Category-Based Routing in Social Networks: Membership Dimension and the Small-World Phenomenon (Short) by David Eppstein, Michael T. Goodrich, Maarten Löffler, Darren Strash, and Lowell Trott.
Abstract:
A classic experiment by Milgram shows that individuals can route messages along short paths in social networks, given only simple categorical information about recipients (such as “he is a prominent lawyer in Boston” or “she is a Freshman sociology major at Harvard”). That is, these networks have very short paths between pairs of nodes (the so-called small-world phenomenon); moreover, participants are able to route messages along these paths even though each person is only aware of a small part of the network topology. Some sociologists conjecture that participants in such scenarios use a greedy routing strategy in which they forward messages to acquaintances that have more categories in common with the recipient than they do, and similar strategies have recently been proposed for routing messages in dynamic ad-hoc networks of mobile devices. In this paper, we introduce a network property called membership dimension, which characterizes the cognitive load required to maintain relationships between participants and categories in a social network. We show that any connected network has a system of categories that will support greedy routing, but that these categories can be made to have small membership dimension if and only if the underlying network exhibits the small-world phenomenon.
So, if identity is a social construct and the result of small-world networks, then we may need a different kind of precision (from scientific measurement) to identify subjects.
Perhaps the reverse of 20-questions, how many questions do we need for a particular subject? Does anyone remember if there was a common number of questions that were sufficient for the 20-questions game?