Network science to correlate COVID-19 and tourism indicators in Mexico

In this paper we analyze tourism as complex system susceptible to external perturbations, like COVID-19 public health emergency. The research objective is to confirm pertinence of using transdisciplinary tools such as complexity approach and network analysis to understand and represent tourism occupancy

• Mexican Hospitality and Gastronomy Jobs.
We justify network science application to analyse COVID-19 impacts on Mexican tourism, based on definition of complex systems as those with many interrelated compounds with difficulty to derive their collective behavior from an isolated knowledge of their components (Barabási, 2016).
Another complex network approach published on Nature by Albert et al. (2000) provides us with reasons to justify our subject belongs to complex systems order.To contribute understanding of tourism as complex system, susceptible to perturbations like COVID-19, having direct implications for destinations occupancy rates and jobs, enabling understanding from interacting components perspective; pertinent to consider significant tourism contribution with 8.7% of Mexico's GDP (Gobieno de Mexico, 2019) and according to National Survey of Occupation and Employment (ENOE from its Spanish initials) first trimester 2019 employed population in tourism sector reached 4 million 246 thousand direct jobs, meaning 8.7% of total employment nationwide ratifying tourism industry importance in mexican economy (Gobieno de Mexico, 2019).
In each section of the article, the reader will find: • In Literature Review, the main trends and gaps in existing literatura • In Methodology the description of networks following Power-Law mathematical formalism, the software used, analysis of each network, limitations of the method and technique used • Results and Discussion about metrics for tourist destinations occupancy distributions; hospitality and gastronomy jobs; COVID-19 confirmed cases and implications.
• Conclusions describe research contribution, limitations and future directions.

Literature Review
We contribute with tourism data analytics using network science, emphasizing correlations among different databases.Proposing interdisciplinary approach for tourism studies.Network science, according to Barabási (2016) is possible because fast data sharing methods and cheap digital storage that made viable creation of network maps to describe behaviour of complex systems consisting of multiple interacting components.Since the size of most networks of practical interest have huge amount of data behind them; we consider tourism indicators can be mapped as a network.We applied network analysis based on graph theory (Barabási, 2002;Barabási & Albert, 1999;Watts, 2004;Watts & Strogatz, 1998); our results are representative to scale free networks theory that defines networks whose degree distribution follows a power law that persists in different network sizes (Barabási, 2016).Another theoretical argument congruent with our results is that in networks with power law degree distribution most nodes have only a few links, these numerous small nodes are held together by a few highly connected hubs (Barabási, 2016).In that way, the identification of those hubs in our results show the important role some states and tourist destinations have: driving strong sustained travel demand; their contribution to Hospitality and Gastronomy jobs and COVID19 confirmed cases ranges (COVID.GOB, 2020).
Description of research methodology used begins creating architecture of the networks we want to analyse, then identify their organizing principles and express mathematical formalism behind them to contribute understanding of tourism as complex system.
Our networks model P(k)=ck^(-γ) follows empirical nature, focusing on data, function and utility; describing system's properties and behavior; like power law distribution (Barabási, 2016) revealing key information based on quantitative characterization; deepen in our case into occupancy rates, jobs and COVID-19 confirmed cases distributions on Mexican destinations (COVID.GOB, 2020), towards characterization of pandemic impacts on Mexican tourism industry dynamic.
Our networks distributions are represented by P(k) = ck −γ for k 0 ≤ k ≤ K where: ▪ c is an appropriate normalization factor.▪ γ is the exponent of connections distribution.▪ k 0 is the minimum grade of any given node.▪ K the cut degree depending on the network size.
To prove usefulness of the used method, in Table 2 we compare two main networks models; emphasizing power-law pertinence for our study given its advantages.
1. Fragility in network topology when removing clusters.For our study purposes, this "disadvantage" works in our favor as it confirms our results regarding the important role some tourist destinations have, that we might consider to better understand Mexican tourism industry dynamic.Since network science emphasizes correlations and interactions among different databases, to describe behaviour of tourism as complex system, we elaborate network maps about: 1. Mexican tourism industry indicators: 1.1 Destinations occupancy rates 1.2 Hospitality and Gastronomy jobs 2. COVID-19 in Mexico indicator:

Confirmed cases
We used Netdraw Ucinet software to elaborate network maps (Borgatti et al., 2002)  1. Networks about mexican tourism industry indicators: 1.1.Destinations occupancy rates.First interaction is about tourist destinations and their occupancy rate registered on certain date.Figure 1.Second type: occupancy rates clusters on certain dates, and tourist destinations belonging to those clusters.Figure 2.

Limitations of the method and technique
Relies on accurate data to build the networks, real data may be incomplete, uncertain, or non available; another challenge is to choose indicators or drivers that enable accurate analysis; specifically time consuming and demanding to prepare relational data to interpret causality.

Results and Discussion
Since the contribution of network maps is to describe the detailed behaviour of a system consisting of various interacting components.
The findings for each indicator are as follows.After running Analytic Technologies Harvard software on 2-Mode Centrality (Borgatti et al., 2002) results found Highest Degree Centrality for occupancy rates between 51-60.9 on January toMarch 2018 (Figure 8).Another observation is that maximum occupancy rate for same period was 86-90.9registered by two destinations: Playacar, Q. Roo and Puerto Vallarta, Jal.(Figure 8).On 2-Mode Centrality analysis (Borgatti et al., 2002) January-March 2019 we found Highest Degree Centrality for occupancy rates between 46-50 .9(Figure 9).COVID-19 decreasing occupancy effects is confirmed again in Nuevo Vallarta, Nay; that in same period of previous year registered maximum occupancy 86-90.9(Figure 9) decreasing 10 percent by January-March 2020 with maximum occupancy 76-80.9(Figure 10).2-Mode Centrality analysis (Borgatti et al., 2002) for April 2020 COVID-19 decreasing occupancy effects in destinations is clearly visible, having Highest Degree Centrality for occupancy rates 0-5.9 in most destinations; an unprecedented situation with highest occupancy rate registered by Mazatlan, Sin.16-20.9(Figure 14).The most important metric for our research purpose is Highest Degree Centrality for occupancy rates in figures 8-17, given we looked for destinations that concentrated bulk of tourism and maximum occupancy levels registered.We generated those data using Analytic Technologies Harvard software on 2-Mode Centrality (Borgatti et al., 2002).The analysis generated other 4 metrics that support our metric of interest, which is degree centrality (Table 3).Personal elaboration using Ucinet (Borgatti et al., 2002).

That degree centrality identified in
Degree, consists of the sums of ties values, meaning most common occupancy level registered by destinations across all periods analysed is 46-50.9%.Complementary metrics: 2-Local represents our mode network as bipartite graph with balanced incoming and outgoing links.Eigenvector, calculates eigenvector of the largest positive eigenvalue as measure of centrality, ratifying robustness.Closeness is a metric that gives the overall network closeness centralization and is useful to measure distance by sums of the lengths of all the paths or all the trails; a metric that can be thought as an index of the expected time-until-arrival for things flowing through the network via optimal paths.
Betweennes is a measure of information control.
Highest values in all metrics support our finding that destinations represented with brown circle node linked to jan-mar 2019 cluster, are robust destinations that constantly ensure tourist consumption for Mexico; represented in tourism behavioral dynamic (figure 11).
Although it is necessary to carry out more indepth analysis integrating other indicators to quantify correlations degree; as well as verifiable effective incentives application; both are beyond this research paper scope.However, we have identified some essential characteristics and destinations that concentrate bulk of tourism that might be considered when focusing marketing intelligence initiatives and public-private partnerships.
Having concluded analysis for the first Mexican tourism industry indicator: Destinations occupancy rates (Figures 8-17   Analysis for states of the republic reveals highest degree for Puebla, supporting is the state with most tourist destinations (Table 4).Personal elaboration using Ucinet (Borgatti et al., 2002).The next mexican tourism industry indicator for this research analysis is: Hospitality and Gastronomy jobs.Bipartite: states-employment ranges network was built to connect data following type of interaction in Figure 4.
After running Analytic Technologies Harvard software 2-Mode Centrality (Borgatti et al., 2002) for Hospitality and Gastronomy jobs in Mexican territory by April 21 st 2020, five employment ranges were identified from Scarce to Maximum; finding considerable number of states and therefore tourist destinations classify on Few employment range 51755-96577 in contrast Maximum range 883776 hospitality and gastronomy jobs reported by Baja California state (Figure 19) with its 5 tourist destinations: Tecate, San Felipe, Mexicali, Tijuana and Playas de Rosarito.
Our Network analysis allows sizing and graphically represent number of Hospitality and Gastronomy jobs affected in Mexico by COVID-19.Personal elaboration using Ucinet (Borgatti et al., 2002).
Having concluded mexican tourism industry indicators; the last set analyzed is COVID-19 indicator: Confirmed cases.Bipartite: states-confirmed cases ranges network was built to connect data following type of interaction in Figure 5.Even though it is out of scope of this paper, some insights for most affected areas providing emergency economic assistance through monetary measures like credit lines at reduced rate or exemption/reduction of social security contributions, wage subsidies or special support mechanisms for hospitality and gastronomy jobs might be helpful.Personal elaboration using Ucinet (Borgatti et al., 2002).
To complement our study we support our findings with quantitative characterization of our networks, given networks distributions reveal information towards better understanding of tourism mobility dynamic during analyzed periods.
We analyzed occupancy levels on different months and years.Finding that under normal conditions without COVID-19 visited destinations that concentrate bulk of tourism behave according to power law.

𝑃(𝑉
Conserving same statistical distribution regardless year or month of the information (Figure 22).Regardless each destination conditions, we found statistical similarity of visitors distribution among different periods.Which supports two generic properties seen in social networks: alien to single characteristic scale and high clustering degree.Implying small destinations are organized hierarchically into larger groups, maintaining free-scale topology, following power law distribution.
Our interpretation of scale free and scale invariance generic properties found is that tourism occupancy is preserved regardless period or destination type; another finding is that distributions confirm tourism occupancy is not random.And we consider it is one of the firsts steps to understand underlying dynamic of tourism as complex system.
On Figure 23 we analyzed correlation between confirmed cases and reduction in tourism, finding by may 2020 moderate level of confirmed cases prevailed among destinations with reduction in tourism occupancy from 1-5.9 level.Identifying that Puebla state occupancy, was the most affected.

Conclusions
This is an attempt to confirm network science pertinence to analyse tourism dynamics, useful to provide quantitative characterization for our understanding of tourism organization principles and some underlying patterns behind this activity.
Our research contributes: • With verifiable application of network science to tourism análisis.Perhaps our findings don't have capacity to influence tourism decision makers, still our metrics results add value to project some characteristics of tourism dynamic, and are congruent with reality having strong correlation between confirmed cases and employment rate in densely populated areas; confirming correlation between confirmed cases and reduction in tourism.
This paper shows network science pertinence in tourism; and usage of transdisciplinary tools.

Discussion on the limitations of the study
Scope in terms of considered indicators remains limited yet, in tourism network analysis real demanding phase is to acces and then gather representative elements of the tourism complexity, and foresee connections between those elements; being careful on the data classification; unveil constantly changing and evolving dynamics over seasons and destinations; such as the possible lack of generalization of the results in this research case to other countries or contexts linked to other sociodemographic characteristics.It is also important to have in consideration several different patterns that might arise from the network analysis given tourism inherent complexity according to market segments and tourist offer; in that way depending on the type and intention of the network designed making sense out of the relational data analyzed for enhanced predictability of tourist indicators as well as their practical significance and visualization as a complex system.

Future directions for research
In future works we can do similar analysis in other countries for degree distribution and organization principles comparison purposes; to be able to make generalizations.And to consider the analysis of other variables like marketing strategies, consumer segments, tourist preferences, currency flows, flights availability, classification of natural, cultural tourist attractions, destinations internet access, sustainability indicators, demographic impacts derived from tourism activity and also perturbations or elements that affect and limit tourist activity like insecurity, emitted warnings for certain destinations, visa restrictions, adverse political environment or considerable cultural differences between visitors and host communities.Still network science to analyse tourism susceptible to external perturbations like COVID-19 in this paper; is pertinent to reveal some tourism dynamic basic properties, providing evidence to develop understanding of tourism complexity.
Error and attack tolerance of complex networks.Nature, 406( 6794

Figure 1 .
Figure 1.Tourist destinations and its occupancy rate.Personal elaboration.

Figure 2 .
Figure 2. Tourist destinations by occupancy rates clusters.Personal elaboration.

Figure 5 .
States by confirmed cases ranges 11 th June 2020.

Figure 5 .
Figure 5. Confirmed cases range by state.Personal elaboration.For integral perspective Figure6integrates both jobs and confirmed cases ranges, with their corresponding states.

Figure 6 .
Figure 6.States by jobs and confirmed cases ranges.Personal elaboration.

Figure 7
Figure 7 offers structure of analysis findings.

Figure
Figure 7. Results.Personal elaboration.Results: 1.On networks about mexican tourism industry indicators: 1.1.Destinations and occupancy rates.Bipartite networks (Figure 1) which first set of nodes are 70 mexican tourist destinations; and second set occupancy rates each destination had from January-May 2020, 2019 and 2018 (DATATUR, 2020, 2019, 2018).Considering in Mexico flight suspensions, selfisolation and quarantine began entirely on april 2020, first graphs for this research illustrate January-March accumulated rates in 2018, 2019 and 2020 (Figures 8-10) to evidence how mexican tourist destinations registered occupancy rates under normal consumption conditions without COVID-19.
https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.

Figure 9 .
Figure 9. Degree centrality for accumulated occupancy January-March 2019.Personal elaboration.On 2-Mode Centrality analysis (Borgatti et al., 2002) January-March 2020 COVID decreasing occupancy effects in mexican destinations became visible, given flight suspensions and measures including self-isolation were applied in Mexico's travel market sources like United

Figure 10 .
Figure 10.Degree centrality for accumulated occupancy January-March 2020.Personal elaboration.Deepening analysis January-March accumulated rates 2018, 2019 and 2020 (Figures 8-10) a fourth network map (Figure 11) was built from second type of interaction represented in Figure 2 focusing on destinations that concentrated bulk of tourism in three periods: ▪ 20 destinations January-March 2018 ▪ 12 destinations January-March 2019

Figure 12 corresponds
Figure 12 corresponds April 2018 analysis for previous occupancy rates registered by destinations under normal consumption conditions without COVID-19.Finding Highest Degree Centrality for occupancy rates 46-55.9;

Figure 12 .
Figure 12.Degree centrality April 2018.Personal elaboration.Likewise, Figure 13 corresponds to April 2019 analysis for previous occupancy rates registered by destinations under normal consumption conditions without COVID-19.Having found Highest Degree Centrality for occupancy rates 41-45.9and 61-65.9;i.e having concentrated greater amount of tourism flow on 21 destinations: Mexicali, B.C; Zacatecas, Zac; San Jose del Cabo; Queretaro, Qro; Ciudad de

Figure 14 .
Figure 14.Degree centrality on April 2020.Personal elaboration.May analysis was done separately to get information about COVID-19 decreasing occupancy effects in destinations.

Figure 15
Figure 15 corresponds to May 2018 analysis refering previous occupancy rates registered under normal consumption conditions without COVID-19.Having found Highest Degree Centrality for occupancy rates 41-45.9and 51-55.9;i.e concentrated greater amount of tourism flow on 19 destinations: Zona Corredor Los

Figure 16 .
Figure 16.Degree centrality on May 2019.Personal elaboration.For May 2020 COVID-19 pandemic decreasing occupancy effects were exacerbated, nullifying tourism activity in most destinations and registering Highest Degree Centrality for occupancy rates 0-5.9 in 7 destinations: Toluca,
); before continuing with the rest indicators Hospitality and Gastronomy jobs and COVID-19 Confirmed cases, given INEGI and COVID.GOB primary data sources are displayed by state; Figure 18

-
https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.was built following type of interaction in Figure 3.To specify correspondence between states of the republic and tourist destinations; even though in Figures 8-17, names of the corresponding states were abbreviated after name of tourist destination.

Figure 18 .
Figure 18.Correspondence between states of the republic and tourist destinations.Personal elaboration.
https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.Identify States of the Republic with more tourist destinations, is useful to propose focalized restart of tourism after COVID-19.

Figure 19 .
Figure 19.States by Hospitality and gastronomy employment ranges.Personal elaboration.Our finding about most states classifying on Few employment range is supported by software After running software 2-Mode Centrality(Borgatti et al., 2002) for COVID-19 confirmed cases in Mexico by 11 th June 2020, four ranges were identified from Scarce to Maximum; finding that considerable number of states and therefore tourist destinations classify on Low level range of confirmed cases 1320-2959 compared to Maximum range 21631-34077 https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.COVID-19 confirmed cases reported by Mexico state and Ciudad de Mexico (Figure 20) and their corresponding 5 tourist destinations: El Oro, Toluca, Ixtapan de la Sal, Valle de Bravo and CDMX.Useful information for responsible tourism restart having identified the most and the least infected destinations, crucial to restoring trust and confidence in the sector focalizing promotional campaigns and tourism product development initiatives.

Figure 20 .
Figure 20.States by COVID-19 confirmed cases ranges.Personal elaboration.Our finding about most states classifying Low level confirmed cases is supported by software metrics with .43degree and .18 on 2-mode local Figure 21).Besides occupancy pattern in Oaxaca and Campeche evidencing their role as generators of sustained tourism flow (Figure 11).In fact, on June 22nd Campeche obtained the Safe Travel Stamp from the World Travel and Tourism Council (WTTC) because of sanitary protocols standardization in hotels, restaurants, tour operators and other tourism service providers; hence the first POSTCOVID Corridor in Latin America was inaugurated in Mexico integrated by Campeche, Yucatan and Quintana Roo destinations (Mexico desconocido, s.f).https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.

Figure 21 .
Figure 21.States by employment and COVID19 confirmed cases ranges.Personal elaboration.Most states according to software analysis classified Low level of confirmed cases and Few hospitality and gastronomy jobs with degree metrics .43 and .40;as well as .18and .16 on 2mode local linkage.Probing correlation between confirmed cases and employment rate; verifiable on lowest degree and 2-Local metrics for Maximum hospitality and gastronomy jobs as well as confirmed cases; finding there are more cases per capita in densely populated areas.
https://amazoniainvestiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.

Table 1 .
Literature Valle et al., 2021)estiga.info/ ISSN 2322-6307 This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).Reproduction, distribution, and public communication of the work, as well as the creation of derivative works, are permitted provided that the original source is cited.(DoValleet al., 2021) having links between nodes to indicate existent interactions.UCINET for Windows is a software package for the analysis of network data.It was developed by Lin Freeman, Martin Everett and Steve Borgatti on 2002.It comes with the NetDraw network visualization tool, that we used to create and analyze our networks.

Table 3 .
Metrics for tourist destinations that concentrated bulk of tourismjanuary-march 2018, 2019 and 2020

Table 4 .
Correspondence degree between states and tourist destinations

Table 5 .
Metrics for states by hospitality and gastronomy employment ranges

Table 6 .
Metrics for states by COVID-19 confirmed cases ranges

Table 7 .
Metrics for States by employment and COVID19 confirmed cases ranges