Structural Models in Anthropology ( Cambridge Studies in Social and Cultural Anthropology )

Publication series :Cambridge Studies in Social and Cultural Anthropology

Author: Per Hage; Frank Harary  

Publisher: Cambridge University Press‎

Publication year: 1984

E-ISBN: 9780511868542

P-ISBN(Paperback): 9780521273114

Subject: C912.4 cultural anthropology, social anthropology

Keyword: 文化人类学、社会人类学

Language: ENG

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Structural Models in Anthropology

Description

Hage and Harary present a comprehensive introduction to the use of graph theory in social and cultural anthropology. Using a wide range of empirical examples, the authors illustrate how graph theory can provide a language for expressing in a more exact fashion concepts and notions that can only be imperfectly rendered verbally. They show how graphs, digraphs and networks, together with their associated matrices and duality laws, facilitate the study of such diverse topics as mediation and power in exchange systems, reachability in social networks, efficiency in cognitive schemata, logic in kinship relations, and productivity in subsistence modes. The interaction between graphs and groups provides further means for the analysis of transformations in myths and permutations in symbolic systems. The totality of these structural models aids in the collection as well as the interpretation of field data. The presentation is clear, precise and readily accessible to the nonmathematical reader. It emphasizes the implicit presence of graph theory in much of anthropological thinking.

Chapter

Advantages of graphical models

Implicit and explicit structural models

2 Graphs

Basic definitions

Trees

Blocks

Centrality

3 Signed graphs

Coloring of a graph

Coloring of a signed graph

Structural balance

"Positive and negative relations"

Clustering

4 Digraphs

Definitions

Relations

Axiomatization of relations

Acyclic digraphs

Semilattices

Cyclic structures

Connectedness

5 Graphs and matrices

The adjacency matrix

Matrix operations

The reachability matrix

The distance matrix

6 Structural duality

Duality

Structural duality

Marked graphs

7 Networks

Networks and matrices

Reachability in networks

Flows in networks

Markov chains

8 Graphs and groups

Group models

Groups

Klein groups

"Multiplicative groups"

Larger groups

Conclusion

Appendix: Axiomatics

References

Index

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