1
A kinship network analysis project that began 20 years ago
• French/American: White, Paul Jorion• Michael Houseman/White• NSF support• Pajek team: Batagelj and Mrvar• Laurent Barry• Klaus Hamberger• Isabelle Daillent• French NSF support• Cyril Grange• and many other collaborators on case studies
2
Software & Graphs• Commercial, e.g., GED, Brother’s keeper• P-graph (Pgraph & Bipartite Pgraph) Pajek, R
– Families as nodes linked by parent/♂♀child– Conceptually independent arcs, no edges– DAG, generations computed, adjusted with dates– Permits simulations, easy census, bicomponents
• Ore-graph (Puck)– Individuals as nodes, relations nonindependent– Fuller reporting of marriage census– Analysis of cycle overlaps homom
3
Kinds of kinship analysis
• Statistical Google:• Graph theoretic (e.g., cohesive.blocking)• Manhattan (Controlled) Simulation• Bootstrap• Census• Generative• Temporal• Structural dynamics
4
Example from the wiki page• San Juan Sur• This community network has 75 nodes and an average density of 4
to 5. Takes less than a minute to run. Uses cutsetHeuristic=FALSE to avoid an algorithm error.
• http://intersci.ss.uci.edu/wiki/Vlado/SanJuanSur.net source("http://intersci.ss.uci.edu/wiki/Vlado/MW_SanJuanSurNet.R")
• • The chapter 3 San Juan network data from de Nooy, Batagelj, and
Mrvar 2005 (Jim Moody drawing)• Vlado Batagelj extracted only the kinship visiting portion of the
San Juan Sur network, which works with the default (cutsetHeuristic=FALSE)
• source("http://intersci.ss.uci.edu/wiki/Vlado/MW_SanJuanSur_kin.R")
• Copy and paste into R to run– Data at one URL– Algorithm at another URL– Commands at a 3rd URL
5
Example from the wiki pagerequire(igraph)
require(digest)
require(RSQLite)
g <- read.graph(file="http://intersci.ss.uci.edu/wiki/Vlado/SanJuanSur.net", format="pajek")
source("http://www.charting1968.net/CohesiveBlocks.R")
gBlocks <- cohesive.blocks(g,verbose=TRUE,cutsetHeuristic=FALSE)
plot.bgraph(gBlocks,layout=layout.kamada.kawai,vertex.size=13) max.cohesion(gBlocks) [1] 2 2 2 2 2 2 3 2 3 2 2 2 2 3 3 2 3 3 3 3 3 3 3 3 3 2 2 3 3 3 3 3 3 3 3 3 3 3[39] 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 2 1 2 3 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3>
6
7
Example: San Juan Sur small farmers and Atirro Hacienda (Turrialba, Costa Rica): visiting among families & other vars. K-cohesion predictions in a kinship community
K-cohesion and kinshipDoug White, INSNA, 2009
8
Charles P. Loomis and Reed M. Powell 1949 Sociometric Analysis of Class Status in Rural Costa Rica - A Peasant Community Compared with an
Hacienda Community Sociometry 12(1/3): 144-157.
A peasant family-sizedfarming community
12 cliques and outliers for visiting patterns among families
black nodes: rated by 10 judgesas lower class
white area = % rated as higherclass
9
Preview of Summary• A well-known example (San Juan Sur) discussed by
de Nooy, Mrvar and Batagelj 2006 shows that adding the time dimension and fitting visiting patterns to those of P-graphs produces useful hypotheses for an ethnographic case study. Further, cohesive.blocking measurement (k-cohesion) correlates with social status. The Hacienda community has a completely different structure.
• P-graph (Pgraph, Pajek, R), & Bipartite P-graph– Conceptually independent arcs, no edges– DAG, generations computed, adjusted– Permits simulations, easy marriage census, bicomponents, and
cohesive.blocking (Structural Cohesion)
10
• Example: San Juan Sur (Turrialba, Costa Rica) visiting among families & other vars. This is a family-based social organization of small farmers.
• Hypothesis 1: The visiting patterns follow a P-graph/P-systems pattern for families– Test with Triads census actual/expected ratio– DAG Test for oriented ties, 0 exceptions, giant
component size c=46, p=1/2(c-1) = 3 x10-14 (ci=1:4 = 46,4,3,3)
Hypothesis 2: K-cohesion in kin visits predicts social class differences, community leadership
11
• Example: San Juan Sur (Turrialba, Costa Rica) visiting among families & other vars. This is a family-based social organization of small farmers.
• Hypothesis 1: The visiting patterns follow a P-graph/P-systems pattern for families
• Test with Triads census actual/expect (ratio)– Visit H & W parents, they visit 11:0.07 (160:1)– Hierarchical to GrandPar 9:0.14 (60:1)– Pairwise to Parent only 2543:109 (23:1)– Noncohesive line to GrPar 81:5.5 (15:1)
Hypothesis 2: K-cohesion in kin visits predicts social class differences, community leadership
12
San Juan Sur (Turrialba) kinship network Bicomponent level 3=red 2=green 1=yellow 0=white nodes lines – kin visits purple lines=reciprocal visits red arrows=directed visits
Nodes are families – arrows are DAG - like P-graph– most visiting with parents, CoP
13
Kinship cohesion with social class• Cohesion Lower Higher Class Status
– Low (0-1) 18 4– Hi (2-3) 24 29
– p=.003 Fisher exact test Likelihood Ratio 9.03 V=0.335
EntailmentsHigh status High cohesionLow Cohesion Low status
Class status judgments by 10 local informantsVisiting kin reported in 75 family interviews
In 4 families the visiting is complete reciprocal triadic and the correlation with Class Status is Spearman’s = .31 but p=n.s.
14
San Juan Sur (Turrialba) kinship network Bicomponent sizes 39=gold - 7 - 5 - 3 – 3 line width ~ nonkin – kin – compadres red=symmetric visiting black-asymmetric visiting
Nodes are families – arrows are DAG - like P-graph– most visiting with parents, CoP
15
San Juan Sur (Turrialba) kinship network Bicomponent sizes friendship groups colored; linewidth ~ nonkin – kin + compadres red=symmetric visiting black-asymmetric visiting
Nodes are families – arrows are DAG - like P-graph– most visiting with parents, CoP
16
Seven families are 3-connected (in gold); 86% are in the same friendship group (purple)
17
Seven families are 3-connected (Moody-White algorithm implemented in R by Peter McMahan)
18
San Juan Sur (Turrialba) kinship network Bicomponent sizes status groups darker&color; linewidth ~ nonkin – kin + compadres red=symmetric visiting black-asymmetric visiting
Do two of the higher status groups have country cousins?
19
San Juan Sur (Turrialba) kinship network Bicomponent sizes friendship groups colored; linewidth ~ nonkin – kin + compadres red=symmetric visiting black-asymmetric visiting
Nodes are families – arrows are DAG - like P-graph– most visiting with parents, CoP
20
San Juan Sur (Turrialba) kinship network Bicomponent sizes leaders in ored; linewidth ~ nonkin – kin + compadres red=symmetric visiting black-asymmetric visiting
Like the death notices, Leaders are distributed (Spearman’s =..55 with status)3-connected (Spearman’s =.41 with status)
21
Seven families are 3-connected or k=3-cohesive (Cramer’s V =.41 with status)
And if we add death-notifications, which occur not with close relatives but at a distance, many many more become 3-connected.
The algorithm for cohesive.blocking computes k-cohesion (implements Moody-White structural cohesion in iGraph (in R) - by Peter McMahan)
22
Atirro: Hacienda-type farming community
No ritual kin; few kin relations, mostly nonkin; neither kin nor nonkin visiting cohesion has correlates with class status.
Kin visiting correlated with lowest class status
Largest connected kinset (status 0) has one tie to one highest status (10) family. Patron-client.
23
Kin Visiting order upwards correlates with class status 1-10 Spearman’s = -0.08
Kin cohesion correlates with class status 1-10 Spearman’s = 0.11 BOTH NonSignif
Attiro (Atirro) Hacienda:
No Kinship visiting correlates (Class status colors for 0, 1, 4, 5, 7. 10)
24
NonKin Visiting BICOMPONENT correlates with class status 1-10 Spearman’s = 0.44
NonKin Visiting COHESION 0-3 correlates with class status 1-10 Spearman’s = 0.33 NonKin Visiting INDEGREE 0-13 correlates with class status 1-10 Spearman’s = 0.33
Attiro (Atirro) Hacienda:
Non-kinship visiting correlates (Class status colors for 0, 1, 4, 5, 7. 10)
25
Summary• A well-known example (San Juan Sur) discussed by
de Nooy, Mrvar and Batagelj 2006 shows that adding the time dimension and fitting visiting patterns to those of P-graphs produces useful hypotheses for an ethnographic case study. Further, cohesive.blocking measurement (k-cohesion) correlates with social status.
• P-graph (Pgraph, Pajek, R), & Bipartite P-graph– Conceptually independent arcs, no edges– DAG, generations computed, adjusted– Permits simulations, easy marriage census, bicomponents,
and cohesive.blocking (Structural Cohesion)
26
For my intent San Juan isn't a perfect example of overlaying kinship and other ties and then doing cohesive blocking (which is now working in R and thus computable from Pajek), but it is close enough and proved worthwhile. The asymmetric visiting was mostly to kin and ritual kin, and the fact it that it met the DAG condition with a mean of two nodes outbound is consistent with visiting parents and godparents. This enabled me to set up a time dimension rather like a P-graph. There is then broader symmetric visiting in the neighborhood of these vertical family links, and for the more clustered part of the network these were indeed kin or ritual kin ties. One group was more exclusively kin oriented. The neighborhood clusters corresponded well with interfamily friendship groups. Death notices fan out beyond close kin. Some 3-connectivity was found almost exclusively in the more kin oriented family cluster. So this seemed to work. Some of the ties are likely to be indirectly gendered in terms of "visiting husband's kin" versus "visiting wife's kin" I could gender the "P-graph"-like aspects of the intergenerational ties. I asked [[Wouter de Nooy]] if there were more data from the Loomis project and he responded that he had coded all the data from 1948 Turrialba book, but also located an on-line article in pdf from 1949.
27
• .../Documents/ppt/ppt/INSNA
• Pajek/…Ch3
