Status Groups and Structural Endogamy

Douglas R. White, Michael Schnegg, and Hugo G. Nutini[1]

The very existence of a social network involves at least two elements; connectivity and redundancy. The latter provides some level of invulnerability to disconnection and disintegration of the network. An example of connected social networks with minimal redundancy is a bureaucracy in which each member reports to a single supervisor and where the personnel in the bureaucracy, apart from that, do not know each other. Such constained structures of connectivity, however, typically do not function effectively in the performance of complex tasks when and where the modalities of their integration lack redundancies. At the other extreme, namely that of maximum connectivity and internal `sociability,' we find redundancy enacted in the principle of transitivity (if A relates to B and B to C, then likewise A relates to C). With perfect transitivity, every indirect path (e.g., A to B to C) entails a direct path (A to C). Tendencies towards transitivity are characteristic of social ties such as in friendship circuits or sociometric cliques, where everyone in a group is linked to everyone else. These types of networks have a maximum of redundancy and a minimum vulnerability to disconnection.

In many naturally occurring and/or culturally constituted social relationships, for example, related to life cycle or ritual events, there is not uncommonly a balance between non-redundant connectivity (with the image here of "spanning tree" as the idealized model of such a network) and where the connectivity (as with friendship) continues to produce redundant integration. The focus of this study is the exploration of theories of such redundancies, and the specific examination and measurement of redundancies in community-level social organization and their implications for the structure of social groups. Our theoretical approach is exemplified as it applies to a rural community in the state of Tlaxcala, Mexico.

Redundancy in Social Organization

Redundancy and relinking are central concepts for the study of social organization. Redundancy of ties in a social group implies that the group is not vulnerable to disconnection through removal of a single person or dissolution of a single interpersonal tie. Redundancy implies circuits of connection, and the existence of a social unit that has multiple connectivities such that each member can reach another through two or more independent paths. It allows information to flow from the environment of one person to another through independent channels of communication, which allows cross-checking of the contents of the two incongruent sets of information. The operation of social sanctions is likewise more effective if there are multiple channels through which the sanctions can be applied and monitored. Finally, since all systems of circuitry have their limits, redundancy necessarily implies both the existence of boundary conditions and the means of monitoring information at these social boundaries.

These implications of social redundancy as a component of social organization or social structure have not been fully explored. Social anthropologists working with kinship networks in European populations, however, have developed the concept of marital relinking as a component of complex social organization in a way that is useful for the study of social redundancies and the exploration of social boundary conditions (Brudner and White 1997).

Substantively, the theory of redundancies and systematic patterns of marital relinkings encompasses the huge area in anthropology called alliance theory stimulated by the classic work of Lévi-Strauss (1969[1949]). It is not our intent to review that body of work here (but see Schweizer and White 1997). Formally, White and Jorion (1992, 1996) built a body of network theory that deals with such structures. Houseman and White (1997, 1998) have further developed these formal network theories of marriage alliance and applied them to substantively rich ethnographic cases. Much of the focus of these studies has been on the implications of the elective aspects of kinship - operating through marriage choice and role behavior - for different aspects of kinship and social structure. This tradition is known as the pgraphs approach in deference both to Paul Jorion (the p in pgraph as first named by his collaborator De Meur) and to the graphic models of marriage systems developed by Guilbaud (the p in graphes de parenté).

The present study is the first in this tradition to include the study of the co-parental (compadrazgo) relationships generated by godparenthood, which is so important in Mexican social organization, along with a network study of kinship and marriage.

Relinking

Marital relinking occurs when a new "endogamous" marriage occurs among a set of families whose members are already connected by chains of kinship and marriage ties. White (1997) and Brudner and White (1997) were the first to observe that marital relinking leads to the formation of well-defined social unit boundaries among clusters of families in which every family is linked to every other by multiple and distinct paths of blood and marriage connections. They noted the correspondence between endogamous social units defined by relinking, where every subset of families in a block are connected not just by chains of ties but by one or more circuits within the block, and the graph theoretic concept of blocks.

Blocks and Social Circles

The definition of a block as a maximal bounded unit within a network can be stated in terms of a graph G=(V,E) with a set V of vertices and a set E of edges connecting pairs of vertices. A path in G is a sequence of vertices along with an interpolated sequence of edges such that no edge or adjacent pair of vertices are repeated, each edge connects an adjacent pair of vertices, and no vertex appears twice unless it is the vertex that starts and ends the sequence. In this latter case, a circuit is a path in which the starting and ending vertices are the same. A block is a maximal set of arcs and the vertices they connect such that every pair of vertices are connected by a circuit (e.g., Gibbons 1985). In the graph in Figure 1, for example, the order of vertices x,y,e,a,w and their connecting edges describe a path but not a cycle, while a,b,d,e,a describes a cycle that together with b,c,d,b forms a block; y,z,e,y forms a separate block.

Figure 1: Illustration of Paths, Cycles, Blocks

Sociologically, a block of social relations defined in the graph theoretic sense is a unit formed by social circles that may overlap by sharing one or more ties or edges. For example, the redundancies in the circuits of Figure 1 are contained in two blocks that overlay in point e but share no edge in common. If we properly define a graph of social relationships in such a way that the circuits in the graph reflect relinkings between structural units which themselves contain no circuits, then we can capture with the concept of blocks important aspects of the self-organization of social behavior into meaningful social units. Graphs which contain no circuits are known as trees. Hence we will be interested in connections between trees as basic structural units in order to define patterns of relinking and block membership.

Structural Endogamy

White (1997 and Brudner and White 1997) developed the theoretical concept of structural endogamy (and the basis for its empirical measurement) that is well suited to the study of self-organization in social networks. Structural endogamy emerges as a result of objective behaviors (marriages) which relink clusters of families into blocks in which every family is linked to every other by multiple and distinct paths of blood and marriage connections. The concept of structural endogamy as a bounded entity within a social network is perfectly represented by the graph theoretic concept of blocks if we take trees of descendants from common ancestors as the units of consanguineal kinship and represent marriage as intersections of these lines to form new ancestral couples (White and Jorion 1992, 1996).

Status Groups

Social class and status groups are often regarded as objective entities determined by ranking according to economic criteria or other indicators. In the sociological tradition established by Weber, however, the objective definitions of class and status are distinguished from their subjective manifestations whereby social class, for example, is a matter of the perceptions and rankings internal to a community. The approach taken here is to consider that social class may also reflect objective behavior, not as attributes judged by outsiders, but by actions taken and relations formed by insiders relative to other insiders. Our thesis is that social class and status groups have a network component that reflects behaviors that not only link members of the group but that relink core members to achieve redundant connectivities (multiple paths of connection among core members). Structural endogamy - or relinking through marriage - is thus one of the possible elements of redundant connectivities that we will investigate in relation to social class and status groups. In this paper, however, we extend the concept of structural endogamy to cover fictive or ritual kinship as well as networks of kinship and marriage.

To illustrate and test our theory of status group formation through relinking, we analyze the kinship, marriage, and compadrazgo data collected by White, Nutini and Brudner in a village of rural Tlaxcala.

Research Design and Data Collection

The objective of the larger compadrazgo network study, described in Nutini (1984:411-6), was to discover how social network structure and social integration differed across a tradition - transitional - acculturated continuum of rural Tlaxcalan communities, and to test hypotheses about the relationship between network structure and socioeconomic factors and processes going on within the region. At that time Tlaxcala had the characteristic of being a relatively autonomous state within Mexico, so that a range of community types was evident.

As Nutini (1984:412-3) notes, our conception was that "network analysis is meaningful in its own right only where the behavior of actors in the social setting is related not to roles or characteristics of individuals or groups, but rather to the particular configuration of relationships within a network. [N[etwork analysis… should be able to elucidate (and predict) certain types of individual and group behavior, which are not a function of individual attributes or even dyadic relationships per se." We hypothesized that "the exocentric patterns of social relationships [in compadrazgo] tend over time to form structures that acquire a dynamic of their own: clusters of individuals with a high density of compadrazgo ties emerge, and for certain purposes they exhibit behavioral regularities at the community level, sometimes in relation to concerted economic, religious, and social action, sometimes in relation of conflict resolution or the avoidance of direct confrontation. In other words, there exist strong exocentric patterns in network formation hitherto unnoticed in the Mesoamerican literature, and coherent sets of behavior predicated on the structure of such networks."

The town of Belen, the focus of the present analysis, had a population ca. 1,200 at the time that fieldwork was carried out in 1976-80. Of the four towns studied, Belen was one of the two transition communities chosen to contrast with a highly traditional and partly Nahuatl-speaking village on the one hand and on the other a community that was highly acculturated to the regional variant of Mexican national or Mestizo culture.

Comparable social network data were collected in all four villages. Household heads, both men and women, were interviewed. Ancestries back to the great-grandparents generation were collected in each interview. In addition, extensive structured interviews were conducted to produce an exhaustive compilation of godparent/godchild and compadrazgo relationships, their properties, and the attributes of the compadres asked or doing the asking. In Belen there were 278 interviews in all (138 paired as couples and two female household heads), and a total roster of 984 couples, both respondents and ancestors, were compiled, plus additional children of the respondents who will not be considered here. Isaias Bello Perez, a resident of Belén, did most of the final interviews. The list of the named compadres outside the village included a list of 3383 individuals organized by nuclear families (parents and children).

It is often said that network analysis is easier than the collection of network data ethnographically. Witness the thousands of network analytic studies that all rely on two dozen or so classic network datasets such as Davis, Gardiner and Gardiner (1941), Roethlisberger and Dickson (1961), Kapferer (1969), Krackhardt (1987), Newcombe (1961), Padgett (1989,1993), Sampson (1968), Zachary (1977), etc.

In the present case, our survey approach to collecting kinship and compadrazgo data was more efficient in the field than the standard anthropological technique of collecting eogcentered or community-based genealogies. The collection of network data - on for villages of 2-5,000 people each, completed in 1976-78 - proved far easier than the development of concepts and tools suitable for community-level network analysis, which evolved slowly over a period of 15 years or more years. Pgraph representation, conceptualization and analysis were essential in the development of the analytic approach, which is not contained in a standardized suite of computer programs (White and Skyhorse 1997). The key to the data coding operation, which ties in with the development of the pgraph, was the unique numbering of couples (individuals were identified by a couple number plus a letter designation of H, W, M or F for husband, wife, male or female) and the numeric coding of repeated names in the ancestries.

Bilateral Amnesia

The ability to name ancestors in genealogical interviews reflected the common pattern of contemporary bilateral societies, as for the average Mexican or North American national: most people could remember their grandparents on both the mother's and the father's side, but not their great grandparents. Table 1 provides a summary of the responses. Interviews were conducted with either or both heads of household present. Men's mother's parents were somewhat more likely to be remembered, and women's great-grandparents. Knowledge of the wife's side and the husband's side is correlated, and detailed knowledge of one side entails some knowledge of the other[2]. No couple had complete knowledge of both sides back to the great-grandparents.

                             Men          Men          Women        Women        
                             Remembered   Forgotten    Remembered   Forgotten    
              Parents        140          1            136          1            
              Fa's           107          34           104          33           
              Parent(s)                                                          
              Mo's           118          23           100          37           
              Parent(s)                                                          
              FaFa's            9         132          17           120          
              FaMo's            5         136          9            128          
              MoFa's            8         133          13           124          
              MoMo's            6         135          12           125          

Table 1: The Rembrance of Genealogy

Does the shallowness of remembered genealogies imply that we will have too little data for an analysis of relinking? Not at all: since ancestries overlap, different couples remember different parts of their shared genealogical histories, and then to complement or fill in the gaps for one another. Thus, we can typically fill in many of the great-grandparents for most couples. Further, the couples interviewed are of a wide range of ages, so that the sum total of remembered ancestors covers not just four but six generations. This is more than sufficient for and analysis of relinking.

The Pgraph: Kinship and Marriage

For Belen the list of resident parents and children organized by nuclear families contained double entries noted where a child in one family is a parent in another. In the pgraph these double entries, and the elicited ancestries, are the links between nuclear families, indexed by the couple number of the parents. Figure 2 shows a pgraph for kinship and marriage for all the couples and their ancestors in Belen. The links are of two types: one for males, shown as solid lines connecting couples, and type for females, shown as dotted lines. Each point in the pgraph may have up to two lines connecting to points above it (parents of the husband, parents of the wife), and any number of lines below it connecting to unmarried children or to the marriages the marriages of children.

(Insert Figure 2 about here)

We define our network of kinship and marriage as a graph to represent social relationships in such a way that the circuits in the graph reflect relinkings between families defined by kinship ties. The concept of structural endogamy as a bounded entity within a social network is perfectly represented by the graph theoretic concept of blocks, as given above. Figure 3 shows a reduced network consisting of only marriages that are relinked, and of the relationships that define the relinkings. Included in Figure 3 are all those branches of families which are connected in circular patterns of marriage with other families, all marriages where the spouses were already blood kin to one another. The latter pattern - blood marriages -- is quite rare for Belen.

(Insert Figure 3 about here)

Table 2 gives basic data on the two Belen Pgraphs for kinship ties - the raw graph of Figure 2 compared to the relinked graph - and describes some of the relationships between them, such as the percentages of lines in the graph (representing males or females), and of points or couples, that are involved in relinking.

                            Raw Graph     Disconnected  Relinked   Percentage of   
                                          Trees         Graph      Raw Graph       
              Males         231           23              86 (84)  37%             
              Females       234           26              85 (96)  36%             
              Couples       473           57            138 (147)  30%             
              Cycles          32           0              32 (34)  100%            
              Components        9          8                1      11%             
                                                        (1?)                       

Table 2: Basic Data on the Belen Kinship Pgraph

The pgraph provides basic behavioral data on social organization. In the raw graph there are 9 disconnected components, 8 of them trees containing no relinking through marriage with other members of the community. These residents (23 males and 26 females) are married outside of the village, and most are [____ recent settlers? ____ ] in Belen. Further, a disproportionate number of these residents are couples numbered 200 or higher, which are [the more marginal households or recent immigrants?]. In three cases (219,247,250), as we see from Figure 4, that these [marginal-immigrant] households are related to more central couples (22 and 24).

(Insert Figure 4 about here)

The remainder of the community heads of households and their ancestors (200 males and 200 females - nearly 90%) are relinked through marriage or attached to relinked segments. More specifically, 138 of the couples are relinked in a single large block of marriages where every couple is relinked with every other. Of these 138, 134 (97%) are couples where one or both was from Belen. If we remove these couples (they represent two families, one from Tlacocalpan, Tlaxcala and one from Tantoyucan, Veracruz), the remaining structure of a single block where every couple is relinked with every other stays entact, but loses 4 members who were linked only through these outsiders. The remaining 130 couples a single kin group core consisting of an endogamous single village deme. From the intervillage marriage matrix among ancestors, there is no indication that any other villages are implicated in this deme. Within this deme, the marriage relinking

pattern is not distinguishable from a random assortment of marriages within successive generations. The deme is of the size predicted from a random choice of spouses for residents of Belen as they come to marriageable age; the proportion of Belen residents outside the block are also predicted by this model, which is to say that the whole village can be said to pertain the same deme, and it is the randomization of marriages rather than a conscious strategy, which produces relinked marriages for the majority, but no relinking for others who, in the randomization process, were those who married outsiders, but did so randomly given the contraints on the number of outside marriages overall. The only systematic pattern shown by comparison of actual to randomized marriages for the entire set of residents is that there was a greater tendency towards systemtic relinking in the earlier generations that at present, but this tendency results from the fact that siblings often migrated to Belen together and their descendants were relinked by marriages with Belenos.

Compadrazgo

As an elective relationship, compadrazgo has the potential to span a much greater set of individuals since its only prerequisite is prior contact and existence of friendship, work or patron/client relationship, respeto or confianza. Typically, compadrazgo ties span not only individuals or couples within a community but outside, over an extensive area of social contacts. Table 3 lists in order of their frequency within the community the common types of compadrazgo in which either a godchild is involved (baptism, first communion, confirmation, graduation, marriage, burial, and "first mass") or an important religious ritual is involved (Coronation of the Image of the Virgin associated with the village church; setting of the Christ child in the home manger at Christmas time).

          Type      Label                      Total          Non-Repeats    Among          
                                                                             Interviewed    
          1         Bautizo                    118            90             17             
          3         Primera Comunión           103            77             13             
          2         Confirmación               76             57             6              
          19        Graduación                 39             29             9              
          4         Casamiento                 19             18             0              
          28        Coronación de Santísima    12             12             4              
                    Virgen                                                                  
          9         Acostada Niño Dios en      10             9              4              
                    Casa                                                                    
          5         Parada de Cruz de          9              8              4              
                    Entierro                                                                
          11        Sacada a Misa              8              0              0              
          Total                                394            300            57             

Table 3: Types of Compadrazgo

To utilize these social relations as indices of block formation so as to study self-organizing social units that may correspond to status groups or social class formations, we need to define the graph of compadrazgo ties to interface with that of kinship and marriage. The unit of compadrazgo, just as with kinship, is a couple, and not an individual. Typically, a couple asks another couple to sponsor a padrinazgo ritual for one of their children (sometimes, instead of a child, a ritual object and not a godchild or ahijado is involved). A pgraph of compadrazgo is constructed by taking each child or ritual object as a point in the graph (a "virtual couple") and giving each of these points one parental link to the parents and one parental link to the godparents[3]. Table 4 shows the basic data on the pgraph of compadrazgo for Belen. There is a high degree of relinking observed in this graph, nearly 65% higher than that for kinship and marriage, with a single block of relinkings containing 61% of the individuals in the graph. There are also ten small disconnected components that contain no relinkings, but involve only 14 of the 325 compadrazgos, less than 4%. About 31% of the individual links in this graph are not themselves relinked but are connected to the main relinking structure.

                            Raw Graph     Disconnected  Relinked   Percentage of   
                                          Trees         Graph      Raw Graph       
              "Males"       326           14            199 (194)  61%             
              "Females"     325           14            199 (194)  61%             
              "Couples"     557           39            294 (281)  53%             
              Cycles        104            0            105 (108)  100%            
              Components    11            10                 1     10%             
                                                        (1?)                       

Table 4: Basic Data on the Belen Compadrazgo Pgraph

These results show that compadrazgo is a highly integrative social relationship within the community given the high rate of redundant relinkings, the single block structure containing the relinkings, and the high rate of additional connections to this structure that are not redundant but "ready," structurally speaking, to be relinked.

Kinship and Compadrazgo

As a partly ascribed relation, kinship networks are slow to achieve social integration through relinking, especially if they are open to marriage with outsiders. Only if every marriage represented a relinking among descendants of a community already relinked can the network of kinship and marriage relink every married person. This occurs only in the case of "caste" type systems which are 100% endogamous.

Structural endogamy in a class society is not 100% endogamous in the sense that every new marriage is an endogamous relinking within a social group. Structural endogamy forms "blocks" of relinkings within class societies, however, in which there is a time-lag between the assimilation of outsiders through marriage and the relinking of these marriages through structurally endogamous (relinking) marriages of their descendants or their descendants' affines.

If we examine the marriages of 140 household heads in our survey of Belen, for example, we find a significant number (40%??) who have married outside the village. Since we interviewed all spouses, we do find in some cases that these outside spouses have ancestors in common with Beleños such that their marriage relink with the block of relinked marriages in the village. Most of the time, however, this is not the case.

Compadrazgo links, however, have the potential to integrate these outsider marriages long before any of their children marry. Hence, when we examine the network structure of kinship and compadrazgo in a single pgraph, we should find that the addition of compadrazgo ties to the network have the potential to greatly expand social integration through relinking. Table 5 provides the basic data.

                            Raw Graph     Disconnected  Relinked    Percentage     
                                          Trees         Graph       of Raw Graph   
          Males/"Males"     589           3             377 (391)   67%            
          Females/"Females  593           3             355 (364)   62%            
          "                                                                        
          Couples/"Couples  929           7             478 (495)   53%            
          "                                                                        
          Cycles            255           1             255 (261)   100%           
          Components           2          1                  1      10%            
                                                        (1?)                       

Table 5: Basic Data on the Belen Kinship and Compadrazgo Pgraph

We find in Table 5 that the percentage of relinking on an individual basis has risen only slightly in comparison to compadrazgo alone. This is because we have in this network a great many ancestors in the early generations who do not relink but whose descendants relink. For an assessment of relinking, then, we turn in Table 6 to the data on the couples interviewed.

Relinking Frequencies Frequencies for Interviewees

Families for Those Interviewed Connected to Relinking Block

Relinked by     Frequencies   Percent           Frequencies  Percent   
Kinship         63/138*       46%               132          94%       
Compadrazgo     72            51%               130          93%       
Kinship or       99            70%                                     
Compadrazgo,                                                           
separately                                                             
                100 -          74%              100 -         99.6%    
(expectation)   (54%*49%)                       (6%*7%)                
Kinship          122**         87%               139          99.3%    
and/or                                                                 
Compadrazgo,                                                           
jointly                                                                
Total           140                             140                    

* numerator not 140 because of two female household heads with no husband

** all but 5 exceptions are couples numbered over 200, where 46% (13/41) are NOT relinked; hence a rate of 94/99 = 95% applies to couples under 200

Table 6: Relinking Rates and Connectedness for those Interviewed

Table 6 shows the limitations on relinking through kinship and compadrazgo: Only 48% if those interviewed were themselves relinked. Since this includes some relinkings through children's' marriages, there is a high degree of "outsider" marriages. Further, compadrazgo alone relinks only 51% of those interviewed.

The combination of kinship and compadrazgo, however, begins to overcome some of these limitations. Kinship relinking and compadrazgo relinking are nearly orthogonal to one another (r=.10; 1% covariance). Together, one or another or both, taken as separate networks, relink 70% of those interviewed (the expectation for two fully independent or orthogonal variables is 74%). However, as would be expected from network considerations, when the two are combined into a single network, the rate of relinking among those interviewed is a hefty 87%. Independent relationships that combine in a network have synergetic effects on integration through relinking.

Further, when we consider the higher frequencies of interviewees who through kinship and/or compadrazgo are either relinked or connected to the relinked block of the villages, as shown in the rightmost columns of Table 6, the rates of integration rise above 99%. Further, while kinship alone connects to relinking blocks 94% of the couples, compadrazgo alone also connects to relinking blocks 93% of these as well as 93% of the remainder. ALL residents of Belen, with the exception of a single couple (224H&W) and their ancestors, are relinked or connected to a relinked core through kinship and compadrazgo. Compadrazgo integrates couples simply by cross-cutting the integration of kinship.

Diachronic Perspective

The potential for time-lag between compadrazgo relinking and kinship relinking is examined in Table 7, which lists by generation the percentage of couples involved in the single relinking block of the village. The excess of compadrazgo relinking above kinship relinking is highest in the current generation. Partly, however, this is an artifact of our asking about kinship retrospectively but compadrazgo contemporaneously.

                       Generation       Kinship        Kinship plus   
                                                       Compadrazgo    
                       2                33%  (29%)     39%            
                       3                24%  (18%)     27%            
                       4                22%  (11%)     31%            
                       2-4              23% (15%)      30%            
                       5                34% (10%)      44%            
                       6                33%            57%            
                       + compadrazgo    n.a.           74             

Table 7: Relinking by Generation

The figures in parentheses in the Kinship column of Table 7 indicate the percentage of relinking achieved by generation 5, excluding the most recent generation. Note that if two descendants of the relinked core married outsiders in one generation, they could become part of the relinked block through a marriage of their children. Hence, the figure of 10% in parentheses for generation 5 (there own relinking) becomes 33% when we add generation 6, who relink additional marriages in their parents' generation. Since 138 of the 140 household interviews were couples already married, they had the same chance proportionally to relink through marriage as did their parents. The figures in parentheses, then, compared to the other percentages, show a moderate historical shift in Belen, where relinking had begun to fall of in the parental generation but recovered in the current generation.

This shift towards greater kinship relinking in the current generation accompanied what we know ethnographically to be two other important shifts at this time: first, an major increase in the number of people involved in wage labor within the Tlaxcala-Puebla valley, and second, a florescence of the compadrazgo system in terms of greater numbers of persons asked and a greater number of types of compadrazgo employed.

The Beleño Status Group Hypotheses

Our network results support the hypothesis that the Beleños as of 1976-80 constitute a single status group, where in addition to kinship and marriage ties, resident members are quickly assimilated through compadrazgo. As stated by Nutini and Bell (1980:210): "Hitherto, Belen has been truly egalitarian, like most of rural Indian and Mestizo Tlaxcala."

Historically, we see Beleños increasing their investments in the compadrazgo system and in social integration in the generation interviewed in the late-1970s. Our hypothesis was confirmed that the Beleños were operating for the most part with a concept of status equality in spite of the increase in differential access to wage labor. This is because the type of wage labor, arising from new factory work in the automobile and other industries that was easily accessible relatively close to the community in the Tlaxcala-Puebla valley, facilitated a circular migration pattern where wage earners spent considerable time in the home village, and expended the bulk of their disposable consumer income within the village. This led to greater "social investments" such as community forms and personal forms of compadrazgo that tended to stress community solidarity and social equality. Beleños, in short, were fulfilling and expanding traditional obligations and investing in a community-based social security system.

Cognitive tests, however, showed that some of the wage earners were also bringing home with them a new set of moral precepts that placed individual and nuclear family interests over broader community based obligations. These results supported another of our hypotheses, namely that (Nutini and Bell 1980:210): "During the past ten years or so… there have been indications that [Belen] is developing a certain stratification which, in the next generation, may result in the kind of economic stratification one commonly finds in urban and semiurban settings in the Central Mexican Highlands. This consists of a rather marked class differentiation with specific social and religious indicators, based primarily on wealth and property, and the process appears to be proceeding rather rapidly in Belen People with common economic interests within the community tend to band together in a variety of contexts, one of which is the discharge of several types of compadrazgos" (see p. 211 for further description of these emergent groups). Hence, we would expect to find, given additional data, that after the late 1970s, social differentiation would begin to arise and the integrative functions of compadrazgo for the community at large would begin to decline.

One further new hypothesis may be offered for testing with data from new network fieldwork by Schnegg planned for 1998. The egalitarian community ethos that survived up to the early 1980s was associated with a normative prohibition against forming compadrazgo relationships with one's relatives (Nutini and Bell 1980:209). With the emergence of an ethos of social stratification, however, in which groups with common economic or commercial interests intermarry and form dense compadrazgo ties internally, to a level not heretofore witnessed (p. 211 gives the estimate of 40% of the compadrazgos of one of these emergent groups contracted internally, and of 75% of group members so linked), we expect to find the normative prohibition against compadrazgo links between close kin eroding amongst the economic elites of the village, and spreading to the village at large.

Simulation Test

Our integration hypothesis is tested by a simulation model, where all the males within each generation are randomly reassigned wives within the generation in which they have married[4]. Results are shown in parentheses under "Relinking" in Tables 2, 4 and 5. The expectation of the hypothesis is that the actual marriages and compadrazgos will be randomly distributed, and this is what we find in the comparison to the simulation test. Comparison of the number of relinked couples for kinship and compadrazgo together is consistently at or slightly below the random distribution levels.

Conclusion

The innovation of this study is twofold: one in the area of theory and conceptualization of social integration, the other in the substantive analysis of ethnographic data. Most generally, we show how ethnographic data on hundreds and potentially thousands of people and events can be studied using the tools of graph theory to investigate various aspects of the question of social integration.

The conceptual innovation of the theory is the concept of structural endogamy (White 1997, Brudner and White 1997). Looking at patterns of connectedness in network data, we identify bounded social units in which any given relationship is redundant in that its deletion still leaves the unit connected: this is the concept of redundancies in social integration which provide invulnerability to disconnection. Cliques, for example, have maximum redundancy. On the substantive side of the theory, we define kinship networks in such a way that every redundancy is a result of marriage choices that relink families into structurally bounded units that may constitute status groups. We thus focus on the elective side of how marriage choices structure kinship networks, with greater redundancy or relinking interpreted as greater social integration. Marriage structures with redundancies through marital relinking are, by definition, structurally endogamous, and structural endogamy implies the existence of definite maximal units of endogamy within the kinship graph.

The advantage of this approach is that we do not have to rely on cultural, normative, or ad hoc definitions of endogamy. We do not have to treat endogamy as a statistical tendency towards intermarriage within a particular social category or set of ad hoc criteria for group membership. Structural endogamy is self-defining within a network: its limits or its absence are a structural property of a network, much like clique identification. Cliques, however, are not natural social units since they may overlap. Structurally endogamy does define natural social units since the links that compose them are non-overlapping. Endogamous units may overlap in only one very limited way: they may not share edges but they may share at most a single point of intersection.

Structural endogamy, then, is a very natural concept to apply to the problem of measuring social integration in a bilateral kinship network: the more marriages included in units of structural endogamy, the more local integration, the fewer the units of structural endogamy the more cross-local integration, and the fewer and larger the units, the more global or community integration.

Applying these concepts and measures to the Tlaxcalan village of Belen, we the highest possible level of cross-local integration: a single large block of structurally endogamous marriages. Only 50% of the living couples in the village, however, all of whom were interviewed for their ancestries, relinked within three generations into this structurally endogamous block. The principal pattern of marital linking and relinking was that of status homogeneity, or randomly distributed choices within generations, a pattern which is highly integrative. Global integration was lacking, however, because the assimilation of outsiders through marriage precluded their immediate integration through marital relinking.

To examine the possibility that compadrazgo choices within the community tended to foster social integration beyond the levels achieved by kinship, the second theoretical and substantive innovation of this study was to define compadrazgo linkages so that we could generalize the concept of relinking from marital relinking to the analogous case of compadrazgo relinking. This we did by defining each compadrazgo event (godchild or ritual object) as a point in the network graph having to links: one to the parents and one to the padrinos. Compadres were thereby linked in a way that did not entail relinking unless the relationship formed a cycle. Generalizing from structural endogamy, we could thereby identify units of structural endogeny in a combined network of kinship, marriage and compadrazgo.

Examining this network, we found that compadrazgo ties, cross-cutting those of kinship, did indeed provide much broader global integration within the community of Belen. Nearly ninety percent of the couples interviewed were so globally integrated, with marginal households (mostly new arrivals) constituting the major exceptions. Even the exceptions, however, tended to be connected by a single path to the global structurally endogenous unit of the village (99.3%).

Further substantive structure of these networks showed that compadrazgo not only cross-cut kinship in its integrative role but served in particular to integrate those new marriages with outsiders where kinship relinking could not be achieved without the maturation and marriage of children. Second, we found a historical trend for a relative decline in relinking in the parental generation to be followed by a revitalization of kinship and compadrazgo relinking in the current generation. This revitalization followed a period of expanded possibilities for industrial wage labor in the local area that allowed migrants to live in their home communities or migrate cyclically with a period of residence at home.

The concept of structural endogeny thus proves - theoretically and substantively - to be highly useful both in network analysis and in community ethnography. It is a principle that

can be extended from endogamy proper to cover other phenomena, such as compadrazgo endogeny, occupational endogeny, or mixed forms of endogeny if we define each linking event independently of the others. Traditional notions such as in family studies, for example, have often lacked a concept of independent linking events, without which it is not meaningful to measure social integration through structural endogeny. For example, if family relationships are defined as multiple interdependent roles such as husband/wife, parent/child, and sibling/sibling (or more extended roles), then nuclear families themselves contain relinkings, and the idea of measuring the extent of relinkings empirically becomes meaningless since relinkings are implicit in the definition of family. The problem of nonindependence of relationships has not been widely recognized in network studies, but we cannot advance in certain areas of study without recognizing its importance. The pgraph, as a tool for the present analysis, provides a principle way of providing definitions for theoretical concepts that have useful and interesting substantive interpretations, in this case, concerning social integration.

The present case study of a Tlaxcala village is an interesting one because the correlates of the kinship and marriage network structure replicate certain aspects of Brudner and White's study of an Austrian village, using the same techniques, but the two cases also contrasts markedly in other respects. Both studies find a single block of relinked marriages in a stable agricultural community. In the Austrian case, however, those who are connected to the relinked block of structurally endogamous marriages (e.g., as descendants) but do not relink are relegated to a lower class position in which they do not inherit farmsteads, often emigrating or taking up wage or farm labor. Only those who relink through marriage become farm heirs, and reconsolidate fragmented lands in the process.

In the Tlaxcalan village, on the other hand, three quarters of those couples who are connected to the relinked block of structurally endogamous marriages are relinked through compadrazgo ties that they transact after the birth of their children, or when they are asked to be compadres of others' children. The system of relinking is expanded - leaving only a few marginal families who have recently settled in the village -- so that there is no apparent class division between those who are relinked and those who are not.

Click here for Picture Figure 2: The Kinship and Marriage Pgraph for Belen

Click here for Picture Figure 3: Relinked Marriages in Belen

References

· Berkowitz, Steven D. 1975. The Dynamics of Elite Structure: A Critique of C. Wright Mills' "Power Elite" Model. Ph.D. Dissertation, Brandeis University.

· Bourdieu, Pierre. 1962. Célebat et condition paysanne, Études rurales 5-6: 33-135.

· --- 1976. Marriage strategies as strategies of social reproduction. In Family and Society, eds. R. Forster and O. Ranum, pp. 117-44. Baltimore: Johns Hopkins Univ. Press.

· Brudner, Lilyan A. and Douglas R. White. 1997. Class, Property and Structural Endogamy: Visualizing Networked Histories. Theory and Society.

· Davis, A., B. Gardiner and M. R. Gardiner. 1941. Deep South. Chicago: University of Chicago Press.

· Gibbons, Alan. 1985. Algorithmic graph theory. Cambridge: Cambridge University Press.

· Granovetter, Mark. 1973. The Strength of Weak Ties. American Journal of Sociology 78:1360-80.

· Guilbaud, G. Th. 1970. Système parental et matrimonial au Nord Ambrym. Journal de la Société des Océanistes 26:9-32

· Hage, Per, and Frank Harary. 1983. Structural Models in Anthropology. Cambridge: Cambridge University Press.

· Héran, François. 1995. Figures et Légendes de la Parenté. Paris: Institut national d'études démographiques (INED).

· Homans ( Bank Wiring room),

· Houseman, Michael, and Douglas R. White. 1996. Structures réticulaires de la pratique matrimoniale. L'Homme 139:59-85.

· --- 1997. Taking Sides: Marriage Networks and Dravidian Kinship in South America. Transformations of Kinship, eds. Maurice Godelier and Thomas Trautmann. Washington, D.C.: Smithsonian Press.

· Hughes, Austin L. 1988. Evolution and Human Kinship. Oxford: Oxford University Press.

· Jola, T. ,Y. Verdier, and F. Zonabend. 1970, Parler famille, L'Homme 10(3): 5-26.

· Kapferer, Bruce. 1969. Norms and the manipulation of relationships in a work context. In, J.C. Mitchell, ed., Social Networks in Urban Settings. Pp. 181-244. Manchester: Manchester University Press.

· Krackhardt, David. 1987. Cognitive social structures. Social Networks 9:109-34.

· LaMaison, Pierre. 1979. Les stratégies matrimoniales dans un système complexe de parenté: Ribennes en Gévaudan (1650-1830). Annales Economies, Sociétés, Civilisations 4: 721-43.

· Leach, Edmund. 1970. Caste, Class and Slavery: The Taxonomic Problem. pp. 83-94 in Edward O. Laumann, Paul M. Siegel, and Robert W. Hodge, The Logic of Social Hierarchies. Chicago: Markham Publishing Co.

· Lévi-Strauss, Claude. 1969. The Elementary Structures of Kinship. Trans. James H. Bell, John R. von Sturmer and Rodney Needham. Boston: Beacon Press.

· Newcombe, T.M. 1961. The Acquaintance Process. New York: Holt, Rinehart, and Winston.

· Nutini, Hugo G. 1984. Ritual Kinship: Ideological and Structural Integration of the Compadrazgo System in Rural Tlaxcala. Princeton: Princeton University Press.

· Nutini, Hugo G., and Betty Bell. 1980. Ritual Kinship: The Structure and Historical Development of the Compadrazgo System in Rural Tlaxcala. Princeton: Princeton University Press.

· Padgett, John F. and Christopher K. Ansell. 1989. From faction to party in Renaissance Florence: The emergence of the Medici patronage party. Unpublished ms.

· ---1993. Robust action and the rise of the Medici, 1400-1434. American Journal of Sociology 98:1259-1319.

· Richard, Philippe. 1993, Étude des renchaînements d'alliance, Mathématiques, Informatique et Sciences humaines 123:5-35.

· Robertson, A.F. 1991. Beyond the family: the social organization of human reproduction. Berkeley: University of California Press.

· Roethlisberger, F.J., and Wm. J. Dickson. 1961. Management and the Worker. Cambridge: Harvard University Press.

· Sampson, S. F. 1968. A Novitiate in a Period of Change: An Experimental and Case Study of Relationships. Unpublished Ph.D. dissertation, Department of Sociology, Cornell University.

· Schweizer, Thomas, and Douglas R. White, eds. 1997. Kinship, Networks, and Exchange. Cambridge University Press.

· Segalen, Martine. 1985. Quinze générations des Bas-Bretons. Parenté et société dans le pays bigouden sud 1720-1980. Paris: PUF.

· Wasserman, Stanley and Katie Faust. 1994. Social Network Analysis. Cambridge: Cambridge University Press.

· White, Douglas R. 1996 "Enfoque de redes al estudio de comunidades urbanas" Estudios Demographicas y Urbanas. Mexico City: Colegio de Mexico.

· ---, and Michael Houseman. in review. Kinship Networks and the Balance Principle. book ms. Under review by Cambridge University Press.

· ---, and Paul Jorion. 1992. Representing and Analyzing Kinship: A Network Approach. Current Anthropology 33:454-462.

· ---, and --- 1996. Kinship Networks and Discrete Structure Theory: Formal Concepts and Applications. Social Networks 18:267-314.

· --- , and Thomas Schweizer. 1997. Kinship, Property and Stratification in Rural Java: A Network Analysis, in Kinship, Networks, and Exchange, eds. Thomas Schweizer and Douglas R. White. Cambridge: Cambridge University Press. forthcoming.

· Douglas R. White, 1997. Structural Endogamy and graphes de parenté," Mathematique et Science Humaines 137. Paris: Ecole des Hautes Etudes en Sciences Sociales.

· Douglas R. White and Patricia Skyhorse. 1997. Parenté Suite: Users Manual for Analysis of Kinship and Marriage Networks. Social Science Computing Association Decennial Volume, edited by Vernon Burton. National Center for Supercomputing Applications: CD-ROM Diskette

· Zachary, Wayne W. 1977. An information flow model for conflict and fission in small groups. Journal of Anthropological Research 13:452-73.

***




Footnotes

1 University of California Irvine, University of Cologne, University of Pittsburgh, University of California Irvine. White, Nutini and Lilyan A. Brudner, as co-PIs of the 1975-1979 Tlaxcala project, are endebted to National Science Foundation which funded the field research on which this study is based.

2 If the respondent(s) remembered the husband's grandparents, the wife's parents were always remembered, and if they remembered the wife's mo's mo's parents, they always remembered the husband's grandparents. No couple remembered both their fa's fa's parents.

3 It is possible that the padrinos of marriage relationships (one for the groom, one for the bride) would generate an automatic relinking with the two sets of parents to the marriage. This does not occur empirically with the present data, partly because few of these are village-endogamous marriages, and partly because none of these relationships are reported reciprocally in the raw data (both from bride's and groom's point of view). The effect of reporting biases is a separate study and is not reported here.

4 For greater verisimilitude, the constraint on these random simulations are that no marriages or compadrazgos are allowed within a certain degree of relationship: results prohibiting cousins or closer relationships are shown, but are nearly identical with those for prohibition of siblings or 2nd cousins.