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Slides for Anthro talk
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:
- ask someone from one class below your own.
- if you are in the lowest class, ask someone from one class above.
- 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.