Measuring global multi-scale place connectivity using geotagged social media data

Shaped by human movement, place connectivity is quantified by the strength of spatial interactions among locations. For decades, spatial scientists have researched place connectivity, applications, and metrics. The growing popularity of social media provides a new data stream where spatial social interaction measures are largely devoid of privacy issues, easily assessable, and harmonized. In this study, we introduced a global multi-scale place connectivity index (PCI) based on spatial interactions among places revealed by geotagged tweets as a spatiotemporal-continuous and easy-to-implement measurement. The multi-scale PCI, demonstrated at the US county level, exhibits a strong positive association with SafeGraph population movement records (10% penetration in the US population) and Facebook’s social connectedness index (SCI), a popular connectivity index based on social networks. We found that PCI has a strong boundary effect and that it generally follows the distance decay, although this force is weaker in more urbanized counties with a denser population. Our investigation further suggests that PCI has great potential in addressing real-world problems that require place connectivity knowledge, exemplified with two applications: (1) modeling the spatial spread of COVID-19 during the early stage of the pandemic and (2) modeling hurricane evacuation destination choice. The methodological and contextual knowledge of PCI, together with the open-sourced PCI datasets at various geographic levels, are expected to support research fields requiring knowledge in human spatial interactions.


Introduction
Since the proposal of "social physics" in 1948 by John Stewart, an astrophysicist who first attempted to reveal spatial interaction based on the concept of the Newtonian gravitational framework (Stewart, 1948), research on modeling, documenting, and understanding human spatial interaction has been a research hotspot in geography and related fields. From a geographic perspective, human movements form the spatial interactions among places, featured by both social (population, land use, culture, etc.) and physical characteristics (climate, geology, landscape, etc.) (Massey, 1994). Relationships among places are shaped by constant human movement, and the intensity of such movement further quantifies the connectivity strength among places. Thus, understanding connectivity between two places provides fundamental knowledge regarding their interactive gravity, benefiting various applications such as infectious disease modeling, transportation planning, tourism management, evacuation modeling, and other fields requiring knowledge in human spatial interactions.
However, measuring such interactions at various spatiotemporal scales is a challenging task. Early efforts (widely adopted until now) to examine spatial interactions involved survey utilization. Researchers used questionnaires to understand spatial interactions, aiming to gauge both long-term spatial movement, such as migration patterns (Barcus and Brunn, 2010;Boyle, 2014;Salt, 1987;), and short-term spatial displacement, such as evacuation and traveling (Buliung and Kanaroglou, 2006;Calantone et al., 1989;Durage et al., 2014;Pham et al., 2020;Santos et al., 2011;Siebeneck and Cova, 2012). The well-documented spatial interactions from these surveys contribute to our understanding of how people move across space and how places are connected; however, such an approach suffers from limitations of small sample sizes (Martín et al., 2020a), limited temporal resolution (Pereira et al., 2013), and resource demands (Martín et al., 2020b).
The limitations of survey-based approaches largely preclude spatiotemporal-continuous observations in spatial interactions, therefore inducing discrete place connectivity measurements.
However, place connectivity should not be considered as a fixed spatiotemporal property of places. Instead, connectivity is ever-changing and evolving rapidly in modern society (Batten, 2001;Gao, 2015;Macdonald and Grieco, 2007). As argued by many, technological advances in the past decades have greatly facilitated connectivity by weakening geographic limits (Tranos and Nijkamp, 2013). To capture the temporal nature of spatial interactions, researchers have emphasized the importance of transportation data that detail people's moving patterns. Place connectivity has been measured using various transportation means that include airline flows (Derudder and Witlox, 2008;Xu and Harriss, 2008), highway traffic (Zhang et al., 2020), railway flows (Yang et al., 2019;Lin et al., 2019), and intercity bus networks (Ghafoor et al., 2014). The rich traffic information and the derived spatial networks greatly facilitate our understanding of how places are connected via these transportation modes. However, transportation-based approaches pose new challenges. First, such data are generally difficult to obtain, as they are often confidential or collected by private companies. Second, the data themselves are mode-specific, lacking the holistic views of the overall human spatial interactions and place connectivity, which are often needed in fields such as infectious disease modeling. A notable effort to tackle the latter issue is by Lin et al. (2019), who constructed a combined intercity connectivity measurement based on multiple data sources for nine cities in China and demonstrated its advantage over the index derived from a single data source. This study offers valuable insights in understanding how cities are connected using a holistic approach. Due to data availability issues, however, it is challenging to construct such a combined index that are spatiotemporal-continuous for a large area (e.g., a country or the entire world) at various geographic settings and scales (e.g., urban, suburb, or rural; county, state/province, or country).
The emerging concepts of "Web 2.0" (O'Reilly, 2007) and "Citizen as Sensors" (Goodchild, 2007), largely benefiting from the advent of geo-positioning technologies, offer a new avenue to actively and passively gather and collect the digital traces left by electronic device holders . For example, passive trace collection involves data obtained from mobile phone data (Amini et al., 2014;Gonzalez et al., 2008), smart cards (Agard et al., 2006;Ma et al., 2013), or wireless networks (Perttunen et al., 2014). The spatial interactions documented from these passively collected traces tend to have high representativeness, given their high data penetration ratios. However, privacy and confidentiality concerns have been raised for such approaches, as individuals do not intend to actively share their locational information and are unaware of the usage of the generated positions (de Montjoye et al., 2018;Kontokosta and Johnson, 2017).
An approach less encumbered with privacy issues is based on spatial information from social media, a digital platform aiming to facilitate information sharing that has been popularized in recent years. Owing to their active sharing characteristics, social media data are less abundant compared to passively collected GPS positions from mobile devices but are less intrusive (Huang et al., 2020a;Jiang et al., 2019a), more accessible (Hu et al., 2020), and more harmonized (Huang et al., 2020b). The huge volume of user-generated content covering extensive areas facilitates the timely need for summarizing human spatial interactions. Twitter, for example, has quickly become the largest social media data source for geospatial research and has been widely used in human mobility studies (Fiorio et al., 2017;Jurdak et al., 2015;Li et al., 2020a;Soliman et al., 2017), given its free application programming interface (API) that allows unrestricted access to about 1% of the total tweets (Hawelka et al., 2014). We believe that the enormous sensing network constituted by millions of Twitter users worldwide provides unprecedented data to measure place connectivity at various spatiotemporal scales.
As an essential component in human interaction, social connections that involve online searching, friendships, account following, news mentioning, and information reposting can also contribute to place connectivity measurement. For example, the co-occurrences of toponyms on massive web documents, news articles, or social media were extracted to measure city relatedness and connectivity (Liu et al., 2014;Hu et al., 2017;. A recent effort from Facebook explores connectivity measurement among places (called Social Connectedness Index, SCI) utilizing the social networks constructed from massive friendship links on Facebook (Bailey et al., 2018). However, whether or how the place connectivity measured by social connections differs from the one measured by physical connections is worth further investigation.
In view of the existing studies, gaps still exist in 1) the effort to construct a global place connectivity measurement that is harmonized, multi-scale, spatiotemporal-continuous based on the physical movement of social media users, 2) examining the utility of the derived place connectivity from a very large area and/or longer time period in solving some real-world problems, and 3) applications to visualize place connectivity at various geographic levels with downloadable and ready-to-use connectivity matrices to support a wider community research needs. Taking advantage of big social media data and the advancement of high-performance computing, we introduce a place connectivity index (PCI) and an array of PCI datastets based on people's movement among places captured from big Twitter data. Specifically, in this study, we computed global PCI from billions of geotagged tweets aggregated at different geographic levels to reveal place connectivity at multipe scales, including world country (inter-country connectivity), world first-level subdivision (inter-state/province, and intra-country connectivity), US metropolitan area (inter-unban area connectivity), US county (inter-city/county connectivity), and US census tract (intra-city connectivity). We compared population movement derived from Twitter data with the SafeGraph (2020) movement data in the US to evaluate how well geotagged tweets captured population movement. We compared PCI with Facebook's SCI, a popular connectivity index based on social networks, to reveal the association between spatial interactions and social interactions. We also investigated the spatial properties of PCI including distane decay and boundary effect.
The utility of PCI is exemplified in two applications: 1) modeling the spatial spread of COVID-19 during the early stage of the pandemic and 2) modeling hurricane evacuation destination choice. The results demonstrate the great potential of PCI in addressing real-world problems requiring place connectivity knowledge. Finally, we constructed massive PCI matrices and launched an interactive portal for users to visualize the strength of connectivity among geographic regions at various scales. The derived global PCI matrices at various geographic scales are open-sourced to support research needs. Serving as a harmonized and understandable connectivity metric, the multi-scale PCI data with the ability to "zoom in" and "zoom out" are expected to benefit varied domains demanding place connectivity knowledge, such as disease transmission modeling, transportation planning, evacuation simulation, and tourist prediction.

Place Connectivity Index
A Place Connectivity Index (PCI) between two places is defined as the normalized number of shared persons (unique Twitter users) between the two places during a specified time period (e.g., one year; Fig. 1). For example, if a user is observed at both places during the time period, the user is considered a shared user between the two places. PCI can be computed at various geographic scales. For example, a place can be a county, state, or country. PCI does not aim to capture the real-time population movement between places (though it is derived from such movement); rather, it provides a relatively stable measurement of how strong two places are connected by spatial interactions. The strength of the connection between two places can be determined by many factors, such as geographic distance (the first law of geography; Miller, 2004), transportation, administrative/regional limits (e.g., states), physical barriers (e.g., rivers and mountains), social networks, demographic and socioeconomic similarities or differences.
The shared users among places derived from Twitter data can be considered as an observable outcome of the combined force of these factors, and thus is modeless, with the understanding of Twitter data limitations (e.g., population bias). In this sense, PCI should be calculated in a relatively long time period (e.g., a year) to gather sufficient information to summarize the general patterns. Following the general geometric average and normalization strategy (Liu et al., 2014;Bailey et al., 2018;Lin et al., 2019), the PCI between place i and place j (denoted as PCIij) is computed by Eq. 1.
where Si is the number of observed persons (unique social media users) in place i within time period T; Sj is the number of observed persons in place j within time period T; Sij is the number of shared persons between places i and j within time period T; and n is the number of places in the study area.
Places with a larger population size tend to have more social media users, and thus tend to have more shared users among them. The denominator in Eq. 1 is used to normalize the metric based on the relative populations in the two places. PCI ranges from 0 to 1. When no shared user is observed between two places, PCI equals 0. If all users in place i visit place j (vice versa) and the two places have the same number of users (or when i = j ), PCI equals 1. PCI provides a relative measurement of how strong places are connected through human spatial interactions when assuming all places have the same population (social media users). This allows us to compare PCI among different places to reveal potential spatial, population, and socioeconomic structures. The PCI derived from Eq. 1 is non-directional. The discussion for a directional PCI capturing the asymmetrical connection forces between two places can be found in Appendix A.

Global PCI Datasets at Various Geographic Levels
The computation of PCI is data-and computing-intensive as it involves billions of geotagged tweets and millions of place pairs at various geographic levels. To address this challenge, the computation was performed in a high-performance computing environment (Li et al., 2020a). The steps for computing the 2019 US county level PCI are detailed in Appendix C.
With Eq. 1, PCI was computed for the following five geographic levels in this study: 1)

Comparing with SafeGraph Population Movement
One of the key concerns of using social media data (e.g., Twitter) for human mobility studies is its low population penetration rate. For example, only 24% of US adults use Twitter (Pew Research Center, 2019), and the public Twitter API only returns about 1% of the whole Twitter streams. A more detailed descriptive statistics of the collected 2019 worldwide geotagged tweets can be found in Appendix B. Also, Twitter data show bias in its representativeness of population groups. This issue has been examined in a few studies Li et al., 2013;Malik et al., 2015). In light of these issues, it is important to evaluate how well geotagged tweets capture population movements (at the county level in this analysis) since PCI is computed from such movement.
For this purpose, we compared the US county-level population movement derived from Twitter to the movement derived from SafeGraph (https://www.safegraph.com), a commercial data company that aggregates anonymized location data from various sources. According to SafeGraph (2019), the data are aggregated from about 10% of mobile devices (e.g., cellphones) in the US, and the sampling correlates highly with the actual US Census populations, with a Pearson correlation coefficient r of 0.97 at the county level. Specifically, the data we used in this study are the publicly available SafeGraph's Social Distancing Metrics (SDM) (SafeGraph, 2020), a census block group level daily mobility data product going back to January 1, 2019 covering the entire US. Since these data only provide aggregated mobility information, deriving the shared users among counties is not possible. Alternatively, we computed the total number of person-day movements between all contiguous US county pairs in 2019 using the SDM (see Appendix D). To make it comparable, we also computed the total number of person-day movements between all US county pairs in 2019 using Twitter data (see Appendix E). We then compared, using Pearson's r, the two person-day movement datasets by county.

SafeGraph person-day movements for all counties (a) Spatial distribution; (b) histogram
The overall Pearson's r for all county pairs (n = 1,516,210) between log Twitter personday movements and log SafeGraph person-day movements is 0.71. The rationale for using log transformation (with base 10) is to address the highly skewed distribution of movements among counties. To reveal the spatial variations of the relationship for different areas, we further evaluated the association between the two movement datasets for the county pairs from each county to other counties. The spatial distribution of r illustrates lower values generally clustering in less populated areas, such as the Great Plains portion of the US (Fig. 3a). This is as expected, as Twitter data generally suffer in less populated areas due to insufficient tweets collected using the public free API. The histogram (Fig. 3b) indicates the most repeated r ranges between 0.65 and 0.75.
To further examine the associations between the two movement datasets and the impact of county population size on the associations, we selected four counties with different geographical contexts and populations ranging from 3,300 to 10,000,000 and plotted the Twitterderived person day movements and SafeGraph-derived person day movements in 2019 for each county. The scatter plots (Fig. 4)

Comparing PCI with Facebook SCI
We contrasted the PCI for each of the US counties with the Facebook Social Connectedness Index (SCI) data (Bailey et al., 2018a). This comparison allows us to evaluate the hypothesis that places connected through (social media) friendship links are likely to have more physical interactions (e.g., population movement). This hypothesis has already been suggested in recent studies (Kuchler et al., 2021) but not corroborated using SCI data. Thus, demonstrating this connection is relevant for many reasons, such as understanding spatial behavior under normal circumstances (e.g., business or commercial relationships, tourism, and migrations) or during extraordinary events such as a pandemic (e.g., the spread of infectious diseases) or a natural hazard (e.g., evacuation corridors).
As a measure of social connectedness based on friendship links on Facebook, SCI revealed that the majority of these links are found within 100 miles, showing an intense distance decay effect (Bailey et al., 2018b). The hypothesis of a positive association between social and spatial connections makes intuitive sense and helps understand population dynamics at different scales. To evaluate this, we first analyzed the correlation between PCI and SCI using all county pairs that had both PCI and SCI values (n = 1,702,531). Log transformation was used to address the highly skewed distribution of the PCI and SCI values among counties. Note that PCI values were multiplied by 1000 before taking the log to avoid negative values. The overall r of 0.62 indicates a strong linear association between social and spatial connections.  with an index of spatial connectivity. The scatter plots also reveal that the association between SCI and PCI is not always stronger in more populated counties (e.g., r for Harris County is 0.66 while for the less populated Horry County, it is 0.75). Another interesting observation is that the slope of the best-fit line is higher in more populated counties (e.g., Los Angeles County) than in lowly populated areas (Ford County), indicating that the same amount of change in friendships (SCI) is associated with a larger change in people's movement (PCI) in more populated counties, vice versa. To further examine the variations of such association among counties, we computed the Pearson's r between PCI and SCI for each county to other counties. Fig. 6a shows that strong correlations are generally clustered in Midwest US, Texas, and Southeast Georgia. The histogram (Fig. 6b) shows the most repeated r ranging between 0.70 and 0.75. The strong association between PCI and SCI confirms the hypothesis that regions connected through (social media) friendship links are likely to have more physical interactions.
However, our findings also suggest caution about the relationship between these two variables.
Although PCI and SCI are associated, one cannot substitute one for the other, as they represent different phenomena: social versus spatial behavior. More studies are needed to better understand the driving forces (e.g., urban-rural, demographic, and socioeconomic factors) behind the associations of the two variables. We believe PCI is an important addition, as it involves a new standardized measure of spatial connectivity based on population movement.

Distance Decay Effect
Our analysis revealed that PCI expresses a clear distance decay effect. In other words, the spatial connectivity between two distant places is likely to be lower than that observed between two near counties. However, there are some nuances in this broad assertion. Fig. 7 illustrates the association between log PCI and the log distance for each county to all other counties. The map ( Fig. 7a) shows that less populated (rural) areas of the Midwest, Pacific Northwest, or Texas have a stronger negative association between PCI and distance, meaning that these communities are more tightly knit with surrounding areas than with more distant communities (stronger distance decay effect). This phenomenon is also reflected in Fig. 8, where R 2 values of the power-law function decrease dramatically from lowly populated Ford County (0.494) to Harris County (0.154) to highly populated Los Angeles County (0.065). Pearson's r was not used as the scatter plot, as the relationship is nonlinear. It should be noted that population size is likely a compounding factor that goes along with urban centers (e.g., metropolis) with large airports.  The maps in Fig. 9 depict how the selected four counties are connected to other counties based on the PCI, which agrees with the above observations. On the other hand, Fig. 9 also shows that highly populated and touristy urban areas (well connected through airports), such as New York City, Miami, Orlando, Chicago, or Las Vegas, act as poles of attraction for people from distant locations. This is clear in Fig. 9a, where we can see how Los Angeles County, for instance, is more closely linked through spatial interactions with the New York City metropolitan area than with some California or Nevada counties. This behavior is also easily detected in Fig. 8 through the outliers of the point distributions in Los Angeles County.

Boundary Effect
Inspired by Bailey et al. (2018b), we also considered the effect of administrative borders shaping spatial connectivity. A higher PCI between a county pair indicates a strong relationship geographically. In a general sense, people tend to travel to their adjacent counties more frequently than non-adjacent counties. However, do the residents near the state border prefer the in-state counties as their destinations rather than the adjacent county across the state border? Or are the out-of-state counties more attractive? If state borders have a role in explaining spatial connectivity, people will tend to travel more within their home states than in neighboring states, even when the distance is fixed.
To evaluate the state boundary effect for each of the four counties, we first ran a linear regression with the following variables: the distance between the county and all other counties in the contiguous US (distance), a categorical variable (same_state), and PCI (as the dependent variable). The result indicates that the same_state variable shows a strong positive effect (p < .001) on PCI even after controlling for distance (Table 1). This implies that these four counties are more tightly (spatially) connected with other counties within the same state, even when compared to nearby counties in other states. Note: * p < 0.1 ** p < 0.05 *** p < 0.01. The county centroid was used for the distance calculation between two counties (distance unit: mile).
To test whether existing state borders are similar to the borders formed when we grouped together the US counties into communities (clusters) based on their spatial connectivity (i.e., PCI), we used a hierarchical agglomerative linkage clustering method following Bailey et al. (2018b) to create such homogenic spatial connectivity communities and compare them with the state administrative division of the US. Hierarchical agglomerative clustering groups county pairs based on their distance in feature space. In our experiment, the "distance" is defined as the inverse of PCI, which means a low PCI in a county pair has a long distance, and vice versa. In the beginning, every county is viewed as a separate community, and the two closest communities are combined into a new community. Distances of combined communities will be updated by the average of distances between county pairs of community pairs. The clustering stops when all counties are combined into a target number of communities. We chose 20, 50, and 75 clusters as the targeted number of communities. As shown in Fig. 10, most resulting distinct communities in the three maps are spatially contiguous, revealing the strong spatial connectivity of neighboring counties, an obvious consequence of spatial proximity. However, the resemblance of these three maps with state boundaries is quite remarkable across many areas, supporting the assertion that state boundaries do play a decisive role in shaping the spatial behavior of the population. For example, we can see how several clusters in the southwest US are essentially the state boundaries. Also, many other smaller clusters also respect the actual state boundaries. This pattern holds in the three maps with different cluster sizes. A strong state boundary effect was also observed in social connectivity with Facebook SCI (Bailey et al. 2018b). These two findings are likely to be related; however, we do not know which one drives the other or if there are other variables conditioning this behavior (e.g., socio-spatial factors based on institutional or administrative circumstances).
Further studies are needed to better understand the state boundary effect of PCI and its connections with SCI.

Applications
PCI can potentially be applied in diverse fields that can benefit from a better understanding of human movement at varying spatial scales, such as infectious disease spread in public health, transportation, tourism, evacuation, and economics. Two examples are provided to exemplify how PCI can be used as a potential factor in analyzing and predicting infectious disease spreading and hurricane evacuation destination choice.

PCI as a Factor in Predicting the Spatial Spread of COVID-19 During the Early Stage
Westchester County was an early (March 2020)  The travel restrictions between the US and Europe were not in place until March 12, 2020 (BBC, 2020). In this application example, we explored the relationship between the spread of COVID-19 and PCIs of the two epicenters at the US county level on a regional scale (Westchester County, NY) as well as the state level on a global scale (Lombardy, Italy).
Given that the incubation period of COVID-19 is about two to three weeks (Lauer et al., 2020), the number of cases confirmed before the end of March was used in the later calculation to capture the spread of COVID-19 in early and mid-March for the US county level analysis. Fig.   12 shows the county-level infection rate (number of confirmed cases per 10,000 people) as of March 31, 2020. The number of confirmed cases is based on the New York Times (2020) database, and the total county population is based on the ACS five-year estimation (US Census,

2019). Dark red spots show the hotspots of COVID-19 confirmed cases. Westchester County and
surrounding New York City areas were the main hotspots at the end of March. To explore whether outbreaks of COVID-19 in the US are related to people who fled away from New York City in early March (Carey and Glanz, 2020), we used a linear regression model to examine the relationship between COVID-19 infection rate (as a dependent variable) and the connectivity between a given county and Westchester County using four measurements, including PCI computed with 2018 and 2019 Twitter data, respectively, Facebook SCI as of August 2020, and 2020 SafeGraph movement data (the person-day movements computed with the method in Appendix D using data from January to March, 2020). Note that PCI was scaled by 1000 in the regression models to ease the result presentation.   and Lombardy, Italy (Fig. 13a). As shown in Fig. 13b, PCI with Lombardy exhibited a strong positive association with the US state level COVID-19 infection rate at the early stage of the pandemic (r = 0.48, n = 50, p < 0.01).

Findings in this application suggest that the multi-scale PCI, computed from historical
Twitter data, is a promising indicator in predicting the spatial spread of COVID-19 during the early stage, outperforming more current Facebook SCI (data as of August 2020) and SafeGraphderived person-day movement data (from January 1 to March 31, 2020) at the US county level.

PCI as a Factor in Predicting Hurricane Evacuation Destination Choices
Evacuation of coastal residents has been an effective and important protective action before the arrival of a hurricane (Cutter and Smith, 2009). Understanding where coastal residents are evacuating helps in evacuation route planning and resource allocations (Cheng et al., 2008).
Residents of a county are likely to evacuate to a county where they have established relationships (friends, colleagues, familiar lodging stays, etc.). The preexisting relationships would be expressed by the PCI or SCI. In this section, we examined the association between PCI (computed using the 2019 Twitter data) and people's evacuation destination choice using Hurricane Matthew in 2016 as a case study. We hypothesize that people are more likely to evacuate to a county that has a high PCI with the evacuation county (the county being evacuated). For comparison, we also tested the hypothesis that people are more likely to evacuate to a county that has a high SCI with the evacuation county.
Hurricane Matthew was a Category 5 hurricane that visited the east coast of the US at Charleston County evacuees ended up in 118 destination counties (Fig. 14). To test our hypotheses and the potential of PCI in predicting evacuation destination choice, we used linear regression to model the relationship between the number of evacuated users in the destination counties (dependent variable) and PCI of the county pairs between Charleston County (origin) and each of the destination counties (n = 118). Note that PCI was scaled by 1000 in the regression models to ease the result presentation. Distance between the evacuation county and each of the destination counties were used in the regression model as controls. SCI was tested by replacing PCI in the regression model for comparison. The same model configuration was used for Chatham County (n = 120). Table 4 shows the regression results for the four models.

Discussions
The evidence of spatial inter-dependency is increasingly apparent across scales, captured by the digital records of growing human mobility and socioeconomic activities. Geotagged social media data records many space-time social contexts where people perceive, act, and interact with each other, allowing researchers to quantify how specific locations are mentioned and related in physical, virtual, and perceived worlds. As a popular social networking platform, Twitter records a substantial portion of human communication and events at various space-time scales. The geotagged tweets can reveal where people visit, with a much larger sample size than conventional surveys. Such large samples can particularly identify the behavior of underrepresented population groups that are not easily accessed by traditional surveys (Hu et al., 2020 The world should be portrayed as networks instead of the mosaic of cities (Beaverstock et al., 2000). As a classical and fundamental research topic, the interactions between locations convey the urban or regional spatial structure. The PCI computed from billions of tweets offers promising opportunities to measure and compare intra-and inter-city connections and flows.
Also, PCI can be linked to other large geotagged data, such as Yelp and Transportation Network Company data, to reveal a more completed picture of spatial structure dynamics. Combined with PCI, the place hierarchy and spatial clusters can be revealed based on both virtual and physical interactions.
Although the outcome of the behavior of PCI largely matches our expectations and with the results of other big social data sources, using social media data to identify spatial interaction has the following limitations. We caution that studies using the open-sourced PCI datasets should be aware of such limitations when interpreting the results. First, research using social media has been criticized for being biased for representing specific population groups. For example, young adults are more likely to use Twitter, compared to their older counterparts (Malik et al., 2015;Jiang et al., 2018). Second, the correlation between PCI and other indicators from social networking platforms in the US is largely relevant to the cultural and policy context. Hence, the results may not be readily generalized or used for prediction in other areas. Further studies are needed to evaluate the PCI for geographic areas other than the US. Third, episodic events, such as holidays and hurricanes, would largely attract/hinder users' movement to specific places. It might distort the connectivity if data is only collected for short periods, and thus affect the accuracy and consistency of measurement results. This issue can be addressed by computing PCI over a relatively long period (e.g., one year or longer) or filtering out the data during the affected time period. Lastly, geotagged tweets are unevenly distributed across space and time, which also affects the reliability of such measurements. The data sparsity issue is caused by a variety of factors such as population density, Internet access, and governmental policies on social media.
More studies are needed to evaluate the performance of PCI at different geographic areas and scales by associating and comparing it with other data sources and testing it with other applications.
Despite these limitations, to the best of our knowledge, Twitter data is the most accessible dataset offering the opportunity to extract worldwide human movement at various spatiotemporal scales for a relatively long time period. By open-sourcing the global PCI datasets at various geographic levels, we call for more efforts to tackle these issues and further validate PCI following the suggested future studies and beyond.

Conclusions
The relationships among places are shaped by dynamic human movement, whose intensity further quantifies the connectivity (strength of the linkages) among places. With the advances in technologies in the past decades, the connectivity among places is ever-evolving dynamically, thus demanding spatiotemporal-continuous observations with harmonized approaches. Fortunately, the emergence of big social media data, benefiting from the advent of geo-positioning techniques and the popularity of social media platforms, offers a new venue where collecting human spatial interactions becomes less-privacy concerning, easily assessable, and harmonized.
In this study, we introduced a global multi-scale place connectivity index based on people's spatial interactions among places revealed from worldwide geotagged Twitter posts.
Defined as the normalized number of Twitter users who shared spatial interactions during a specified time period, the proposed PCI is a harmonized and spatiotemporal-continuous place connectivity metric, expected to benefit various domains requiring knowledge in human spatial interactions. The interactive web portal aims to facilitate place connectivity visualization and provide downloadable connectivity matrices to support research needs.
To better understand the characteristics of PCI, we conducted a series of experiments using PCI and other data sources. An overall Pearson's r of 0.71 between the population movement derived from Twitter and SafeGraph (10% penetration in the US population) reveals that geotagged tweets can well capture the population movement at the US county level. The comparison between PCI and Facebook SCI (a popular connectivity index based on social networks) with an overall r = 0.62 suggests a strong connection between spatial interactions and social interactions, confirming the hypothesis that "regions connected through many friendship links are likely to have more physical interactions between their residents" (Kuchler, Russel & Stroebel, 2021). Like many connectivity measurements that are bounded by the first law of geography, we found that PCI generally follows distance decay form tested at the county level, while the distance decay effect is found weaker in more urbanized counties with a denser population. This phenomenon can be explained by the existence of long-distance transportation facilitates (e.g., airports, railways, and bus stations) that, to some extent, express a hierarchical diffusion relationship rather than a contagious diffusion. We further observed a strong boundary effect in PCI, indicating that counties in the same state and states/provinces in the same country are more connected, evidenced by their higher PCI values. The different regions identified in the US and the world by using the hierarchical agglomerative clustering suggests that PCI can be used as a tool in regionalization analysis to reveal how places are connected at different geographic levels and scales.
We demonstrated that PCI could address real-world problems requiring place connectivity knowledge using two applications: 1) modeling the spatial spread of COVID-19 during the early stage and 2) modeling hurricane evacuation destination choices. In the first application, we found that the PCI for Westchester County, NY, an early hotspot of  in the US, could explain 22% of the variance in COVID-19 cases among US counties at the early outbreak, which was much higher than Facebook SCI (8%) and the population movement derived from SafeGraph (13%). In the global scale analysis, we found that PCI for Lombardy, an early epicenter in Italy, had a strong association with the infection rate at the US state level at the early stage of the pandemic (r = 0.48, n = 50, p < 0.01). In the second application, we found that PCI explains a considerably higher percentage of variance in local residents' choices of destination county during 2016 Hurricane Matthew compared with Facebook's SCI, suggesting the superiority of spatial interactions in modeling evacuation choices than social interactions.
With the effects of geographic distance being weakened by technological advances, place connectivity quantified by human spatial interactions has been evolving since the very first day of modern society and will continue to evolve at an accelerating pace in the future.

A. Directional (or Asymmetrical) PCI
The same number of shared users between two places may have a different impact on each place. Suppose that two places i and j have 50 shared users, place i has 100 users in total, and place j has 1000 users in total. In such a case, place j can be considered to have a larger impact on place i as it has 50% of users shared with place j. Similarly, place i has a smaller impact on place j as it only has 5% of users shared with place i. Same as the PCI (non-directional or symmetrical) discussed in the paper, the directional (or asymmetrical) PCI was also computed for the following four geographic levels: 1) 2019

B. Descriptive Statistics of Worldwide Geotagged Tweets in 2019
We collected 1,437,611,832 worldwide geotagged tweets in 2019 using the public Twitter Streaming Application Programming Interface (API). Following Martin et al. (2020), we filtered out the non-human tweets (e.g., automated weather reports, job offers, and advertising) by checking the tweet source from which application a tweet is posted. For example, tweets automatically posted for job offers from the source TweetMyJOBS and CareerArc are removed.
A list of the Twitter sources that indicate human-posted tweets selected by manual checking is shown in Table B1. Only tweets posted from these sources were included in the analysis and PCI computation. After filtering, a total of 1,409,404,996 geotagged tweets posted by 17,013,612 unique Twitter users were selected. Fig. B1 shows the spatial distribution of these filtered tweets at the country level. The top 40 countries with the most observed unique Twitter users in 2019 are reported in Table B2.
The locations embedded in the geotagged tweets have different spatial resolutions (e.g., exact coordinates, neighborhood, city, and country, etc.). We also analyzed the locations of the 1.4 billion geotagged tweets as the spatial resolution of a geotagged tweet needs to be considered when computing PCIs at different geographic levels. For example, for computing PCI at the US county level, we need to filter out tweets geotagged at a geographic level lower than a city (state level and country level tweets were excluded). As shown in Fig. B2   TweetCaster for Android, TweetCaster for iOS, Tweetings for iPad, Tweetings for Android, Tweetings for Android Holo, Tweetings for Android Tablets, Tweetings for iPhone, Tweetings

C. Computation of US County Level PCI Using 2019 Geotagged Twitter Data
A total of 391,503,203 geotagged tweets from 4,892,458 distinct Twitter users were extracted within the bounding box covering the contiguous United States. For computing PCI at the county level, we filtered out tweets geotagged at a geographic level lower than a city (e.g., state level). If a tweet is geotagged at the place level, the coordinates (latitude and longitude) of the place centroid was used in the analysis. We filtered out the non-human tweets following the procedure introduced in Appendix B. After spatial filtering and non-human filtering, a total of 316,797,441 tweets remained from 4,609,040 unique Twitter users. The process was performed using Apache Impala in a Hadoop environment.
After data cleaning, each Twitter user was assigned to a county based on that user's tweet location daily. For example, if a user tweeted in three counties on a specific day, then for that user on that day, three rows were generated. After processing all users, counties, and days in 2019, a big were derived: 1) the number of shared users with other counties and 2) the number of total observed users in each county. Finally, PCI was computed for each county pair (those with shared users) using Eq. 1. This process was conducted using Apache Hive coupled with Esri GIS tools for Hadoop (Esri, 2019).

D. Computation of the County Person-Day Movements Using 2019 SafeGraph Data
The SafeGraph's Social Distancing Metrics (SDM) data (SafeGraph, 2020) were downloaded and loaded to our Hadoop cluster. There were 23 fields in the SDM table, and three were used to derive the population movement, including origin_census_block_group, destination_cbgs, and date_range_start. The origin_census_block_group is the unique 12-digit FIPS code for the Census Block Group. Destination cbgs contains a list of key-value pairs with key indicating the destination census block group (from the origin census block group) and "value is the number of devices with a home in census_block_group that stopped in the given destination census block group for >1 minute during the time period" (https://docs.safegraph.com/docs/social-distancing-metrics). The date_range_start was used to extract the date information.
Based on the three fields, we generated a new For instance, if there are m number of movements from county A to county B, and n number of movements from county B to county A, then the number of movements between the two counties is calculated as m + n. The entire process was conducted in our in-house Hadoop cluster using Apache Hive and Impala.

E. Computation of the County Person-Day Movements Using 2019 Geotagged Twitter Data
After data cleaning, each Twitter user was assigned to a county based on that user's tweet location daily. For example, if a user tweeted in three counties on a specific day, then for that user on that day, three rows were generated. After processing all users, counties, and days in 2019, a big