1 Data Collection One of the major contributions of this work is a dynamic, heterogeneous, attributed graph that describes various real-world indicators and travel patterns from January 2020 to August 2020. The dataset is divided into two groups to describe global data and domestic US data. Global Covid-19 data model each country as a node in the graph and air-travel between two countries is modeled as dynamic edges. Similarly, the domestic US dataset models each US state as a node and airtravel between them as dynamic edges. This work uses di↵erent indicators curated for the Covid19 dataset extracted from sources such as US Census, Google geocoding, JHU C19 database, etc. The edge data for global passenger flow is simulated from a model developed by Mao et al. [4]. It uses a Poisson regression model to predict monthly passenger volumes between directly connected airports.

We use The Bureau of Transportation Statistics (BTS) [1] to collect open-source domestic US airtravel data. We also repository [2] and Geocoding API to extract temporal data for each US state. We also open source the code to set up the repository and provide instructions to daily update the dataset.

All the data and the data curation pipeline are available at https://github.com/fshelobolin/C19DynamicGraph. 2 Independent Temporal Motif (ITeM) Independent Temporal Motif (ITeM) is an edge-disjoint temporal motif [6] used to model transactional networks [5]. We use ITeM to observe temporal patterns in the Covid-19 travel graph. The ITeM provides insight into the temporal evolution of the travel graph, such as its rate of growth, neighborhood, and the change in the travel pattern of a state over time when modeled as a node in the graph.

We create a dynamic graph to model air travel between di↵erent US states. Each US state is modeled as a node in the graph. We create edges using the total air-travel passenger count. We create a logarithmic bin to reduce the number of edges between any two states for a given day, without the loss of overall travel trends as shown in the Figure 1. We also create a sequence of weekly temporal graphs to measure temporal trends in the Covid-19 air-travel dataset. We generate a weekly average for all Covid-19 indicators. As shown in Figure 2, we qualitatively observe three di↵erent classes of realworld Covid-19 indicators. The "Hospitalization Rate" and the absolute number of "People Hospitalized" in the US averaged over a week show opposite trends. In contrast, indicators such as "Active Cases", "Confirmed Cases", "Deaths" show a slowly-increasing trend over the time window. The "Mortality Rate" does show an initial sharp upward and slowly decreasing trend similar to "Hospitalization Rate" but in contrast to the other indicators. We also compute ITeM distribution for each week and a scalar value for each distribution using Principle Component Analysis (PCA) to compare temporal trends measured using ITeM with the rest of the indicators. As shown in Figure 2, ITeM shows a similar temporal trend as "Hospitalization Rate". To quantify ITeM similarity with the rest of the indicators, we use Dynamic Time Warping (DTW) [3]. DTW measures the similarity (or distance) between two time-series by computing optimal matches between them. We compute the pair-wise distance between all real-world indicators and ITeM distribution for each week from April 2020 to August 2020. We used the degree distribution of the travel graph as the baseline similarity with each indicator. As shown in Figure 3, degree distribution does not show any variation in the similarity with any of the real-world indicators. The overall similarity is as good as with a random time series. In contrast, ITeM distribution in Figure 4 shows an interesting trend as it shows high similarity with average travel and "Hospitalization Rate". Specifically, it shows that the ITeM-based time series has the most similarity (or lowest distance) with "Hospitalization Rate" that corroborate our initial observation as shown in Figure 2.