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Block modeling and equivalence. Christopher McCarty October 23, 2012. Introduction. Social structures are often not simply the pattern of interaction between nodes that are equal There are positions within social structure and roles (expectations) associated with those positions

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Block modeling and equivalence

Block modeling and equivalence

Christopher McCarty

October 23, 2012


Introduction
Introduction

  • Social structures are often not simply the pattern of interaction between nodes that are equal

  • There are positions within social structure and roles (expectations) associated with those positions

    • Parent-Child

    • Manager-Employee

    • Advisor-Student

  • The idea of block-modeling and equivalence is to discover roles that are emergent (not named)



Blocks
Blocks

  • Procedures to find subsets of a graph that are distinct from other sets

  • Bi-component – Identifies parts of a graph that are vulnerable to disconnection using cut-points

  • Factions maximize local density

  • Think of block-modeling as creating subsets that have similar profiles of connections



Factions
Factions

  • Because it is easy to use in UCINET

  • Factions is a sort of “relaxed” blockmodeling, based on the hypothesis testing that the network is composed by only two types of blocks (null between clusters, and complete within clusters) – structural equivalence

  • It is deductive and direct because you can manipulate the raw data, pre-specify the number of factions and interpret it based on goodness of fit.



Concor convergence of iterated correlations
Concor(CONvergence of iterated CORrelations)

  • Create correlation matrix

  • Split matrix into two blocks so members of the same block are positively correlated

  • Blocks are successively split

  • Blocks containing only two nodes are not split any more


Concor on class data standard and interactive
CONCOR on class data (standard and interactive)



Graph of Equivalence Classes (Wasserman and Faust, 1994)Structural equivalents (the same relationships): {A}, {B}, {C}, {D}, {E,F}, {G}, {H,I}Automorphic equivalents (the same positions): {A}, {B,D}, {C}, {E,F,H,I}, {G}Regular equivalents (the same kinds of relationships): {A}, {B,C,D}, {E,F,G,H,I}


Some conclusions
Some Conclusions

  • You should try different partitions of your network based on attributes and relations

  • You can try block models as exploratory analysis

  • If you have good ideas (based on theory and experience), you can test some hypotheses

  • Blockmodeling is less sensitive to large and sparse networks (in this case, you should consider blocking the components or big clusters)

  • There’s no right solution, only optimal. Try as many solutions as possible


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