Social Structure and Kinship in Rural Mexico - The Tlaxcala Project       
D. White, H. Nutini, L. Brudner and M. Schnegg

      
 

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initial text of article
Some first impressions of the Kinship Network      Three features of the graph are striking: (1) The 26 shortest elementary cycles are long; none are short; (2) Families do not cluster in the center but are spread out along the edges in cycles of very large diameter or as points connected to the cycles; (3) The families of economic rank 1 and 3 tend to occur more frequently in the cycles of the graph while 2 and 4 are more common in the peripheries of the graph. The next inset is a view of this structure from the top, and shows the relative emptyness of the center given the lack of short cycles.

Click for detail and larger Image      

Note the contrast with the following inset, a graph of the compadrazgo network, which is drawn with the same spring embedding algorithm but has a starkly higher concentration of short cycles in the center of the graph.  

Some first impressions of the Compadrazgo Network      

Click for larger Image (39K)      
      
      

The colors mark different structural positions in the network       
       
       
People who live in Belen and are connected to the largest relinked block. 
People who live in Belen  and are NOT connected to the largest relinked block.
People from outside Belen who are integrated in the largest relinked block.
People from outside Belen who are NOT relinked.

       
      
Here is the Frequency distribution of the different patterns:     
     
     
Pattern
Freq.
Percent
113
8,6
29
2,2
1028
78,5
140
10,7
     

      

From this classification of people a classification of links can be generated. There are for example links the well integrated Belenos (yellow) have to the not integrated outside world (red). Those links are likely to different from the links - let's say - the well integrated Belenos have to other well integrated Belenos (links from yellow to yellow). The general question is whether links that are structurally different differ also in other matters.    
    

In the classification we find seven different patterns:     
     
     
Classification
Freq.
Percent
 
 
 
 
 
 
 
 
 381
    7
 1436
  502
    7
  118
   50
 
15,2
  ,3
57,4
20,1
  ,3
 4,7
 2,0
     

     

For a first analysis those patterns will be combined to only three. These are the tree like ties that link to the outside world (3 and 6), those that link to the outside but integrated non Belen community (4 and 7) and links that stay within Belen ( 1, 2, and 5)    

A first question would be through what kinds of compadrazgo those structurally different links are established. Here is a the raw data:    
    

 

    
Type of Compadrazgo
Tree like links to the outside
Ties to Belenos
Ties  to "integrated" outsiders
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 116
 117
 119
 120
 121
 122
 123
 126
 127
 128
 131
 132
 208
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 516
 517
 519
 520
 521
 522
 523
 526
 527
 528
 529
 530
 531
 532
437
260
155
 44
  4
  8
  8
 15
  9
 11
  9
  1
  3
  2
  4
  9
 29
  4
  1
  1
  8
  4
  6
  0
  0
  0
  0
181
141
 29
 35
  7
 10
  5
 17
  5
 15
  3
  3
  7
  3
  4
 11
 22
  4
  1
  1
  1
  1
  9
  4
  0
  1
  0
  2
 54
 26
 40
  1
  7
 13
  9
 10
  9
  8
  1
  0
  4
  1
  2
  2
  7
  0
  1
  0
  3
  1
  0
  3
  0
  1
  0
 39
 11
 26
  3
  4
 11
  5
  8
  9
 11
  1
  1
  4
  3
  2
  3
 20
  0
  0
  1
  1
  0
  0
 15
  7
  4
  2
  1
 159
 110
  42
  37
   4
   7
   3
  11
   9
   4
   1
   0
   7
   0
   0
   2
   6
   0
   0
   0
   0
   3
   3
   3
   1
   1
   1
  23
  19
  15
  14
   4
   4
   4
   4
   4
   4
   1
   0
   3
   2
   0
   3
   6
   0
   0
   0
   0
   3
   6
   8
   3
   5
   3
   0
 
 
 
 

    

 

Correspondence Analysis helps to make some of the structural patterns visible. Since the matrix rank is 2 we have a perfect fit in two dimensions  (60% variance on the first eigenvalue which means that you primarily need to look at that dimension).    

Here are the results:    

Click here for larger image (10K)    

The red dots are the sacramental compadrazgos. The analysis clearly shows that the most important relationships are  the tree like ends of the networks.  These important relationships  are clearly  not established within the community nor within the redundant block that surrounds the community. The explanation is pretty strait forward:  the structurally  weakest ties (the dead ends) become the highest symbolic or cultural emphasis. Another argument would be that people try to integrate far away but potentially important people  in their personal network.     
    
  

In which regions do those structurally different ties reach  
   
Code Name of Place
Integrated ties
Percent
Tree like ties
Percent
22
21
101
348
23
51
181
341
630
12
462
362
241
403
404
24
142
361
401
431
311
452
100
312
381
237
437
 
Belen
San Bernabe
Santa Ana Chiautempan
Acxotla del Rio
San Matias
Apizaco
Contla
Tlaxcala
Mexico D.F
San Damian
Puebla
Los Reyes
Pontla
San Lucas
San Simon
Tecolotla
San Simeon
Toluca
Xalostoc
Yauhquemehcan
Terrenate
Altixo
Santa Elena
Tenayucan
Tzompantepec
.not in code
Santa Ursula
 
186
61
58
30
28
18
14
14
13
10
9
9
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
 
26,6
50,4
24,4
66,7
31,5
31,6
11
20,6
11
24,4
12
81,8
42,1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
 
119
60
180
15
61
39
113
54
105
31
66
2
11
25
25
17
16
16
16
16
10
10
9
9
9
8
8
 
17 
49,6
75,6
33,3
68,5
68,4
89 
79,4
89 
75,6
88 
18,2
57,9
100
100
100
100
100
100
100
100
100
100
100
100
100
100
 
 
 
 
 
 
 

  
  

There is a general tendency that most of the integrated ties stay closer (in physical terms). Some cases are interesting and ask for an ethnographic explanation. 

1) Why is it that Acxotla del Rio and Los Reyes are so well integrated? Acxotla is a town on the highway from Belen that is the edge of the capital of Tlaxcala and is the "urban settlement" for Belenos; Los Reyes is nearby and a bit further from the city. 

2) The tree like relationships go Tlaxcala, Puebla, Mexico D.F, Contla, Santa Ana Chiautempan, Apizago and San Matias. Tlaxcala and Mexico D.F. are the state and national capitals, Puebla the capital of the neighboring state, Contla is the regional weaving industry, Santa Ana and Apizaco the nearest market towns, and San Matias the next village along the highway in the direction of Santa Ana and Tlaxcala city. 

3) What is the difference between San Bernabe and Santa Ana Chiautempan?  San Bernabe is a neighboring village similar to Belen; Santa Ana the closest market town. 
 

Ties and occupations

Do people with different occupations have different patterns of ties? And if yes - is there any change over time?. The following analysis shows how the proportion of ties that goes in the relinked block has developed over the last years.  

(click for larger image 90K) 

The analysis shows that there was an overall peak in the late 50s and 60s where many relationships were invested into relinked ties. Thought that pattern is not the same for all occupations: the labradores show a very stable pattern, some others (like the oficios corrientes invest more ties in the relinked structure than in tree like relationships to the outside. If we look at the picture only from the latest point in time there are some differences in how much the group spends in the community. 
 
 
 

Social Class and Stratification

Which role does the economic rank of the two compadres play for the establishment of the relationship? In theory we can distinguish at least three different systems: a class  system, where almost all relationships are within ones social and economic class, an egalitarian system, where the economic position is not reflected in the social relationships and a patronage system, where wealth differences can be expected to be very high. Let us take a look, which model fits best to the compadrazgo data   the relationships within Belen?  Here is the matrix  of relationships: 

                   being asked 
  

asking             |                              Row 
                   |     1      2      3      4  Total 
                 --------+---------------------------- 
Los Ricos          |    13     12     26      7     58 
                   |                              15,3 
                   | 
Los que estan bien |    12      7     35      3     57 
                   |                              15,1 
                   | 
Los de recur. med. |    55     34     75     32    196 
                   |                              51,9 
                   | 
Los Pobres         |    12     11     36      8     67 
                   |                              17,7 
                   | 
            Column      92     64    172     50    378 
             Total    24,3   16,9   45,5   13,2  100,0 
  

To understand more about the relationship between the four economic groups it helps to convert the matrix into a vector of distances between the groups. The distance between the "very rich" and the "very poor" can be defined as 1 - 4 = -3. The other way around the distance would be 4 - 1 = 3. This way we keep the asymmetry of the relationships.  The results look like this: 
  

                               Expected   
   Value  Frequency   Percent  Percent  
      -3         7       1,9      1,6   
      -2        29       7,7      7,2   
      -1        79      20,9     13,2   
       0       103      27,2     26,0   
       1        82      21,7     16,5   
       2        66      17,5     19,0   
       3        12       3,2     16,3   
            -------   -------           
   Total       378     100,0    100,0   

How to read the table? The zero in the middle are all the relationships that are along the diagonal. If we were looking at a class system most of the relationships should concentrate here. This is not the case. In an egalitarian system all relationships should be equally distributed. This is not the case as well. What we find is that most relationships are one step below or above the class one belongs to, and these relationships are the only ones with higher than expected frequencies. In addition, there are more relationships that go up the economic ladder than there are relationships that go down. 

But who is it that establishes those relationships? Is there any pattern here? Let us move a step further and consider which of the relationships in the matrix above are stronger than would be expected by chance. This statistical logic might uncover some of the patterns in the matrix. Here are the results:

(click for larger image 5K )
           

The diagram shows all the relationships from the above matrix that are larger than would be expected from the row and column distributions. The first number on the arrow gives the number of relationships and the value in brackets indicates how much it is above the expected value. The direction of the arrow indicates who asked whom. 
For the interpretation one needs to keep in mind that these are only the relationships within Belen. The picture would lead to the following simplfication:

  1. ask someone from one class below your own.
  2. if you are in the lowest class, ask someone from one class above.
  3. the arrow from the 3. class to the 1 one needs an interpretation (any idea - doug ???).

Only because there is not much relinking in the elite does that mean that the elite does not have a special structural position?

                                   BetW     (s.d.)    cases
 
Los ricos                     435,4733   607,2260       18
Los que estan bien            268,6289   663,1602       18
Los de rec. medios            187,5595   254,2094       59
Los pobres                    185,5016   396,5005       31
 

As it looks it does not. The above table gives the mean results from  betweenness centrality measures for each of the four groups. The results clearly indicate that centrality in the system declines with the economic rank of the actor. The elite does not "close up" by high internal integration but becomes an integrated center of the network. This might be a somewhat typical  situation for a community that is in a transition stage. No class but structural stratification.