With the domestic and international spread of the COVID-19, much attention has been given to estimating pandemic risk. 1, 2 We propose the novel application of a well-established scientific approach, network analysis, [3] [4] [5] [6] [7] [8] [9] [10] to provide a direct visualisation of the COVID-19 pandemic risk. By showing visually the degree of connectedness between different regions based on data that are readily available (such as reported confirmed cases of COVID- 19) , network analysis offers a relatively simple yet powerful way to estimate the pandemic risk.
Network analysis has been used for many decades to assess connectedness and systemic risk in financial and banking sectors. [10] [11] [12] In the financial system, a collection of interconnected institutions with mutually beneficial business relationships (e.g. contribution is to construct a pandemic network for studying the relationship of changes in the number of confirmed cases. We also argue that when applying network analysis to a pandemic situation, the degree of connectedness between the regions can help visualise the pandemic risk.
In medical research, network analysis has also been used in studying gene coexpression, disease co-occurrence, and topological dynamics of the spread of infectious disease. 8, [13] [14] [15] Network analysis is relatively easy to execute as it uses data readily accessible, such as publicly available confirmed number of cases in databases. 14 Here, we retrieved the number of confirmed COVID-19 cases in China from late January to March 2020 and constructed plots of confirmed cases for nine time periods (Period 0 to 8) ( Figure 1A ). 17, 18 We also retrieved the number of confirmed cases worldwide (excluding China) for the same time periods and constructed the plots (Figure 2A ). 19 Next, we constructed network graphs based on the correlation of changes in the number of confirmed cases between two geographical areas (e.g. provinces). If the correlation is >0.5, the two areas are connected in a network. Below are the summary steps in constructing the network Calculate the daily changes in the square-root of newly confirmed cases, i.e.
. [20] [21] Statistically, the 'square-root transformation' is to make the transformed counts more stable. Network connectedness provides more timely prediction on pandemic risk than relying on the raw data of daily confirmed cases. In Figure 1B suggesting that the situation in Europe and America was getting worse. There is sign of decrease in connectedness in Period 8 (Mar 19 -Mar 25) ( Figure 2J ) though the number of daily confirmed cases did not soar until Period 8 ( Figure 2A ).
We have demonstrated that, compared to just relying on reported confirmed cases of COVID-19, network analysis can provide a powerful and clearer visualisation of the pandemic risk through the degree of connectedness in pandemic network graphs. Being data-driven and based on data that are readily accessible, network analysis can supplement traditional modelling techniques to enhance estimation of pandemic risk and provide more timely evidence to inform preparedness plans. 