Constructing algebraic models for local social networks using statistical methods
Two types of social networks can be distinguished in the social network literature. The first is a complete network, comprising a collection of individuals and a set of relations recording their interpersonal links of various types. In many studies, complete networks are assumed to posses a boundary that is transparent to network members, so that members express some agreement about network composition. The second type of network is a local (or ego-centered) one and, by contrast with a complete network, is rarely assumed to possess a boundary that is recognised by all network participants. Instead, the network records the relations of various kinds among a focal individual, termed ego, and those individuals, termed alters, in ego's ``immediate'' or extended social circle. Often, data on local networks are gathered using survey techniques, so that statistical techniques for the analysis of local networks can be difficult to apply. The focus of this paper is on the analysis of local social networks. We examine the relationship between algebraic constructions for local networks and methods for obtaining local network data, and we argue that it is useful to adopt a method-sensitive statistical approach to the evaluation of algebraic relations. We begin with a discussion of the different types of local networks that arise in practice, followed by a review of the basic concepts of algebraic modelling. We then introduce a statistical approach to the construction of algebraic models, specifying the steps necessary to find an algebra based on statistical evaluations of algebraic relations. The constraints placed on relations due to data-collection techniques can be quite easily incorporated into our approach. We conclude with an illustrative example.
algebraic constructions for local networks
scientific article; zbMATH DE number 792513