## 3 Influence Metrics
### Global Influence
#### 3.2.2 Social Closeness Metric
The tuning parameter is this normalized value, which enables us to gauge the degree of dispersion between low and high \(ORI_{T}\) values. As a result, the following is how the definition of \(\alpha\) is stated:  
\[\alpha_{s,s+1,\ldots d}=\frac{\left(\prod_{i=s}^{d-1}ORI_{T}(i,i+1)\right)^{ \frac{1}{[s,d]}}}{max(ORI_{T}(s,s+1),ORI_{T}(s+1,s+2),\ldots,ORI_{T}(d-1,d))}\, \tag{20}\]  
where \(|\{s,d\}|\) represents the number of hops in the path from the source device \(s\) to the destination device \(d\). By adding considerations of the shortest pathways, social interactions between nodes, and communication cost, we use the opportunistic-based shortest path approach to expand the Closeness measure in this way. The Social Closeness metric (\(CLO_{opp}\)) is calculated in the manner described in the following:  
\[ \begin{split} CLO_{opp}(v)=\frac{1}{|V|-1}\sum_{k=1,k\
eq v}^{|V |}\left(\frac{1}{\min\left(Cost_{opp}(vk)\right)}\right)=\\ =\frac{1}{|V|-1}\sum_{k=1,k\
eq v}^{|V|}\left(\frac{1}{min\left( \sum_{i=s}^{d-1}\left(\frac{1}{ORI_{T}(i+1)}\right)^{2}\right)}\right)\,\end{split}  \tag{21}\]  
Figure 5: Illustration of the paths from device \(A\) to device \(B\) of example in Figure 1, where the weights represent the ORI. Regarding the methodology for analyzing the dataset, it has undergone processing using a similar approach employed when implementing Machine Learning models. In this manner, the dataset is partitioned into two distinct non-overlapping graphs known as the training (GT) and probe (GP) graphs. The Training Graph (GT) is constructed by selecting a subset that represents the initial 75% of node interactions within the dataset. The remaining edges, not included in GT, constitute the Probe Graph (GP). Likewise, the edges included in GT are denoted as ET, while those in GP are referred to as EP, i.e., E = ET + EP. It should be noted that ET and EP are mutually exclusive; however, there may be overlapping nodes between GT and GP. For our experiments, we have allocated 75% of the edges to ET and the remaining 25% to EP. The simulations have been conducted by simulating the GP (Probe Graph) with an implementation of a total of five routing algorithms. On one hand, we include the conventional ones typically used to evaluate QoS in OppNets, that is Spray and Wait (S&W), Prophet versions 1 and 2, and Epidemic (four algorithms). On the other hand, we incorporate a modified version of the S&W algorithm, which is evaluated three times based on a parameterized ranking of the most significant nodes according to the metrics described in the previous sections (Dynamic Degree, Dynamic Closeness, and Social Closeness), which sums a total of five routing algorithms. The results of the simulations will be presented in Sections 4.3.4-4.3.6. The algorithms have been developed using The ONE (Opportunistic Network Environment) simulator [34] and can be accessed from a public repository located at [[https://github.com/sito25/pubtesis.git](https://github.com/sito25/pubtesis.git)]([https://github.com/sito25/pubtesis.git](https://github.com/sito25/pubtesis.git)), (accessed on 21 September 2023) under the GNU Lesser General Public License v.3.0. This simulator is specifically designed for opportunistic networks and was initially developed at Aalto University in 2009. The ONE provides a wide range of capabilities, including the generation of node movements using various models, replication of message traffic and routing, cache management, and visualization of both mobility and message transmission through its graphical user interface. Additionally, it offers diverse reporting options, such as node movements, message transmission, and general statistics. Currently, it is collaboratively maintained by Aalto University and Technische Universitat Munchen, boasting a robust user community. The version utilized in our research is 1.6.0, implemented in Java.