# Topology of the World Tourism Web
## 3 Results and Discussion
### Does the Tourism Network Behave as a Social or Technological Network?
#### 3.2.1 Small-World and Scale-Free Network Properties  
The observed tourism network follows the properties of small worlds, as it demonstrates a small diameter and a small average path length. Both studies [6,7] found tourism networks to be small worlds, i.e., to have a relatively small diameter and a small average path length. Both studies [6,7] revealed a certain amount of reciprocity. Our research results are in line with their findings. However, the degree distributions do not exhibit classic fat tails and are not scale-free distributions. At first glance (Figure 7a-c), it may seem that there is a possibility for a power-law adherence. However, for weighted degrees (Figure 7d-f), it can be observed that there are many nodes with a lower number of links, but the right tail suggests the existence of more hubs than expected in a scale-free network. Additional analysis to check whether the distributions follow the power law reveals very weak adherence to the power law (estimations were conducted with and without the constant and better-fitting models are stated here). For the in-degree distribution, the estimated power function is \(p_{k}\sim 3.54\ +k^{-0.215},R^{2}=0.246\), and the model is statistically significant \(\left(p(F=38.804)=7.3\cdot 10^{-9}\right)\), so is the constant \(\left(p(t=6.615)=1.114\cdot 10^{-9}\right)\) and \(\alpha\ (p(t=-6.229)=7.319\cdot 10^{-9})\). The out-degree power model is \(p_{k}\sim k^{0.134}\) with \(R^{2}=0.454\), and it is statistically significant \(\left(p(F=92.393)=0;\ p(t=9.612)=0\right)\). The degree distribution shows even weaker adherence to the power law \(\left(\ p_{k}\sim k^{0.054},R^{2}=0.233\right)\), but it is statistically significant (\(p(F=48.386)=0\) and \(p(t=6.956)=0\)). While a much stretched conclusion may be that the network does follow the power law, it can be seen that these models explain a very small amount of variations in the degree frequencies, while the majority of the variances (75.4% in the first, 54.6% in the second, and 76.7% in the third model) remain unexplained. In addition, the \(\alpha\) values are unusually small, given the commonly reported values in the literature (such values of \(\alpha\) should not be seen in large finite networks, as the number of links connected to the hubs grows faster than the size of the network and will eventually be connected to every node [63]). However, these results are not entirely unexpected. The prerequisite for a scale-free network is the possibility of link creation to an arbitrary number of other nodes. This might not be satisfied for the world tourism network, as tourism also depends on the diplomatic relationships between countries [7], for example, a visa requirement that might discourage some tourists. Despite the ever-present endeavors of a search for scale-free networks because of their properties and regularities in their growth, they are rare in the real world [64]. With additional analysis, we find that the out-degree, degree, weighted out-degree, and weighted degree distributions best fit the Weibull distribution, while the in-degree and weighted in-degree best fit the log-normal distribution. This shows that this network is not scale free. In addition, it sheds a new light on the behavior of arrivals and departures from the observed countries, as it indicates that they are governed by different underlying regularities. There are three comparable studies that deal with tourism on the global scale [6, 7, 8], so we consider these as initial observations. Given their findings, the tourism network seems to be governed by most of the typical social and economic network characteristics. [PERSON] and [PERSON] [6] find that degree distributions seem to be scale free and follow the power law, while [PERSON] and [PERSON] [7] obtain different results (the topological network does not display scale-free behavior, but the in- and out-degree strength distribution analyzed separately can be fitted to the power law).