## 3 Methodological Approach
### Visualization and Validation  
The final graph shows the intensity of the relation among factors by providing a clear visual representation of how the variables interact and influence each other within the FCM, aiding in understanding system behavior and relationships. Specifically, the system generates a directed graph where the nodes represent the main identified factors' variables and the edges show the strength and direction of the influence between them. This graphical representation helps illustrate how the risks interact and, in particular, which risk (or subset of risks) may likely impact the occurrence of other related risks. We will outline the methodological approach we developed to create the network. This network visualization technique aims to represent and highlight the connections and influence between elements within the input dataset. The key steps in this approach are explained.  
* Node creation: an object is created to construct the network. We start by extracting factors' ID values from the dataset, representing the elements under consideration. These values serve as the nodes in the network.
* Edge formation: we iterate the procedure through the dataset and, for non-zero values, establish directed edges between nodes. Each edge's weight corresponds to the value of the dataset element, indicating the strength of the relationship. Notably, the edge with the maximum weight is identified, signifying its exceptional significance.
* Visualization layout: the layout for visualizing the network is developed, focusing on presenting nodes with higher TE values prominently. The procedure organizes nodes into layers based on their TE values, ensuring that nodes with equal TE values are grouped. This step results in a more intuitive and informative visualization.
* Network visualization: the network is plotted and the edges between nodes are drawn with varying attributes, such as width and color, depending on their weight. Edges with the highest weight (TE) are accentuated in a distinct color, making them easily distinguishable. The use of arrows indicates the direction of the influence in the network.
* Node labels: the network nodes are labeled with the same IDs as the factors they represent. These labels are placed on the nodes and formatted for clarity.
* Visual output: the procedure generates the final visualization, showcasing the network of relationships, with arrows indicating the direction of the influence, node labels displaying the element names, and varying edge attributes representing the strength of the relationships.  
This methodological approach results in a visual representation of the relationships and influences within the dataset, allowing for a clear understanding of which elements have the most significant impact and how they relate to one another. It aids in identifying key elements and their interactions, which can be valuable for decision making and analysis. By updating input evaluations, the approach confirms its consistency in recommending predefined measures for the most interconnected elements. As previously specified, this flexibility allows the proposed method to be extended to any business sector and any decision-making problem focused on analyzing dependence within a dataset.