Algebraic Models for Social Networks Book

	List of figures and tables
	Preface
1	Algebraic representations for complete social networks	1
	Complete network data	5
	Sources of network data	13
	Structure in social networks	20
	Properties of a structural representation	32
	An algebra for complete social networks	36
2	Algebraic representations for local social networks	56
	Types of local networks	58
	An algebra for local social networks	62
	Role algebras	73
	Partial networks and partial role algebras	81
	Partially ordered semigroups and role algebras: A summary	88
3	Comparing algebraic representations	90
	Isomorphisms of network semigroups	91
	Comparing networks: Isotone homomorphisms	96
	Lattices of semigroups and [pi]-relations	104
	Local networks with isomorphic local role algebras	116
	Comparing local role algebras: The nesting relation	119
	Other classes of networks with identical algebras	123
4	Decompositions of network algebras	135
	Decompositions of finite semigroups	137
	Direct representations	138
	Subdirect representations	146
	Factorisation	152
	A decomposition procedure for role algebras	166
5	An analysis for complete and local networks	172
	An analysis for complete networks	173
	Relational conditions of semigroup homomorphisms	173
	The correspondence definition	190
	An example: Relational structure in a self-analytic group	201
	Local networks	206
	A correspondence definition for local role algebras	208
	Some applications	212
6	Time-dependent social networks	224
	A language for change	225
	Some relational conditions for smooth change	226
	An analysis of time-dependent blockmodels	228
	A local role analysis of time-dependent blockmodels	234
7	Algebras for valued networks	238
	The semigroup of a valued network	238
	Local role algebras in valued local networks	247
	Using valued network algebras	250
8	Issues in network analysis	251
	Describing social context: Positions and roles	251
	The structure and content of relations	253
	Some models for relational structure	256
	Describing common structure	261
	Social structure	270
	Analysing large networks	271
	References	273
	Appendix A: Some basic mathematical terms	289
	Appendix B: Proofs of theorems	292
	Author index	303
	Subject index	307