Efficient limited-time reachability estimation in temporal networks

TL;DR

This paper introduces a highly efficient method for estimating limited-time reachability in large temporal networks, enabling new large-scale analyses of spreading processes and network dynamics.

Contribution

The authors develop a novel approach that significantly improves the efficiency of reachability estimation in temporal networks, scalable to hundreds of millions of events.

Findings

Method achieves orders of magnitude speedup over simulations

Enables analysis of large-scale temporal networks on commodity hardware

Facilitates new insights into spreading processes and network centralities

Abstract

Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited waiting-time processes, and they are particularly important for systems modelled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting time temporal paths from a source node and time. We propose a method yielding orders of magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in- or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyse reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak.