Decentralized Systems and The Invisible State: Low Density Multiconnected Cohesion in Large-Scale Social Networks in Tlaxcala, Mexico


Table 1: Case Study Sample
Conference on Decentralization
Table 2:
Level of Connectivity (generating bounded subgroups)
Concepts of Cohesion
1-Connected (1-) component
2-Connected (bicomponent)
3-Connected (tricomponent)
...
k-Connected (k-component)
Scale of Cohesion:
Vulnerable to disconnection
potentially Large Scale, low density
Clustered within bicomponents
...
Hierarchically Clustered
Definition 1: A (1-) component of a network (or graph) is a maximal set of nodes and arcs such that every pair of nodes is connected (e.g. nodes 1 to 8 above, also 9-18, 19-29).
Definition 2: A bicomponent of a network (or graph) is a maximal set of nodes and arcs such that every pair of nodes is connected by two or more independent paths (e.g. nodes 9 to 14; 9 with 15-16; 19-28).
Definition 3: A tricomponent of a network (or graph) is a maximal set of nodes and arcs such that every pair of nodes is connected by three or more independent paths (e.g. nodes 19 to 26 above).
General Definition 4: A k-component of a network (or graph) is a maximal set of nodes and arcs such that every pair of nodes is connected by k or more independent paths (no examples above for k>2).
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

General Hypotheses:
(a) Biconnectivity is a source of emergent, potentially decentralized social cohesion that can occur (with observable effects) at low density in (the bicomponents of) relatively stable social networks.
(b) This is especially true for relations that have very high "currency" or life-support salience, such as relations of political influence, property transmission, or kinship and marriage connections.
(c) Hence, social class, elites, wealth-transmission, and marriage systems are especially well-suited for analysis.

(d) Dynamic evolution of 1-connectivity and biconnectivity (and higher order connectivities having both global "giant component" effects and localized interaction effects) can give rise to phase transitions in network configurations (a likely example: the co-evolution of states and markets in Renaissance Florence).
 
 
 
 


An Invisible State: Case Study in Tlaxcala, Mexico, of a Decentralized Social System Santa Maria Belen, the focus of our case study of a decentralized social system, is a small town in Tlaxcala, municipio of Apetatitlan, about 8 km north of Chiautempan. Tlaxcala is the smallest state in Mexico.
location in MexicoTlaxcalan locationstlaxcala map

The map of Tlaxcala shown below was part of the indigenous census of 1555. This was a period of during more than a century (1525-1640) when the early Franciscan Friars protected the autonomy of the indigenous kingdom. Its four principalities are marked on the map along with the proportion of nobility in each district. In Belen, in the lower left corner of the district of Tizatlan, 22% of the population at that time were nobility (pipiltin). 
The nobility quickly learned Spanish but continued to record historical events in their traditional manner, as in the Lienzo de Tlaxcala from which this map was taken.

Members of the Tlaxcalan nobility continued to live in the indigenous towns until the Tlaxcalan centralized government was abolished by the Spanish settlers after 1660, following the expulsion of the Friars. The Tlaxcalan heartlands had acquired permanent land rights, however, thanks to the Francescans and to the service of the Tlaxcalans to the Crown and to the Conquistadores in their conquest of the Aztec, the traditional enemy of Tlaxcala.

For over a century, to the 1660s, the Tlaxcalans were largely left alone (except by the Friars) by other Spanish colonialists and settlers, whose efforts to buy Indian lands were largely thwarted by the surviving Tlaxcalan state organization. This resistence to Spanish acquisition continued in the "Free Indian Lands" long after their government was abolished in the 1660s and their nobility expulsed to Saltillo, Santa Fe, and Guatemala. The Tlaxcalan population that remained constructed a decentralized social organization during their "century of isolation" from 1660 to 1750, when even the new and more secular Spanish priesthood spent little effort on the Tlaxcalan villages.
 
 
 
 
 
 
 

Network dynamics in Belen, 1500-2000: Overview of Sociocultural Adaptation and Organizational Change.
 
 
 
 

Network statics: We did our network survey in 1978. Here is a drawing of the kinship and marriage network as we found it then. P-graph of Belen Kinship and Marriage Network Three features of the graph are striking: (1) The 26 shortest elementary cycles are long-girth in their number of edges; none are short; (2) Families do not cluster in the center but spread in cycles of very large diameter or nodes connected to these cycles; (3) Families of all different economic ranks intermarry. 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-girth cycles.

Click for "birds-eye-view" and larger Image

The relinking of families by marriage -- as shown above right -- is almost entirely among families WITHIN the community

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

The compadrazgo network also has many more links and, unlike kinship, extends 4-to-1 OUTSIDE the community.

Click for larger Birds-eye-view of the Compadrazgo Network (39K)
 
Colors marking different structural positions in the compadrazgo network:
 
People who live in Belen and are connected to the largest relinked block. ________8% (KINSHIP: 51%)
People who live in Belen and are NOT connected to the largest relinked block. ____2% (KINSHIP: 41%)
People from outside Belen who are integrated in the largest relinked block. ______10% (KINSHIP: 0%)
People from outside Belen who are NOT relinked. _________________________81% (KINSHIP: 8% CURRENT)

Analysis of Cohesion: Evidence of Cohesion from Bicomponents
  Belén Ancestorsė (generations 2-4) Core/Periphery Positions as defined by kinship and marriage
Outsiders
 
Giant Relinked Bicomponent
Giant 1-component
Small Components
Not Rrelinked
26-30
3
0
0
0
7-24
15
14
0
6
1-6
9
48
8
109

Table 3A:Kinship Relinking of Ancestors Predicting Number of Descendants (r=.43, p<.005)


  Belén Ancestorsė (generations 2-4) Core/Periphery Positions as defined by kinship and marriage
Outsiders
 
Giant Relinked Bicomponent
Giant 1-component
Small Components
Not Rrelinked
Civil/Religious councils membership
55
13
3
1
Not in town councils
43
31
20
86

Table 3B:Kinship Relinking Predicting Civil/Religious councils membership (r=.44, p<.005)


  Beleños Core/Periphery Positions as defined by compadrazgo
Outsiders
 
Giant Relinked Bicomponent
Giant 1-component
Small Components
 
Civil/Religious town councils 
82
20
0
0
Not in town councils
75
122
12
1147

Table 3C:Compadrazgo Relinking Predicting Civil/Religious town council (r=.60, p<.001)



 

Beyond Bicomponents: Analysis of Subvarieties of Cohesion
Average Length of Independent


Average
Level of Connectivity
(generating bounded subgroups)
Paths within subgroups
Path Length overall
1-Connected (component)
2-Connected (bicomponent)
3-Connected (tricomponent)
Small World Simulation 
Ö
k-Connected (k-component)
  1. Very short

  2. (<< random)
very long
Proximal

Tree

Proximal (2-) Cohesion
Proximal (3-) Cohesion
Local World
 
Proximal (k-) Cohesion
B. Short
(< random)
Long
Proximal

Tree

Proximal (2-) Cohesion
Proximal (3-) Cohesion
Small World
Proximal (k-) Cohesion
C. Short

( = random)

Medium 
Random 

Tree

Random bicomponent
Random tricomponent
Random world
   
D. Long

(> Random )

Short
Radial

Tree

Radial (2-) Cohesion
Radial (3-) Cohesion
 
Radial (k-) Cohesion
E. Medium

(> Random )

Medium (Bounded)
Radial

Tree

Radial (2-) Cohesion
Radial (3-) Cohesion
Radial (k-) Cohesion

Table 4: Concepts of Cohesion, expanded
















Row B. Proximal Cohesion (example): Members of the Town Councils  Row C. Random Graph: Giant Components
(a Monte Carlo simultion within generations is also done as a baseline model for the marriage network)
 
 
 
 
 
 

Row D. Radial Cohesion (example): Bicomponent members not on the Town Councils

1. Zone
2. Zone
 
1. Zone
0.048
0.079
 
2. Zone
0.079
0.031
Overall Density: 0.017

Deviation from the Expected Values: These numbers tend to 1.0 ("random graph") if town council participants are excluded.
 
  1. Zone
2. Zone
 
1. Zone
2.8
4.6
 
2. Zone
4.6
1.8





REVIEW - General Hypotheses

(a) Biconnectivity is a source of emergent, potentially decentralized social cohesion that can occur (with observable effects) at low density in (the bicomponents of) relatively stable social networks.
(b) This is especially true for relations that have very high "currency" or life-support salience, such as relations of political influence, property transmission, or kinship and marriage connections.
(c) Hence, social class, elites, wealth-transmission, and marriage systems are especially well-suited for analysis. (d) Dynamic evolution of 1-connectivity and biconnectivity (and higher order connectivities having both global "giant component" effects and localized interaction effects) can give rise to phase transitions in network configurations (co-evolution of Belen networks and organizational changes).

The relations that have very high "currency" or life-support salience, studied here, are those of political and religious influence (esp. religious town council), property transmission (indigenous ownership of land, bilateral inheritance), kinship and marriage connections ("structurally" endogamous, within the community, with ca. 8% migration in and out per generation of others from Tlaxcala), and ritual kinship or compadrazgo (multiply connected in a larger "invisible community" reaching outside Belen to adjacent communities).

From the Tlaxcalan evidence reviewed below: The existence of an egalitarian social class and the absence of elite differentiation is well accounted for in this case. Wealth transmission also works on an egalitarian basis in terms of bilateral inheritance divided equally among males and females. "Structurally endogamous" relinking marriages reinforce intra-village social class solidarity. The compadrazgo relations are also of high currency in social support, and, given the greater number of ties they provide, extend the egalitarian social organization out to inter-village relations, presumably adding coordination in ritual and economic life. The core of leading participant in the ceremonial and town council positions within the village tend to be a subset of more intense local interaction WITHIN the bicomponents of kinship and compadrazgo, and are reflected in the network by proximal as opposed to radial cohesion. 









Review of Decentralized Organization given the specific hypotheses for Belen and the rural Tlaxcalan "Invisible State"

 
 


In Conclusion: reflecting on what this general approach contributes to conference aims: and what the case study contributes in particular