Algebraic models for social networks / Philippa Pattison.
Addressing the need for new models for the analysis of social network data, Philippa Pattison presents a unified approach to the algebraic analysis of both complete and local networks. The rationale for an algebraic approach to describing structure in social networks is outlined, and algebras repres...
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Full Text (via Cambridge) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY, USA :
Cambridge University Press,
1993.
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| Series: | Structural analysis in the social sciences ;
7. |
| Subjects: |
Table of Contents:
- 1. Algebraic representations for complete social networks. Complete network data. Sources of network data. Structure in social networks. Properties of a structural representation. An algebra for complete social networks
- 2. Algebraic representations for local social networks. Types of local networks. An algebra for local social networks. Role algebras. Partial networks and partial role algebras. Partially ordered semigroups and role algebras: A summary
- 3. Comparing algebraic representations. Isomorphisms of network semigroups. Comparing networks: Isotone homomorphisms. Lattices of semigroups and [pi]-relations. Local networks with isomorphic local role algebras. Comparing local role algebras: The nesting relation. Other classes of networks with identical algebras
- 4. Decompositions of network algebras. Decompositions of finite semigroups. Direct representations. Subdirect representations. Factorisation. A decomposition procedure for role algebras
- 5. An analysis for complete and local networks.
- An analysis for complete networks. Relational conditions of semigroup homomorphisms. The correspondence definition. An example: Relational structure in a self-analytic group. Local networks. A correspondence definition for local role algebras. Some applications
- 6. Time-dependent social networks. A language for change. Some relational conditions for smooth change. An analysis of time-dependent blockmodels. A local role analysis of time-dependent blockmodels
- 7. Algebras for valued networks. The semigroup of a valued network. Local role algebras in valued local networks. Using valued network algebras
- 8. Issues in network analysis. Describing social context: Positions and roles. The structure and content of relations. Some models for relational structure. Describing common structure. Social structure. Analysing large networks
- Appendix A: Some basic mathematical terms
- Appendix B: Proofs of theorems.