Network reachability of real-world contact sequences

TL;DR

This paper investigates how quickly information or diseases spread in real-world contact networks by analyzing reachability times and ratios, highlighting the importance of network core, clustering, and contact order.

Contribution

It introduces measures of network reachability in contact sequences and demonstrates their dependence on network structure and contact ordering using empirical data.

Findings

Network reachability depends on a core with short paths and frequent communication.

Clustering of contacts in time tends to decrease reachability.

The order of contacts significantly affects dynamical spreading processes.

Abstract

We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time -- the average shortest time for a series of contacts to spread information between a reachable pair of vertices (a pair where a chain of contacts exists leading from one person to the other) -- and the reachability ratio -- the fraction of reachable vertex pairs. These measures are studied using conditional uniform graph tests. We conclude, among other things, that the network reachability depends much on a core where the path lengths are short and communication frequent, that clustering of the contacts of an edge in time tend to decrease the reachability, and that the order of the contacts really do make sense for dynamical spreading processes.