SNA of Kin-Based social-economic networks

7/29/2019 SNA of Kin-Based social-economic networks

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A Social Network Analysis Approach to Modeling Social-Economic Complexity in

Traditional Kin-Based Systems

Brian D. Jones

IntroductionThis paper explores changes in the organization of kin-based social-economic

networks utilizing methods from Social Network Analysis. Social Network Analysis

(SNA) is a growing approach to investigating large, complex data sets comprised oflinked actors. SNA provides tools for the researcher interested in network topology, that

is, the morphology and structure of a network. Analytical software provides a means to

visualize large data sets as sociograms, and more importantly, to quantify many of theircharacteristics. Some important network variables include group cohesion, number of

components (cliques), brokerage roles of actors, measures of centrality, information

diffusion, and measures of prestige and rank. Although these variables have clearapplication to anthropological theory, social network analysis has remained primarily a

research tool among sociologists.The networks I will describe are intended to model changing social-economic

organization among traditional (non-state-level) kin-based social groups. A constantpower-law based economic organization underlies the model. Power-law distributions

typify many complex social and economic networks and are referred to in the literature as

scale-free because they express the same organization at any scale of analysis (Barabsiand Albert 1999). Scale-free networks consist of actors among whom many are loosely

linked to others, and very few are quite strongly linked. Such relationships express

themselves as straight lines on log-log plots that summarize the number of links and theircumulative proportion in a population (Bentley 2003). Power-law distributions are

considered ubiquitous, appearing in a variety of networked systems as diverse as moderncorporate organizations, Hollywood actor networks, numbers of sexual human partners,

connections between airline hubs, the electrical power grid structure, and university

research funding (Barabasi 2002, Bentley and Maschner 2007: 15-4).Barabasi and Albert (1999) established that that scale-free organization typifies

networks that grow over time based on a rich get richer algorithm. This means that the

probability of a new actor linking to an existing one is based on the proportion of links

the established actor already controls. Thus, if one university has a long-standing trackrecord of attaining NSF grants, it has a greater probability of receiving new ones. I use

this underlying principle to model traditional human economies because it has become

increasingly evident that even the simplest foraging economies are underlain by a highdegree of variation in terms of individual hunted meat yield, or access to trade partners

(e.g. Bentley 2003: 39-40). Bentley (2003) has determined the existence of scale-free

social-economic organization among Somali and Gabbra pastoralists, and in the size ofNeolithic long barrows, while Maschner and Bentley (2003) discuss scale-free

organization among Northwest Pacific house floor sizes as it relates to social rank.

In all of these cases, the presence of scale-free relationships points to the existence ofsignificant variation in levels of social prestige, rank (Frieds positions of valued status

[1967: 109]) and/or social stratification (Frieds unequal access to basic resources

[1967: 186]). Other classic examples would likely include the Trobriand Kula exchange


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network in which one or two high-status participants have hundreds of trade partners,

while most have one or two (Malinowski 1920). Among foragers, where social pressuresmay exist to promote cooperation rather than competition, differential prestige among

actors will nevertheless likely be present because of the rich get richer phenomenon

inherent to growing networks. I would anticipate, for example, that among Khoisan

women, very few have collections of beaded necklaces acquired through social contactsthat weigh in the kilogram range, while most have tens of grams of beads in their

possession. In the scenarios explored here, each model is seeded with 2 linked trade

partners, each with an initial 50% probability of acquiring the next partner. Thisparticular power law relationship results in a best linked actor with between about 44

and 86 incoming links after all of the 1,000 trade ties have been established (based on a

1-sigma range of 15 sampled networks). The exact number varies in each iterationbecause of the probabilistic nature of the model.

In addition to a scale-free economic organization, the model is grounded in a simple

kinship-based organization. Each actor in the model represents an 8-person householdconsisting of two grandparents, a married couple and four sub-adult children. In the

model, the spouse who marries into the household represents a directed link in, while themarriage of a son or daughter into another family represents a directed link out (Fig. 1).

Such households could be patrilocal or matrilocal in organization, such that a daughtermarries in, in the first example, or a son marries out in the second. The simple

assumption for the model is that each household produces a marriageable son and

daughter. This is meant to represent a mean condition in a stable population. It isassumed that two of the four subadults would not survive to adulthood. While the model

could have been created to reflect more variability, this modal form was selected for the

sake of simplicity. The 8-person household size of each actor in the network of kin isused to calculate larger-scale populations.

The complete model consists of 1,000 actors representing a population of 8,000individuals. Three related computer programs were written using FreeBasic, an open-

source variant of the BASIC computer language. The program permits the user input of

certain variables, such as the number of exogamous bands, or the proportion of elite inthe population. Graphic output is produced, largely to reassure the user that the program

did what it was asked to do (Fig. 2). The programs produce three types of additional

output in the form of ascii text files. These include a comma-delimited csv file that can

be imported into a spreadsheet or database, and network and partition files that can beread by Pajek social network analysis software (de Nooy et al. 2005). These files

summarize the network, characterizing the kinship and economic links of each actor, or

family unit. Every actor produces an outgoing economic link and an outgoing kinshiplink. All actors receive one kinship link, but may receive many or no economic ties (Fig.

3).

The model was developed to examine the effects of increasing kinship restrictions onthe topology of the resultant social network. Kinship restrictions are utilized to model

change between very open, exogamous systems as occur among small-scale foraging

societies, through tightly-controlled endogamous ranked systems where an elite classmakes up as little as 1% of the population, as might occur among chiefdom levels of

socio-political organization. Two basic systems are thus explored. The first models

exogamous societies with a decreasing number of clans. Beginning with 100 clans, 99%


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of the population is potentially marriageable, while with just two clans (essentially a

moiety-based system) only 50% of the population is marriageable. The second systemexamines the effects of prestige-based rank on the network. A transitional system is

explored in which actors are ranked into two moieties, but marriage remains exogamous

(e.g. following a Natchez marriage pattern [Tooker 1963]). Increasing restrictions on

marriage, now based on rank rather than clan affiliation, are then further explored byincorporating endogamous marriage rules. Models start with a ranked endogamous

moiety-based system, and then examine social organizations in which an endogamous

elite represent an ever-shrinking portion of the population, while the pool of commonersgrows proportionally.

I use increasing marriage restriction rules as a proxy of increasing social complexity,

and secondarily, growing population density. If we allow the simple assumption that atleast 200 individuals are required within a human breeding population to maintain long-

term viability (Wobst 1974), then group size must increase to compensate for the

decreasing proportion of available marriageable partners. This relationship issummarized in Table 1. It indicates that marriage regulations may become more

restrictive only as populations grow.

Table 1: Modeled Relationship Between Marriage Restriction and Base Populationassuming a 200-person minimum breeding population

exogamous endogamous

100 clans 10 clans 2 clans 25% elite 10% elite 5% elite 1% elite

% marriageable 99% 90% 50% 25% 10% 5% 1%

minimum population 202 222 400 800 2,000 4,000 20,000

modeled family actor units 25.25 27.78 50 100 250 500 2500

The changes observed can be seen as paralleling different levels of socio-politicalorganization. Where few or limited marriage restrictions exist, the modeled exogamous

clan-based societies can be described as bands in Services (1962) original

terminology. Such societies are centered on small, mobile kin groups, loosely linked toothers across a landscape. These societies may have rather low group numbers, falling

between at least 200 and 400 individuals.Social systems anchored in moiety-based marriage restrictions and those in which an

endogamous ranked elite represent a portion of the population falling between about 50%

and 10% are best described as tribes. Tribal societies are typically settled in villages

with populations in the hundreds to one or two thousand. As modeled based on theimposed marriage restrictions, these societies are expected to number between, at a

minimum, 400 and 2,000 members. Finally, large endogamous ranked systems where the

elite represent a small portion of the overall population (e.g. less than 10%) are bestdescribed as chiefdoms. In this case, elite marriage partners are likely to come from

affiliated neighboring villages, or potentially from within a single large urbanized center,

such as Cahokia. Such social systems are likely to number in the thousands or tens ofthousands.

While these dated terms have been the subject of much anthropological debate since

Service first described them, they provide a heuristic, if simplistic, framework for

understanding some of the underlying goals of this study. No attempt was made to model


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specific societies, such as Algonquian or Iroquoisan social organizations that I have

discussed elsewhere (Jones 2010), rather, my intent was to examine more generalnetwork dynamics that likely relate to these, and many other kin-based systems. My

primary goal to introduce some of the advantages of a social network analysis approach

to studies of social complexity and I hope that the reader will consider how my general

conclusions may relate to their own specific areas of interest.

Methods

Three basic measures were made of the modeled networks. The first ranks actors interms of in-coming network links. This measure is referred to as the indegree or

simply popularity of a vertex (actor) (de Nooy et al. 2005: 189). The number of

incoming links is easily quantified for each actor and provides a measure of socialprestige. Sorting the indegrees of all network actors provides a way to assess each actors

rank within the population. Arbitrary cut-offs permit the ranked list of actors to be

divided into classes of elites and commoners based on the desired proportion of eachin a given model simulation. Rank divisions only apply to the second group of models,

not to clan-based kinship systems.The second measure determines how well the network is integrated. The simplest

measure of integration is the network diameter. The diameter is most often understood(somewhat confusingly) as the longest shortest path between all vertices in the

network. A shortest pathway through other actors links every two actors in a social

network. The diameter therefore represents the longest of all of these most efficient pathsthrough the entire network. The diameter is measured in terms of the number of steps

required to reach a desired point. This term reflects the popular concept of six degrees

of separation, between two individuals. The difference is that degrees of separationusually indicates the average distance between all actors in a network. (This measure has

only recently been mathematically verified to be 6.6 among the global human network, ashas long been suggested in the popular press.) Average network distance is a useful

value because it reduces much of the variation inherent in modeled networks. The

average network distance is generally significantly less than its actual diameter (forexample, the diameter of the global human social network is about 29). Both measures

are used here to quantify network integration.

A third measure of network integration is the proportion of actors not reachable from

another actor. This can occur in loosely integrated networks, and is also more likely innetworks with directed links between actors. In undirected networks, information

between actors can move either direction along a link (such undirected links are referred

to as edges), but in directed networks, links define the direction of movement (these arereferred to as arcs). The networks modeled are all directed networks, so under some

conditions, actors may fall out of reach of other actors within the network. When

networks become fragmented in this way, information can no longer pass to all of itsmembers, and the network can be qualified as broken or poorly integrated.

These measures can all be provided by a single function within Pajek (Net>Paths

between two vertices>Distribution of distances>From all vertices). Simulations were runthrough the BASIC programs based on each model parameter. The resultant .net files

were then analyzed within Pajek. Because there was no way to iterate this process

automatically, this study is limited to the analysis of 10 samples from each of the nine


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model parameters. Resultant raw data was incorporated into Excel spreadsheets for

statistical analysis and visualization.Because of the probabilistic nature involved in the creation of each network, some

variation in the results of each test is expected. Nevertheless, the sample of 10 networks

under each condition proved sufficient to assess levels of significance between model

parameters. Additional program output (partition files in the .clu format) was used todefine both clan and elite-commoner sub-networks within Pajek. These partitions

allowed the data to be visualized more effectively with Pajeks Draw function (Figure

4). In some cases, commoner sub-networks were extracted from the complete networkusing the partition files (Operations>Extract from network>Partition) to permit additional

analysis of the sub-network. Pajeks Net>Partitions>Degree>Input function was utilized

to produce vector files that were used to scale vertices in the draw window based ontheir number of incoming links. Image files were exported to Encapsulated PostScript

(.eps) from within the Draw window (Export>2D>EPS/PS).

Results

The baseline for all model comparisons consists of a network with no marriagerestrictions and a perfectly even distribution of trade links. This perfect world network

consists in part of a ring-formed chain-like trade network. In graph theory terms, suchnetworks are described as highly clustered, that is, actors are exclusively connected to

their nearest neighbors (Watts 2003). The network also consists of random kinship links.

While the raw trade network has an average distance of 500 steps between its actors, therandom kin ties produce a small world effect (Watts and Strogatz 1998) that create

shortcuts, reducing the average network distance to just 8.66 steps (Figure 5). The

network diameter (longest of all most efficient paths between actors) is just 14 steps. Aswe constrain the network, these distances will increase, indicating a drift from a nearly

random network to one in which there is increasing organization.The first model consists of 100 exogamous clans, seeded by the two pre-established

trade relationships used throughout all of the systems examined. This model of a very

open exogamous clan organization with few marriage restrictions is intended to modelsmall-scale social-economic organization as might be found among highly mobile

foraging societies. Less restricted marriage rules such as these are expected under low

population density conditions where finding an appropriate mate may be logistically

challenging. In North America, Paleoindian and Early Archaic foraging groups werelikely organized in this way. This network organization expresses a significant increase

in average network distance, which is now about 11.7 steps between any two actors.

Most of this change is actually associated with the introduction of the scale-free tradingnetwork rather than the increased restriction on marriage partners. The introduction of the

100 exogamous clans under a balanced trade scenario results in no significant change

from the perfect world results noted above.As marriage restrictions are further increased in the exogamous 10-clan system,

there is an insignificant decline (p=0.477 based on a 2-tailed T-test) in the average

network distance to 11.62. In fact, the same average distance is expressed by the systemwith just two exogamous clans. This indicates that none of these exogamous models

have any significant effect on the network structure once a power-law economic

organization is introduced.


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A subtle, though significant (p=0.0012) change does occur in the system when

identity based on rank is first introduced. This marks an important change in the valuesystem of the society, as suggested by Frieds (1967) original definition of rank as

indicating access to positions ofvaluedstatus. Until this time, clan affiliation was

randomly based, and no realized social value was placed on ones prestige. Some clan

members enjoyed many trade links, while others had few, but this did not affect onessocial identity per se. The ranked 2-clan (moiety) system divides actors into two

groups based on the number of trade links they receive. The half of the population that

receives the most trade partners belongs to the elite clan, and the half that controls theleast belongs to the commoner clan. While this organization seems peculiar, it is not

unprecedented in the ethnographic literature (e.g. as expressed in the ranked Natchez

moiety). Based on the power law distribution of trade links, about two-thirds of actorsreceive no trade link at all, while the remaining third receive one or more links. The net

effect of a bimodal social organization is that the commoner class is isolated from

incoming trade links, while the elite class receives them all. Under exogamous marriagerules, the isolated commoners are reunited with the dense elite network. The net effect is

that the average distance between actors in the network is actually reduced slightly fromthat of the unranked exogamous system.

The next scenario reflects a second value transition within the society. In thisscenario, the elites redefine the marriage rules and enforce an endogamous system to

better maintain control over the trade network. Instead of elites marrying commoners,

elites now marry one another, and commoners do the same. This small change in therules results in a drastic reorganization of the social-economic network. Under

endogamous marriage rules, the commoners now form an isolated kin-network with all

trade links directed toward the elite group. This network is likely to be comprised of anumber of disassociated loops with an average (but highly variable) network distance of

about 170+/-50. The elite enjoy a complex, dense small-world network of kinship andtrade ties. This close network has an average network distance of about 10.15+/-0.18.

Not only does this represent a very effective communication network, it also controls

100% of the trade economy. The 1000 trade links are divided unequally among the 500elite, but provide a mean per-capita wealth of 2 trade ties.

As a whole, the endogamous network comprised of a 50% elite, 50% commoner ratio

must be considered broken. Its average network distance is 30.38, and is highly

variable (+/-17.2). Thus, while the elite sub-network may be enjoying an optimalstructure, the network as a whole is fragmented and communication between many of its

members based on exchange and kin networks cannot occur. On average, 39.8+/-4.5% of

the networks members cannot be reached by its other members. Such a disrupted social-economic structure is not likely to function for any length of time.

There are two options for change. The first is to return to the prior system of ranked

exogamy. This will require the elite to relinquish their complete control over theeconomic wealth in trade partners. The second option is to increase the size of the

commoner network by redefining the cutoff point for elite status. This option actually

benefits both the elites and commoners. The commoners need to attract additionalmembers from among the elite if they hope to participate in the full social-economic

network. The elites can increase their per-capita wealth in trade ties by shrinking their


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numbers so that only those with the greatest number of trade links are counted among

themselves.The net effect of these two goals is likely to move the network in the direction of

additional increased restrictions on marriage. As the definition of who qualifies as an

elite becomes narrower, network functionality is gradually restored. Under the power-

law that underlies this particular system, the benefits of a smaller elite to the overallnetwork are only realized after the elite comprise less than 33% of the network. After

this point, some individuals receiving trade links will be counted among the commoners.

At first, their numbers are few and the links they provide are also limited, but by the timethe network defines the elite class as comprising the upper 20% of incoming trade wealth,

the number of isolated network actors falls on average well below one individual (0.26+/-

0.41).At this point, the network can be seen as restored. With a 20% elite, the average

network distance is still high and remains quite variable (23.6+/-3.5). Elite wealth is

reduced to about 88% of the total (that is, the commoners now have access to 12%), andper-capita trade ties have increased to 4.4. As the definition of elites is constrained to

the wealthiest 10% of the population, the average network diameter drops to 17.3+/-1.2.Elite per capita wealth is increased to about 7 links, and the commoners now have access

to about 31% of the trade network. When the elite comprise 5% of the population, theaverage network diameter drops to 15.5. Elite per capita wealth in incoming trade links

is raised to about 10 links, and the commoners have access to about 49% of the total trade

economy. At 1% of the population, the average network diameter is 12.6, and variationabout the mean is quite low (+/-0.28), indicating the establishment of a relatively robust

and efficient network. Elite per capita wealth averages close to 21 incoming links, while

the commoners control nearly 80% of the remaining network. After this point,increasingly narrowed definitions of the elite continue to reduce the average network

slightly, but even at 0.2% of the population (two individuals in a thousand) the value is11.97+/-0.23, and additional change comes very slowly as the limit is approached. This

limit can be calculated using an exogamous network with no marriage restrictions and an

initial seed of two trade links. Its value is 11.81+/-0.26 based on a sample of 10 suchnetworks, which is not significantly different from the sample of 0.2% elite networks at

this sample size. In sum, the effectiveness of ranked endogamous networks with elites

making up to 1% or less of the overall population begins to approach that observed under

exogamous conditions.

Discussion

The societies modeled above go through two important social transitions based on 1)a revaluation of prestige and a redefinition of identity based on rank and 2) a redefinition

of marriageable partners based on rank. In the first transition, group membership is

linked to ones level of prestige. This is a critical value change that marks the emergenceof rank as an aspect of identity. In the second transition, endogamy provides a means for

one group to monopolize its economic status. The transition to an endogamous marriage

custom redefines group solidarity so that the definition of us and them becomes moreexplicit. Neither of these should be seen as simple transitions, as they are likely to

conflict with the established sense of cosmological order, as expressed in most moiety

organizations.


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In non-judgmental terms reflecting the efficiency of the social networks in question,

the first transition is a good one, because it reduces average network diameter, and thusincreases the effectiveness of communication between its members. This strategy

appears to increase small world network dynamics by effectively combining a pseudo-

random kin network with a power-law-based economic network. The second transition is

disastrous, however. In this case, through separating the two kinship networks, thestrongly biased economic network only reaches half the members of the population. The

society is rent asunder, and communication to half of its members becomes severely

compromised. This may explain why such social constructs are very uncommon in theanthropological literature.

Should the new endogamous rank-based identity structure remain intact (rather than

reverting to the effective exogamous system typified by the example of the Natchez), theonly way to repair the fabric of society is to reduce the overall proportion of those

defined as elites. This benefits the commoners by allowing some members with

incoming trade ties to be included in its kin network, reestablishing opportunities forsociety-wide communication. The benefit to the elite class is an increase in per capita

wealth, at the cost of giving up some control over the economic system. In this way, theelite become more elite and can differentiate themselves more strongly from the

commoner class.A notable transition in the behavior of the new network occurs when the proportion of

elite approaches 1% of the population. At this point, the network is quite well integrated

(with an average diameter of about 12.5) and very few members are likely to be isolatedfrom the overall network. As summarized in Table 1, such a restricted marriage system is

only sustainable in societies numbering about 20,000 members, that is, within chiefdoms.

In fact, the transition to a ranked endogamous social organization is unlikely to occuruntil a local population reaches at least 4,000 members (a 5% elite class), at which point

the transition to a very restricted endogamous elite can occur without compromising theoverall social network stability. Ranked endogamous societies numbering less than 4,000

members (that is, with an elite proportion between 50% and 5%) are simply unlikely to

sustain themselves for any period because of the inherently unstable and fragmentednature of the resultant kinship and economic networks.

Importantly, a tipping point occurs in the economic organization of endogamous elite

networks with an elite class comprising less than 5% of the overall population. At this

time, elite control over the economic portion of the network rapidly falls below 50%. At4% of the population, the elite control on average 45.3% of the economy, but at 2% they

have access to only 35.4% and at 1% only 26.2% (based on 10 sampled networks). This

indicates that in the system modeled above, when the elite comprise less than 5% of thesociety, the commoner class begins to control the majority of the economy.

While this transition is occurring, the commoner class sub-network is becoming

increasingly effective on its own. When the elite represent 5% of the population, thecommoner network diameter approximates that of the full network (average

diameter=16.5+/-0.4 vs. a complete network of 15.5+/-0.7). While the difference

between the two values is significant (p=0.0013 with a 2-tailed T-test), the ranges overlapat 1-sigma. With a 1% elite, the difference between the two networks is less than 1

degree of separation, and there is little incentive for the commoners to continue to take

part in the portion of the trade economy controlled by the elite. They now control on


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average 73.8% of the economy. At this point, it is increasingly likely that the commoners

will abandon the elite, unless other strong incentives keep them in the system.

Conclusions

The use of a Social Network Analysis approach has proven effective at examining a

social-economic model designed to explore the network dynamics of a kin-based socialorganization overlain by a power-law-structured economy. The modeling process itself is

rewarding, as it challenges one to deconstruct traditional (non-state-level) social-

economic dynamics into just a few critical variables. The variables selected in this modelwere related to the definition of marriageable partners and the degree of social value

placed on prestige. These alone appear to have a significant effect on the efficiency of

the social networks examined, as measured by their average network diameters (degreesof separation between actors). Actor prestige was evaluated by the calculation of

incoming economic links and provided a means of establishing the rank of each actor.

The measure of network diameter quantified the efficiency of the movement ofinformation across the entire network. Other factors measured by the Pajek SNA

software included the proportion of actors unreachable by the rest of the network, whichprovided a measure of network viability. The proposed relationship between increased

marriage restrictions and degree of social complexity is, to my knowledge, a new one, butit appears to have functioned well as a central variable in the models explored here.

Underlying the organization of all of the networks examined was a power-law

distribution in economic ties between actors. This structure was selected because itappears to underlie many natural and human systems that add elements over time. The

nature of the power law was arbitrarily established, and was based on seeding a growing

economic network with just two active participants. A more equitable power lawdistribution could have been modeled by seeding the trade network with a greater number

of actors, but the simplest organization was selected. Only by seeding the populationwith more than 100 or so initial trade partners can one move beyond the general rule that

only about a third of the population receives any incoming economic links at all. The

primary effect of altering the strength of the power-law distribution in the economy is onthe point at which the commoner class controls more than 50% of the economy. In the

model presented above, this transition occurred when the elite class was comprised of the

wealthiest four to five percent of the population. Given a more equitable distribution of

wealth, the commoners will control the majority of the economy sooner (for example,with 300 seeded trade relationships, the commoners will already control over 50% of

trade ties when the elites comprise about 10% of the population).

The models examined suggest that exogamous kin systems become only slightlymore efficient as marriage restrictions (based on a reduction in the number of clans) are

introduced. A system comprised of just two exogamous clans is not very different in its

network topology than a system comprised of 100 clans. Interestingly, a subtle, butsignificant improvement in exogamous network efficiency occurs when individuals

become ranked based on their level of economic prestige, and when that rank defines

their band membership. Such moiety-based exogamous ranked kinship systems typifiedgroups such as the Natchez, likely descendants of a Mississippian chiefdom society.

An important result of this study is the recognition that at some time, under a system

of endogamous elite marriage and as marriage restrictions are increased (as the definition


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of who qualifies as an elite is narrowed), some point will be reached where the

commoners control the majority of the economy. If at this point their own kinshipnetwork is well enough integrated, the commoners may elect to remove themselves from

the elite-controlled network at little organizational cost. A similar balance of elite vs.

commoner control of the economy may underlie the dynamics of many traditional

chiefdom-level organizations. The network study presented here may provide at least apartial explanation of the observed fragility of such systems in the archaeological record.


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Figure 1: The 8-individual kinship organization representing a single actor in thenetwork. Assumes a stable modal population where two children survive to reproduce.

The example shown is patrilocal, with females marrying out and into family units,

forming the kinship links between actors.


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Figure 2: Sample output of BASIC program used to produce the network models. The

output summarizes a 10% elite endogamous kinship network seeded with two trade

partners. The total number of incoming links and the calculated rank of the first 30 actorsare summarized on the right.


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Figure 3: The modeled kin-based economic network simplified with 12 actors.


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Figure 4: Example of Pajek Draw output of 50% elite endogamous network (elite: red,commoner: green). Size of vertex reflects the rank of the actor. Note the isolated

commoner kin chains resulting from this organization.


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20%

elite

10%

elite

5%elite

1%elite

0.5%

elite

0.2%

elite lim

it

Figure 5: Average Network Diameters of the Modeled Networks.

Documents

SNA of Kin-Based social-economic networks