**4. Discussion**

In the discussion of the model presented and evaluated in the previous sections, let us pay attention to the example studied, the network of football team components. Results have been presented related to the proposed centrality measure APABI for a biplex network like this one.

We also consider that it may be relevant to calculate the nodes centrality in each of the layers, that is, separately and independently. In this way, it is possible to analyze the differences in the calculation of centrality in a single or multiplex networks, respectively, verifying if there is a certain correlation between the results obtained. We have calculated the APA centrality of the nodes in each of the layers. The numerical results obtained are shown in Table 2, where the numerical values of the centrality and the position of the nodes in the classification or ranking can be seen.

It should be noted that all the calculations have been made taking the value of the alpha parameter equal to 0.5. This means that we assign the same importance in the centrality computation to the connections of the nodes as to the data associated with them.

As it was already mentioned, the APABI centrality provides a classification of the nodes according to their importance in the biplex network studied. So, nodes 20 and 18 were the most important in the team. This can also be analyzed when the layers are considered independently.

The comparison between the APABI centrality and the APA centrality by independent layers offers us some remarkable facts. For instance, the most active nodes from the point of view of social networks are 20, 18, 10 and 5. The most important nodes from the point of view of the game are 4, 7, 1, 15. It is evident that there is no correlation between both relationships; leaders from the social point of view are not necessarily the most decisive players in the team's game. Thus, the most participative player of the team, the one who most relates to the game with his teammates, is not socially the most active nor will he be the most influential individual within the group.

We appreciate that the most important nodes in a biplex network are nodes that maintain high positions in the two rankings obtained in each of the layers. The node 20 is the one that presents a greater importance from the social point of view, however, it is not among the first three nodes that have a greater participation in the team game. On the other hand, node 18 is not as socially active as node 20, although it has a greater degree of association with its teammates in the team game than the first one and has had a greater presence in the team games, specifically participating in more than 5 games. The numerical results show that this positive rating does not compensate the high social importance of node 20, although it should be highlighted that the difference in the centrality between both nodes is very small. It can be concluded that both nodes are the team leaders.
