Networks of strong ties

TL;DR

This paper investigates the use of transitivity as a criterion for trusting social ties in covert networks, analyzing the structural effects of removing non-transitive ties and deriving conditions for the emergence of connected components.

Contribution

It introduces a transitivity-based trust model for social networks and analyzes its impact on network connectivity and the formation of trusted subgraphs.

Findings

Removing non-transitive ties preserves a giant component with minimal path length increase

Transitivity-based filtering reduces network complexity while maintaining connectivity

Conditions for the emergence of large trusted components are derived for random graph models

Abstract

Social networks transmitting covert or sensitive information cannot use all ties for this purpose. Rather, they can only use a subset of ties that are strong enough to be ``trusted''. In this paper we consider transitivity as evidence of strong ties, requiring that each tie can only be used if the individuals on either end also share at least one other contact in common. We examine the effect of removing all non-transitive ties in two real social network data sets. We observe that although some individuals become disconnected, a giant connected component remains, with an average shortest path only slightly longer than that of the original network. We also evaluate the cost of forming transitive ties by deriving the conditions for the emergence and the size of the giant component in a random graph composed entirely of closed triads and the equivalent Erdos-Renyi random graph.