Dynamic Network Discovery via Infection Tracing

TL;DR

This paper introduces a new model and algorithms for discovering temporal networks from infection data, extending static graph methods to more accurately reflect real-world dynamic interactions, with theoretical and experimental validation.

Contribution

It presents a novel model for temporal graph discovery, algorithms with tight bounds, and analysis of infection dynamics in changing networks, broadening understanding of temporal infection processes.

Findings

Algorithms often tight bounds for temporal graph discovery

Uncovered threshold behavior in Erdős-Rényi graphs

Experimental validation on real-world interaction data

Abstract

Researchers, policy makers, and engineers need to make sense of data from spreading processes as diverse as rumor spreading in social networks, viral infections, and water contamination. Classical questions include predicting infection behavior in a given network or deducing the network structure from infection data. Most of the research on network infections studies static graphs, that is, the connections in the network are assumed to not change. More recently, temporal graphs, in which connections change over time, have been used to more accurately represent real-world infections, which rarely occur in unchanging networks. We propose a model for temporal graph discovery that is consistent with previous work on static graphs and embraces the greater expressiveness of temporal graphs. For this model, we give algorithms and lower bounds which are often tight. We analyze different variations of the problem, which make our results widely applicable and it also clarifies which aspects of temporal infections make graph discovery easier or harder. We round off our analysis with an experimental evaluation of our algorithm on real-world interaction data from the Stanford Network Analysis Project and on temporal Erd\H{o}s-Renyi graphs. On Erd\H{o}s-Renyi graphs, we uncover a threshold behavior, which can be explained by a novel connectivity parameter that we introduce during our theoretical analysis.