A testing example for positional analysis techniques

TL;DR: A decomposability metric that assesses the deviation of a real network from the ideal one that contains only perfect hierarchical subgroups is described and suggested how it can be used in a complementary way to Generalized Blockmodeling for hierarchical decomposition.

TL;DR: A novel formalization of roles in social networks that unifies the most commonly used definitions of role equivalence is proposed and a single, straightforward proof that role equivalences form lattices is obtained.

TL;DR: A novel formalization of roles in social networks is proposed that unifies the most commonly used definitions of role equivalence and obtains a single, straightforward proof that role equivalences form lattices.

TL;DR: This chapter introduces definitions of equivalences from the field of network analysis and discusses algorithms to unearth network nodes that are equivalent from each definition, and measures to approximate this equivalence on large networks.

TL;DR: In all substantive contexts it is necessary to determine if a particular definition of equivalence is appropriate and the extent to which the computational algorithm faithfully mirrors the equivalence definition.

TL;DR: By considering the relative centralities of points connected by an edge, the symmetric graph is decomposed into two asymmetric graphs that provide the input for the regular equivalence algorithm, REGE, of White and Reitz (1983).

TL;DR: The appropriate task in using multiple methods to study the structure of a social network is not to use them all to see what they converge on, but to select the structural properties of critical interest and use the tools most appropriate for those properties.

TL;DR: In this paper, Doreian's solution, which is called the "Doreian Split", is creative and practical, and yields intuitively satisfying results if there really is a problem.