Kinship networks and discrete structure theory: Applications and
implications
White DR, Jorion P
SOCIAL NETWORKS
18 (3): 267-314 AUG 1996
Abstract:
Confusions between substantive
and relational concepts of kinship as a social network have led to a number of
problems that are clarified by a temporally ordered relational theory of network
structure. The ordered-network approach gives rise to a novel means of graphing
the social field of kinship relations, while allowing kinship to be locally
defined in culturally relative terms. Its utility is exemplified in applications
to kinships among US Presidents, Old Testament Canaanites, and native
Australians of Groote Eylandt. The formal concepts treated in the mapping of
kinship networks are: kinship axioms, parental graph structure, core, circuits
of consanguineally and affinally linked kin, sides and divides, homeomorphic
mappings, homomorphisms as potentially simplifying mappings of kinship,
elementary structure, and order-structure. Representational theorems are proven
about homeomorphisms, cores and circuits, and the ambiguity of elementary
structures. The last set of theorems leads to clarifying and redefining some of
the basic concepts of elementary, semi-complex and complex structures of kinship
in terms of properties of generationally ordered networks. The conclusions of
the formal argument are 'post-structural' in the narrow sense of demonstrating
the need for specifying contingent historical processes in the structural
analysis of kinship as a social field. The open-ended approach to change, one
that is implied by the study of ordered structures that unfold in a temporal
succession, connects to issues of population variability, selection, and
evolutionary processes. The kinship structures that are mapped in this approach
are not intended as any sort of complete representations of kinship 'systems',
but merely as scaffoldings that help to bring into view kinship as a social
field, providing a baseline for other mappings (which may be superimposed) of
social processes such as communicative fields, exchange processes, transmission
of learned behaviors, social rights and inheritance, political and religious
succession, and the like.
Addresses:
White DR, UNIV CALIF IRVINE,INST MATH BEHAV
SCI,IRVINE,CA 92717
MAISON SCI HOMME,F-75006 PARIS,FRANCE
Publisher:
ELSEVIER SCIENCE BV, AMSTERDAM