# A Combinatory Framework for Link Prediction in Complex Networks
## 8 Evaluation
### EML Network Dataset  
We have downloaded the EML dataset from Noesis open framework [[https://noesis.ikor.org/datasets/link-prediction](https://noesis.ikor.org/datasets/link-prediction)]([https://noesis.ikor.org/datasets/link-prediction](https://noesis.ikor.org/datasets/link-prediction)) (accessed on 5 March 2023). EML is a network of individuals who shared emails. In Table 1, we show the EML network properties. In Figure 2, we show the visualization of the network as well as histograms of the degrees of its nodes. Figure 2: EML visualization and histograms. Here we present a visualization of EML network, as well as the distribution of its node degrees in the form of a histogram. From the visualization and histograms, we can conclude that the network consists of nodes with relatively few links to each other. Source: [[https://github.com/parisdim/A-Combinatory-Framework-for-Link-Prediction-in-Complex-Networks](https://github.com/parisdim/A-Combinatory-Framework-for-Link-Prediction-in-Complex-Networks)]([https://github.com/parisdim/A-Combinatory-Framework-for-Link-Prediction-in-Complex-Networks](https://github.com/parisdim/A-Combinatory-Framework-for-Link-Prediction-in-Complex-Networks))—Datasets (accessed on 5 August 2023). From the EML network, we created three sub networks. Each of them contains a subset of EML edges, while the edges we have removed (omissible edges) are stored in a separate set. We call these sets Subgraph_0, Subgraph_1, Subgraph_2. In Table 2, we show the edges that we have removed from each set as well as the score of the five basic algorithms that we have applied to each of these sets. We remind you that each score of an algorithm corresponds to the number of edges it has found and are really missing from each set. These edges are at the top of the evaluation list of each algorithm. For example, in the Subgraph_0 network, we have removed 1582 edges. The common neighbor centrality (cnc) algorithm has a score of 297. This means that it has managed to have, in the first 1582 positions of its evaluation list, 297 edges of those we have removed from the original network. We recall that each position in an algorithm's evaluation list contains a missing edge as well as the algorithm's estimate of how likely it is to be added in the future. These lists are sorted in descending order of algorithm evaluation. Therefore, at the top of the evaluation list are edges that are more likely to be added in the future, according to the algorithm we use. From the scores in the table, we can observe that the five basic algorithms do not make such good estimates in the network we are examining, because they find a small subset of the edges that are actually missing. To build and evaluate our enhanced predictor tool, we use one of Subgraph_0, Subgraph_1, or Subgraph_2 as a training set, while we use the remaining two as test sets for our new enhanced predictor tool. With the training set, we create the vector of weights that gives us the participation of each basic algorithm that we use in the final estimation of our enhanced predictor tool. In the test sets, we apply our enhanced predictor tool estimate to each missing edge so that we have a new estimate for each of them. In Table 3, we show four comparative tests. In each test, we compare the performance of the evaluation derived from the composition of specific basic algorithms according to our enhanced predictor tool as well as from a basic algorithm that had the best performance in the sets participating in the test. Each test consists of four columns. In the first column, we report the training set and the test sets. In the next two columns, we report the score of the two estimators, and in the fourth column, we show how much one estimate differs from the other, i.e., how many more edges than the ones that are really missing did the test winner manage to find. In Test 1, we have built our enhanced predictor tool using all five basic algorithms and compare its results with the results of Adamic-Adar, which has the best results of the five basic algorithms we use.