The Entropy of Graph Embeddings: A Proxy of Potential Mobility in Covid19 Outbreaks

In this paper, we propose a proxy of the \(R_0\) (reproductive number) of COVID-19 by computing the entropy of the mobility graph during the first peak of the pandemic. The study was performed by the COVID-19 Data Science Task Force at the Comunidad Valenciana (Spain) during 70 days. Since mobility graphs are naturally attributed, directed and become more and more disconnected as more and more non-pharmaceutical measures are implemented, we discarded spectral complexity measures and classical ones such as network efficiency. Alternatively, we turned our attention to embeddings resulting from random walks and their links with stochastic matrices. In our experiments, we show that this leads to a powerful tool for predicting the spread of the virus and to assess the effectiveness of the political interventions.