# Topology of the World Tourism Web
## 2 Materials and Methods
### Analysis
* Clustering coefficient (triangle method) [51] is the ratio of the number of closed triples to the number of all possible triples in the network. * Number of strongly connected components [52] is the number of subgraphs that contain interconnected nodes. In a strongly connected component, each country can be reached by any other country, and vice versa. * Number of weakly connected components [52] is the number of subgraphs where the links can be formed in only one direction (and observed as undirected in the opposite direction). * Diameter of the largest weakly connected component [53; 54] is the longest shortest path in the subgraph of the largest weakly connected component. * Radius of the largest weakly connected component [53; 54] is a minimum over all eccentricity values in the subgraph of the largest weakly connected component. * Number of nodes in the periphery [53; 55] is estimated by the eccentricity distribution. Countries in the periphery will have high eccentricities and fewer connections to other countries. * Number of nodes in the center [51; 55] is also estimated by the eccentricity distribution, where countries with lower eccentricity will be part of the center. * Number of clusters (Leiden Constant Potts Model (CPM); random seed) [54; 56] is another cluster measure based on the Leiden algorithm using the Constant Potts Model function, multiple iterations, and random seeds. The result of the applied algorithm is the number of clusters. * Modularity [54; 56] is a measure that reveals distinct communities in the network based on the strength of the countries' relationships. * Number of communities [54; 56] is the result of application of a modularity algorithm and answers the question of into how many communities the network is partitioned. The results may differ due to random seeding. * Number of nodes in communities [54; 56] is the other part of the results of the applied modularity algorithm. Each country in the network is assigned to one of the assessed communities. * Eccentricity of the largest weakly connected components [55] can be interpreted as a diameter of each node in the largest weakly connected component. * Eigenvector centrality [47; 57] is a measure of a country's importance in the network, and its calculation is based on how many countries are connected to the observed country and what is their level of eigenvector centrality. * Closeness centrality [48] is a measure of a country's position in the network based on the distance to every other country in the network, where a poorly connected country can have a higher centrality if it has a high proportion of high-degree countries in direct connections. Normalized closeness centrality is more commonly used, where values closer to 0 indicate a greater distance from the center of the graph, meaning a worse position in the tourism network in comparison to neighboring nodes. * Betweenness centrality [48] measures how many times a country appears on the shortest path between every two other countries respective to all shortest paths, which identifies countries that may or may not be central by other parameters but connect otherwise disconnected countries by serving as bridges. From the tourism perspective, this means that tourists from otherwise unconnected countries may find themselves on the same location (a country with a high betweenness centrality) and possibly interact, which emphasizes the importance of such countries for information, cultural, and other exchange. * Bridging coefficient [47; 58] measures a country's position in the network by a ratio of the reciprocal of the country's degree and the sum of reciprocals of its neighbors' degrees. * Bridging centrality [47; 58] indicates a country that connects densely connected components in the network, calculated as a product of betweenness centrality and bridging coefficient. * Prestige rank [41] is a measure of a node's importance in the network based on the inbound tourism.