Category-Based Routing in Social Networks: Membership Dimension and the Small-World Phenomenon (Full)

TL;DR

This paper introduces the membership dimension, a measure of cognitive load in social networks, and shows that small-world networks can support efficient greedy routing with low cognitive complexity.

Contribution

It defines membership dimension and proves its equivalence to small-world properties for enabling greedy routing in social networks.

Findings

Networks with small membership dimension support greedy routing.

Any connected network can support greedy routing with appropriate categories.

Small-world networks have low membership dimension, facilitating efficient message passing.

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.