Constructing algebraic models for local social networks using statistical methods

Abstract In this paper we discuss the construction and fitting of structural models for local, or ego-centered, social networks. We define partial algebraic structures from the collection of network paths having a focal individual as their source. Such structures are constrained in part by different methods of local network data collection. We present a statistical method for deriving algebraic representations from local network data. The method relies on a statistical strategy for evaluating algebraic relations and is sensitive to the various constraints associated with methods of data collection. The outcome of the method is a set of partial algebras constructed from network paths with a fixed, maximum length.