# Zero-one laws for connectivity in random key graphs

## TL;DR

This paper proves a zero-one law for the connectivity of random key graphs, which model wireless sensor networks, under realistic conditions as the network size grows large.

## Contribution

It establishes a new version of the zero-one law for connectivity in random key graphs, improving upon previous work with more applicable assumptions.

## Key findings

- Connectivity probability approaches 0 or 1 as network size increases.
- Results are applicable under realistic conditions for wireless sensor networks.
- Strengthens previous conjectures and theoretical understanding.

## Abstract

The random key graph is a random graph naturally associated with the random key predistribution scheme of Eschenauer and Gligor for wireless sensor networks. For this class of random graphs we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. The results reported here complement and strengthen recent work on this conjecture by Blackburn and Gerke. In particular, the results are given under conditions which are more realistic for applications to wireless sensor networks.