbolic Study of Christian Life in America.
  4. Rosenzweig, Roy. 1977. Boston Masons, 1900-1935: the Lower Middle Class in a Divided Society.

Nonprofit and Voluntary Sector Quarterly 6(304):119-126. http://nvs.sagepub.com/cgi/content/refs/6/3-4/119

Lomnitz and Marisol-Perez Lizaur. 1987. A Mexican Elite Family 1820-1980. Princeton: Princeton University Press.

Bearman Norwich

Turner, Ann. 1994-2002. Correlations: Warren County, Tennessee. 1850 Census Database Project. http://members.aol.com/APTurner/wctnhome.htm. Graph by Douglas R. White, http://eclectic.ss.uci.edu/~drwhite/LocalPopulations/WarrenCoTennessee.html

Laumann and Pappi. the researchers collected data on three networks among the identified influentials in each community, asking each person to indicate the three others with whom (s)he had the closest business or professional relations, the most frequent discussions of community affairs, and the most frequent social meetings (see Laumann and Pappi, 1976: 289 for the exact wording; cf. Laumann et al., 1977: 598-602 on the American data). --- Breiger, Ronald L., and Philippa E. Pattison. 1978. The Joint Role Structure of Two Communities' Elites. Sociological Methods & Research 7(2):213-226. http://smr.sagepub.com/cgi/content/abstract/7/2/213

Padgett, John, and Paul D. McLean. 2006. Organizational Invention and Elite Transformation: The Birth of Partnership Systems in Renaissance Florence. American Journal of Sociology 111: 1463-1568. https://webshare.uchicago.edu/users/jpadgett/Public/papers/published/orginvent.pdf

Padgett, John, and Paul D. McLean. 2006. Economic Credit and Elite Transformation in Renaissance Florence. American Journal of Sociology (accepted for publication) http://home.uchicago.edu/~jpadgett//papers/published/credit.pdf "Douglas White kindly wrote a computer matching algorithm that assisted in this linkage task, during our collaboration at the Santa Fe Institute, for which we thank him. This task is complicated by the fact that names are often not consistent across archival sources. Currently there are 1660 family genealogies in the dataset, viewable through Pajek.

Mexican political elites (Jorge Gil Mendieta)

Groote Eylandt

Nord Pas-de-Calais

Simulations and inferential (bootstrap) statistics for kinship networks

Simulations for kinship networks (White 1999) provide several kinds of tests for expected frequency distributions of different marriage types and sizes of structurally endogamous groups (http://jasss.soc.surrey.ac.uk/2/3/5.html). These simulations calculate the generational levels in the genealogy (Pajek:/Network/Partition/Depth/Generation) and then permute women's choice of husband (or men's choice of wife) within each generation, avoiding marriage with siblings (see: permutation with avoidance). Formerly done in FORTRAN, this is now done with export of the genealogical network from Pajek to R and the simulations are done in R. A one-shot simulation creates a single network with randomized marriages, while a Monte Carlo simulation generates many such networks and derives probability distributions from them for specific parameters such as the probability of marrying someone of type x, which might be a type of relative, like a cousin.

1. Actual compared to a null one-shot random marriages, computing the Fisher-exact significance test (probability estimate) for each type of marriage.
This is a conservative test where the N for presence/absence of each type of marriage is the same because actual marriages are randomly rewired, but the Fisher is a powerful test on a fourfold table and is calculated independently for each marriage type. White (1999) used this test to show that Muslim elite and commoner marriages in a Javanese village fit equally well to the null model of randomly rewired marriages in size of the giant bicomponent (structural endogamy group size) counting ancestors back 1, 2, ..., g=6 generations. What this says is that for whole networks of commoners and elites, neither group has a more compact endogamous subgroup than expected by chance. Actual and random simulated marriage frequencies were indistinguishable for both elites and commoners. Comparing the fourfold tables for each group using Bartlett's 3-way generalization of Fisher exact test (White, Pesner and Reitz 1983) showed the marriage behavior of the two groups to be indistinguishable in a null model of random marriage-type preferences for each. In absolute terms, the much higher raw frequencies of marriages with cousins by elites in Table X was entirely due to status-consistent marriages within a smaller elite population rather than a preference for cousins!
2. Actual compared to a biased model generating frequencies for each type of marriage. This is a bootstrap probability estimate for fit to the biased model.
3. Likelihood ratio tests for two biased models generating frequencies for each type of marriage.

Muslim elite marriages

Table X: Identical marriage probabilities for Javanese village elites and commoners in spite of much higher frequencies of marriage with cousins by elites (White 1999:13.2 Table 7)

| JE	Javanese Elites	
* DH	Dukuh Hamlet	              
|      --Presence---   ---Absence--- Fisher  Marriage  3-way Fisher
|	Act	Simul	Actual	Simul	p= 	type	Test (Bartlett's)
1:JE 	1	0	 4	 3	.625	FBD 	p=
* DH	0	1	 9	12	.591	FBD 	1.00
2:JE 	1	2	 2	 3	.714	MBD 	p=
* DH	1	0	11	16	.429	MBD 	1.00
3:JE 	2	1	 3	 2	.714	FZDD 	p=
* DH	0	0	11	 0	- 	FZDD 	1.00
4:JE 	0	1	 6	 7	.571	ZD 	p=
* DH	0	0	18	24	- 	ZD 	1.00

Early Kinship? Explaining Indigenous Australian forms of exchange

Contemporary ethnographers such as Allen (2008) view one of the early forms of kinship systems as resembling that of the Kariera of Australia, where alternative generations do not intermarry but alternate (A,B,A,B...), form separate local groups according to a rule of residence, succession and/or descent, and form two opposing sets of local groups (1,2) that marry each other. Weil took as the units of Kariera marriage section social structure the marriages of types A1=A2, B1=B2, with the first type giving children of B1 or B2 and the second of A1 or A2, in each case following the gender of the father. In the French tradition, Guilbaud (1970), Jorion (1972), Bertin (1983), Héran (1995) and many others persist in the tradition of describing “systems” of kinship rules by considering relationships among types of marriage. Cuisinier 1962? The anglophone modeling tradition, with Hammel (1960), H. White (1963), and Boyd (1969, 1972) as representatives, model marriage networks using individual males and females in representative marriages. Lorrain (1975) follows Courrège (1965) in defecting to the anglophone convention in identifying homomorphisms from genealogical graphs of individual nodes and their relations to kinship blockmodels, which gave rise to the work of Lorrain and White (1981).

One use of controlled simulation is to test theories of Indigenous Australian (IA) social organization. Allen (2008) argues for section systems as one of the early human kinship systems. White and Denham (2008) argue for age biases (difference in marriage ages of husbands and wives) as a key to the adaptive flexibility of sections in the generation of symmetric versus asymmetric exchange, and Tjon Sie Fat (1980), following Denham, McDaniel and Atkins (1979), shows in deterministic form how variant social structures might cohere into different "double helix" structures. P-graph simulations of complete relatively complete genealogical data for the Alyawarra (Denham and White 2005) would allow probabilistic tests of the transformational and adaptive properties of IA exchange systems.

An untried probability model would involve permutation of marriages according to varying probability distribution for age differences at marriage with means and variances \mu, \sigma. Means approaching zero would predict symmetric marriages, while increasingly younger wife-taking would predict increasingly asymmetric marriages. Predicted effects of demographic stress can be tested by simulating different die-off ratios between males and females.

See: #Age bias and generational helices

(Note later that the Kariera IA "structure" has two dimensions: side-by-side and up-down in its section system]

Explaining Distributions of marriage types

Tests may be run as well for the overlaps between different marriage types or what are called "multiple marriage type" distributions.

Check Short interviews with Didier Sornette -- Embedded distributions.

Kinship and networks

Sociologists Laumann and Pappi (1976) experimented in an ambitious project of network community study comparating the German and U.S. towns of Altneustadt and Towertown (pseudonyms) using kinship relations in community-wide networks as core multirelational elements. Anthropologist Fischer (1992, 1994) tried computing complete matrices of all persons in a network in terms of their kinship ties. Bagg and Colclough (1992) and Bagg (1996) used Fischer’s approach to study marriage and kinship structures in Ascoli, Italy. My experience with a database approach of this sort (White, Scudder and Colson 1997) was richly rewarding (Clark, Colson, Lee, and Scudder 1995) and led to placement of a new generation of three anthropologists in existing field sites, but the census questionnaire survey method of collecting and coding kinship data on an individual by individual basis was difficult, costly, and time-consuming as a means of obtaining kinship networks but extremely productive otherwise (see, for example, Clark 2008). Once databases are constructed, however, Lyon and Magliveras (2006) found much to recommend Fischer's (1992, 1994) approaches to a variety of anthropological problems as well as what he calls the "high performance" analyses of p-graphs.

Somewhat frustrated with the complexity of database network projects, I had the good fortune in 1991 to work with social anthropologists based in France: Paul Jorion and Michael Houseman, referred to me by Professor Héritier-Augé at the College du France. Jorion and I (White and Jorion 1992, 1996) made an important move that combined the anglophone and francophone traditions. We combined the francophone tradition of coding marriages (using the French coding for parental and marriage ties) with the anglo emphasis for working directly on the empirical networks among individuals. We thought that our approach would synthesize the strengths of the two working traditions, providing cross-validation between them as well as the theoretical precision of the network sciences. The two traditions, however, regarded one another with suspicion: the one for being too idealist with top-down and often arbitrary choices in modeling, the other for being too empirical and too committed to strict methodological individualism.

Nevertheless, Houseman and I scoured the Parisian libraries for ethnographic studies that contained actual genealogies for whole communities. The synthetic methods allowed rapid coding of very large networks. Some of the results of analyses made possible by simple changes of coding methods were ones that we found amazing, and motivated further efforts. Later I applied this approach to genealogical databases in GEDCOM formats (GEnealogical Data COMmunication) and computerized historical data. With multiple collaborations, our database grew to over 200 case studies with large, small, and very large kinship networks for very diverse communities around the globe and spanning different time periods as well as providing longitudinal data up to 4-5 centuries in some cases.

Micro, meso, macro kinship network patterns

The French coding method for kinship networks (marriages as nodes, links between a parent(s) node and individual or married children) has two effects, one for local structure, another for neighborhood structure, and a third for global structure.

Local

First, it gives a direct way of reading types of marriages that occurring within a complete kinship network of a community. These are the local relational components of network structure. A diamond

Ancestral couple (ego's\Uparrow Mo\nearrow Fa=wife's \swarrow Fa\Uparrow)
\nearrow \Uparrow
F=M MB=MBW
\Uparrow \nearrow
ego = wife (ego's\Uparrow Mo\nearrow (Fa's Parent's So)\Uparrow Da\nearrow

pattern such as  \Uparrow \uparrow o \Uparrow \uparrow, for example (S to F to M to MB=FMS to MBD) can be read as a MBD marriage or in French notation (Barry 1998) as HFhf for Homme/Femme/homme/femme.

Note that p-graph has parental functions G(x) and F(x) that give unique results for husband/male and wife/female parents of x in a couple or as an individual, given a regular genealogy with parental uniqueness. Barry's (1998) notation uses H(x) and F(x) for these functions. His relational language uses such expressions as HF()HF.H with upward parental links on the left of the ancestral nodes () and downward parental links on the right, hence MBD.HF, with the dot for marriage. The G stands for Garçon to indicate a man's father, while H stands for the same, Homme. F in both cases stands for Femme.

Intermediate

Second, these local graphic configurations, with their different semantic notations, could also overlap in how pairs of marriages might share the same ancestral ties. A  \Uparrow \Uparrow \downarrow \downarrow would parse as FZD marriage.

Global

Third, taking all these overlaps into account, the boundaries of cohesion in the community could be identified as a giant bicomponent within the network. A bicomponent of an undirected graph is a maximal connected set of nodes (in this case marriages) than cannot be disconnected by removal of a single node, and it is also a maximal connected set (the same set, in fact) in which every pair of nodes has two or more independent paths connecting them, that is, with no common mediators. This is the community core in which every marriage is connected to every other in multiple ways.

From networks to realistic graph-theoretic models: Parental networks as P-graphs and weaker algebras

Realizing that these new empirical kinship networks were bound to be important, we called them p-graphs, as did Jorion and De Meur, which for De Meur refers to "Paul", who extended their use to more complex marriage rules, and to those like me, to "Parenté", Graphes du Parenté, or parental graphs, because all the links are child to parent, as attributed by local consensus. There are many oddities in culturally different kinships, but they can usually if not always be represented graphically. Héran (1995), one of the innovators alongside Jorion's work with p-graphs, showed in seven volumes the amazing variety of patterns in marriage behavior as well as many regularities and anomalies discussed by Lévi-Strauss (1949, 1965) and other ethnographers. Similarly, distinctions among same-sex parents (including adoptive, foster, out-of-wedlock, unknown, etc.) may also be distinguished in different graphic and network formats. Widmer and La Farga (1999), for example, study networks of extended reconstituted families through divorce and remarriage. Different graphic formats can distinguish multiple same-sex parents if there is agreement to that effect (e.g., the Trio) or if there is disputation.

The role of graphical-analytic models

The construction of algebraic models of network structure in order to capture marriage and kinship rules has long been a motivation in the study of kinship networks. When applied to real genealogical data, algebras could include the possibilities of missing data (parent or parentage unknown), multiple types of parents, and all kinds of other possibilities, including changes over time in the marriage structure (hence longitudinal algebras representing change through time). Algebraic reductions, however, are typically unable to handle irregularities and exceptions to rule-governed patterns in data, and so are usually only (1) approximative of the actual data or (2) an expression of a rule-set as a prior model. Permutation-group type models studied by Weil (1949) and others for Australian kinship do express what are very strong high-level regularities in section systems, but they fail to capture all the variant patterns of behavior that occur within a simple system of marriage restrictions by section.

Graphic displays of kinship and marriage relations used by commercial genealogical software are not designed for pattern discovery but merely serve as a visual representation of the network. The graphic models of kinship I discuss here can take the data of commercial or freeware genealogical packages as input, but the goals of these models is not only to allow descriptive accuracy in representing actual genealogical relations but to allow both conventional network analysis and to measure basic features specific to kinship that can be used in modeling and that apply network concepts to kinship theory, testing hypotheses, and making discoveries about kinship systems. The p-graph is one of these representations of kinship networks that provides accurate descriptive representations of genealogical networks, without any algebraic reduction, plus a full set of analytical possibilities. Where there are strong role regularities among marriages in a p-graph, of course, analytical reductions such as blockmodels are possible, but that is not the primary concern of this chapter.

There are various ways that genealogical networks can be represented as graphs. Four ways have become standard for analytical purposes, although what we call the O-graph of Ore (1960), with directed links from children to each parent, has become only a mathematical curiosity useful for comparison with the three that derive from the p-graph. Each of the four representations that I discuss use different types of edges and nodes and represent the different utility of their implicit balances in the preponderance of nodes to edges or arcs. Each has differing parsimony and analytic power.

O-graph

The Ore-graph genealogy has few nodes, representing individuals, no edges (undirected links), and for a family with 2 parents and m children, 2m arcs, but no representation of gender other than by adding gender as an attribute of nodes.

P-graph

Here there may be fewer nodes than individuals because two parents may be represented by a single node, but nodes proliferate with multiple marriages. Gender is coded into the types of arcs (son, daughter). This facilitates the analysis of network structure, measures endogamy through cohesion (bicomponents), and makes controlled simulation easier, but requires that siblings with multiple marriages have individual ID codes attached to their arcs to their common parental couple.

B-graph

Here individuals and marriages are represented by two types of nodes, and all arcs are either from individual parent to marriages (not requiring siblings to carry ID codes on these arcs) or marriages to children. This makes the B-graph bipartite, similar to a Petri-net. Here there are more nodes and more arcs than in any other model but perfect accuracy is obtained in describing the network structure without labeling of arcs.

T-graph

Project TIPP: Houseman and Grange (2008). discuss

T-graph nodes represent individuals, like the Ore graph, but here the O-graph arcs are divided into four types to distinguish sex of parent and of child. An extra arc is added for each marriage. This surplus of arcs makes bicomponent computation difficult but with Pajek macros and Java algorithms very precise analyses are possible.

Constructive, Descriptive and Discovery properties of graphical models

Graphical models are constructed to have perfect accuracy in representing kinship networks but they differ in how easy it is to configure the visualization to see structural properties, measure properties, describe micro, meso and macro structure, prove analytical theorems, and to manipulate and reduce the graphs to capture further structural properties. The also differ as to ease of discover of important theoretical findings and empirical regularities. P-graphs are the simplest means of doing all of this, with some loss of visual information (coded however in labeling), while T-graphs allow great precision (e.g., in more precisely distinguishing half-siblings).

Synthesizing the initial tension between global and local structure in kinship networksx (Lévi-Strauss 1949 v. Murdock 1949 as posed in White and Johansen), the P-system (Harary and White 2001:22) "incorporates the best features of each of the previous models of kinship: a single relation of parentage, graphs embedded within the nodes of other graphs, and segregation of higher level descent and marriage structure from nuclear family structure. The latter is also the key conceptual distinction used by Lévi-Strauss (1969) in the theory of marriage alliance. While a P-system is used to represent a concrete network of kinship and marriage relationships, this network also constitutes a system in the sense that it contains multiple levels where each level is a graph in which each node contains another graph structure. In sum, the connections between the nodes at the outer level in a P-system are especially useful in the analysis of marriage and descent, while at inner level we can describe how individuals are embedded in the kinship structure." Although conceived independently, the P-system for kinship resembles the Wikipedia:P-system of biology, developed by Gheorghe Pӑun (1998[2000]), which established the field of membrane computing.

Theory and description

Analysis of kinship networks produce descriptive measures that relate kinship concepts to those of network models:

  1. Generations (levels in directed acyclic graphs)
  2. Sidedness (bipartition, clusters, balance)
  3. Blockmodeling of roles (structural and reqular equivalence)
  4. Centralization (betweenness, degree, closeness, flow, eigen) and node centralities
  5. Structural k-cohesion (bicomponents, k-components)

Descriptive measures that can be made on a kinship network include all of the standard network concepts.

Communities and their kinship structure

Communities and structural bi-cohesion

Having discovered a new type of "unit" of kinship – core kinship communities – we called such a unit structurally endogamous, and the maximal such group structural endogamy. We wrote about the common properties of those in such groups as contrasted with others with less cohesion. The peripherals outside the core and the smaller bicomponents formed kinship trees outside these bicomponents. Sometimes we could identify different large-core communities that did not overlap or were connected only by a single node or link.

Dividedness and sidedness

Houseman and I (1996) chose in one of our first studies of unexpected marriage patterns, even by the standards of Héran, to demonstrate how a bipartite "moiety"-like structure – a society divided into two opposing halves – could occur as a behavioral pattern without any labeling by group names or by principles of descent. The intent was to show definitive evidence that a pattern of dividedness could be defined and found – in the case of the Anuta of Polynesia (kindred to the Tikopia, their famous neighbors) – without any reference to explicit rules that operated at the group level. Rather, the "dividedness" phenomena that we discovered was a pattern in which the parents of the marriages in each generation divide into two opposing sets whose children intermarry, a pattern repeated in each generation, but without inheritance from parent to child of any singular basis for the division. Rather the division is egocentric, emergent by each couple's "choice" of alignment. These kinds of bipolarizing arrangements could also be seen in political and residential alignments, and were consistent with the fact that a large lineage could "split" into two if a marriage occurred within it, among male and female agnates. Segmentary divisions by descent (depending on the ancestor) follow the marriage bipartition in each generation, not the reverse.

In the same and two subsequent articles (1997,1998a,1998b), Houseman and I demonstrated for ethnographic studies with published genealogies a considerable number of cases where a behavioral division of the dividedness sort was present but where there was a further statistical tendency for the divisions to be inherited according to one or the other descent principles (from the father or from mother, and sometimes for both, which implied few or no off-generation marriages). To distinguish this case from dividedness, we called this behavioral tendency "sidedness." Behavioral sidedness is a given in systems of named and inherited moiety divisions, but sidedness may occur without named moieties. Up to this point, many anthropologists had contested the very existence of unnamed "moieties" and ascribed behavioral reality only to named social divisions.

We found that cases of sidedness commonly occurred in that part of India and the Dravidian language-speaking areas in and around India (like Sri Lanka), where the kinship terminologies included a "sidedness" distinction in splitting the "my kin" (unmarriageable) category from “other,” which includes marriageable relatives.

Dividedness is the instantiation of balanced exchange between contemporaries in a single generation. It is not continued through time on the basis of a persistent structure because it is not inherited from generation to generation. Sidedness is the passing on of persistent structural dividedness called "moieties" if they are named, and sometimes called unnamed matrimonial moieties. Sometimes these two forms are mixed, as in the case of the political moieties of the Creek Indians (Murdock 1956). Here, two sides intermarried and sides were inherited, except that when ball games were won by a time of one site its members were obliged to switch sides, a variation on dividedness.

Even hereditary sidedness, balanced by reciprocal exchange at the global level, is not necessarily direct exchange at the meso or micro level. Lévi-Strauss (1949) contrasts types of marriage, such as MBD versus FZD, in terms of their local and global implications for types of exchange. FZD marriage, where father's group marries a sister to another group, which gives back a woman in the next generation, instantiates delayed direct exchange. MBD marriage involves women moving through marriage from one group to another in the same direction in successive generations. Chains of WB sibling-in-law links not uncommonly involve directed movement of wives in one direction between sets of siblings and their kin groups. Age biases for first marriages of men with younger wives promote this asymmetry when the same kin groups intermarry in successive generations.

Directed marriage chains and cycles

Generalized reciprocity contrasts with direct (restricted) exchange when flows of wives or husbands, currency or bullion, goods, gifts, information, or recognition tend to be unidirectional. In restricted exchange the same item, one very similar, or something equated in value flows back in a short cycle: A to B, B to A.

Network scaling methods such as regular equivalence will usually show these patterns (directed and cyclic flows of wives, for example, among groups of men, or the converse, of men among groups of women) where they exist in kinship networks. Such flow patterns are easier to track with p-graphs because they have fewer kinds of links than graphs of marriage and parent-child ties among individuals.

(P-graph with red lines and yellow flows from Alyawarra)

(Ore Graph for individuals as nodes showing the extra marriage tie)

Age bias and generational helices

Examination of the two Alyawarra graphs presented above show a systematic tendency for the average time between generations for men (difference in father-son ages of birth) to differ from those of women. This is confirmed for first childbirth of Alyawarra women (a but over age 14 on average) and that of the men (circa 28 years). Hammel (1976), in a scathing parody of Lévy-Strauss, called attention to how the expected probability of MBD compared to FZD marriage rises drastically with increase in age bias.

Bearman (1997) produced a controversial but I believe correct analysis of the Groote Eylandt data which like the Alyawarra has sections, age bias, and high rates of MBD marriage, and his blockmodel of the genealogical and kin-term data yield an 8-group directed cycle of marriages among groups, leading him to argue for the this case as a clear instance of generalized exchange. The mystery is why the blockmodel did not identify the lineages or generation structure of the groups involved in the exchange. Arguing from analogy with findings for the Alyawarra (White and Denham 2008), once possible answer to this question is that off-generation marriages in a society with alternating generation moieties may be with younger women in the grandchild generation, and/or with elder widows in the grandparent generation of ego. Alternating off-generation marriage is sure to obscure the group structures of lineages involved in generalized exchange. It is also likely, by merger of alternating generations into two opposing sets interconnected internally by sibling-in-law chains, to create two intertwined generational moieties that form a double helix, as proposed by Denham et al. (1979) for the Alyawarra.

see: Alyawarra marital age differences -- Woodrow W. Denham

Network behavior and cognition

White and Denham (2008), White (2008), and Read (2008) show that for the Alyawarra,

Houseman and White (1998b)

Conical clans and complexity

Process Models of a Turkish Nomad Clan

Navigability and strong tie reciprocity

Social Cohesion, Elites, and Social Class

Structural k-cohesion

Elites

Social class

Preference, Contingency, Rule, and Structure

Ring cohesion and complex distributions

attractors

Overlapping communities

Overlapping roles

T-graphs and marriage type formations

KinTipp

Networks and Complexity

Formal properties

P-graph descriptors and axioms

Parental Axiom 1: No one is their own ancestor; i.e., Directed parental links are acyclic and do not loop to ego.

Parental Axiom 2: No child will have more than one "biological" pair of parents.

O-graph (Oyestein Ore)

Node descriptor: individuals.

Arc descriptor: child to parent.

P-graph

Node descriptor: A node may be parental unit and/or a child of a parental unit; an individual or a marriage.

Arc descriptor: A parental link may connect sons to parent(s) or daughters to parent(s), with the possibility of unknown gender. Arcs are directed and designate individuals whose gender is represented by the type of arc.

Co-descendant descriptor: Those individuals in a (marriage) node with separate paths to the same ancestral node are co-descendants (commonly called in social anthropology a consanguineal or blood marriage, although the "common descent" is an attribution not necessarily biological but socially defined).

Affinal descriptor: Those individuals in a (marriage) node with separate paths to one another, exclusive of common ancestors, are affines.

B-graph

Node descriptor: two types of nodes are distinguished type, I for individuals and P for p-graph nodes.

Arc descriptor: distinguished by type, I to P for individuals to their parent node; P to I for parents to individuals in the couple

T-graph

http://eclectic.ss.uci.edu/download/MarriageNetTools.htm
http://intersci.ss.uci.edu/wiki/index.php/TIPP_Kinship_and_computing

Node descriptor: individuals.

Edge descriptor: numbered

  1. W-H Wi-Hu

Arc descriptor: numbered,

  2. M-D Mo-Da
  3. M-S Mo-So
  4. F-D Fa-Da
  5. F-S Fa-So

Theorems

P-graph structural k-connectivity theorem: c_p \le p, the maximum number of parents p, conventionally 2 (biconnectivity).

Generations theorem. P-graph minimum number of generations g_p \equiv l(p), the longest directed path of parentage.

Sections theorem: Any two of these propositions entail the third: virisidedness; uxorisidedness; all marriages same generation.

Algorithms

Pajek Generations /Net/Partition/Depth: Acyclic, Generation, Genealogy

Pajek /Net/Transform/Remove/Lines with value/lines with value ...: select one type of parental link

Pajek Bipartition /Operations/Balance* (Signed graph): Select one type of parental link (son, daughter) and recode arc value to -1.

Pajek lineages /Draw/Partition: Select one type of parental link (son, daughter) and calculate generations; Draw/layers/In y direction; /layers/Optimize in x direction/ (minimizes line crossings)

R Controlled simulation: compute Generation, export to R the p-graph and generation partition; for each generation, detach selected type(s) of parental links from parental sockets, randomly reattach to empty sockets.

R structural k-cohesion: compute Generation, export to R the p-graph, generation partition, and x position vector; run cohesive.blocks() (c) Written by Peter McMahan 2007, posted at http://intersci.ss.uci.edu/wiki/index.php/Cohesive_blocking




Substantive Findings and Examples

Conclusions

Acknowledgements

Initial work kinship and marriage graphs in 1991-2 was supported by a senior scientist award from the Alexander von Humboldt Foundation, the Maison des Sciences de l'Homme (Paris), the Maison Suger (Paris), and the French Ministère de la Recherche et de la Technologie, within the framework of an international and interdisciplinary working group on discrete structures in the social sciences created around the support and research facilities of the Maison Suger. Support for programming developments during 1992 was also provided by Alain Degenne's LASMAS research group at IRESCO (Paris) and the French Ministère de la Recherche. Grants from the NSF (#SBR-9310033) and A.v. Humboldt Foundations supported White's participation in analysis of the Pul Eliyan data. Thanks to Thomas Schweizer and Ulla Johansen for their hospitality at the Institut für Völkerkunde in Cologne both at the time his initial part of the research on Pul Eliya was done in 1993, and at the time of a later workshop funded by the Institute’s Leibnitz program in 1996, when the statistical analysis of the network consanguinal marriages was done. NSF grant #BCS-9978282, "Longitudinal Network Studies and Predictive Cohesion Theory" (White 1999) continued the project in the U.S. It was followed by NSF Grant 2002 BCS-0209295 Developing Theory and Ethnographic Applications for Explanations of Emergent Structure and Network Dynamics. Following an expansion of the kinship project in France L'Agence nationale de la recherche funded the grant to PIs Michael Houseman and Granger for continuation of the project in France.

Contributors and Collaborators

Laurent Barry, Vladimir Batagelj, Lilyan Brudner, Sylvia Casasola, Elizabeth Colson, Isabelle Daillant, Woodrow Denham, Alexis Ferrand, William Fitzgerald, Linton Freeman, Cyril Grange, Klaus Hamberger, Frank Harary, Michael Houseman, Ulla Johansen, Paul Jorion, Adam Kuper, Peter McMahan, James Moody, Andrej Mrvar, John Padgett, Dwight Read, Michael Schnegg, Thomas Schweizer, Thayer Scudder, Patricia Skyhorse, Eric Widmer.

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New

To Alphabetize (referred in text not referred to text as yet)

Links

TIPP Kinship and computing

Kintip - Traitement informatique de la parenté, Kinship and Computing

Other (temporary scratch pad)

Network motifs and motif-profiles

http://eclectic.ss.uci.edu/~drwhite/pgraphs-biblio.html P-graphs bibliography

Austria - Kinship, Class; etc

  1. 1995 The Distribution of Avoidances in Human Societies. (drw & R Wille), fig. p.5, in, Lattice Theory and its Applications: In Celebration of Garrett Birkhoff's 80th Birthday, by K. A. Baker, G. Birkhoff, and R. Wille. Lemgo, Germany: Heidermann Verlag. http://eclectic.ss.uci.edu/~drwhite/Avoidances.htm
  2. Bloomsbury - Adam Kuper
  3. Chuukese - Skyhorse
  4. Bevis Marks - Fitzgerald
  5. Guatemala - Narda, Silvia, Doug
  6. Groote Eylandt – Peter Bearman
  7. Nord-Pas-de-Calais - Doug

Kantian synthetic (Leaf 2007:9) Systems of ideas that are both formally cohesive and genuinely descriptive, including geometry, are what Immanuel Kant was concerned with under the heading of the “synthetic a priori.”

Watsi du Togo [K. Hamberger], chez les Bassari de Guinée [L. Gabail]).

(Kinship, Social Biography and Social Change Database [D. R. White, M. Houseman et T. Schweizer 1993-1999], Kindemo 150 Project on Longitudinal Studies of Kinship Demography [D. R. White et M. Houseman], l’ATIP « Traitement Informatique des Matériaux Ethnographique » [dirigée par L. Barry], Group Compositions in Band Societies Database [W. W. Denham],

PGRAPH (created by D. R. White) GENOS (created by L. Barry), PAJEK (created by V. Batagelj et A. Mrvar, University de Ljubljana).


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