## 3 Results and Discussion  
The HEA interaction network was created using Gephi software version 0.9 based on a Fruchterman Reingold layout, as shown in Figure 2. Each node in the HEA graph was a HEA compound. Figure 2 shows a portion of the HEA interaction network in which some connections were filtered for the clarity of the network presentation. As shown in Figure 2, each node in the HEA network is displayed in a specific color and size. Nodes with the same color placed in the same community are more similar. Using the communities in the HEA network, the nearest neighbors of each node were determined. The size of the node circle in Figure 2 indicates the number of connections for each compound to others. Each node with more relations to its neighbors is illustrated by a larger circle. The gradient color of each color for the edges in Figure 2 shows the strength of the connection. The strong relations are indicated by darker and thicker lines. The degree of a node in an HEA network is the number of connections it has to other nodes. The degree distribution is the probability of the distribution of these degrees over the whole network. The degree distribution shows the average connections of each node, which expresses the number of neighbors of each node. The HEA network degree distribution is shown in Figure 3 and was obtained at 8.212. The KNN algorithm was applied to select the \(k\)-nearest neighbor algorithm in the HEA network. Finally, the phase was predicted with high precision via plurality voting. The value of \(k\) considered in this study was three, that is, three neighbors were used for phase prediction. Figure 4 is a portion of the network that shows the target node in red and its nearest neighbors in dark blue. It predicts the phase of the target node based on the nearest neighbors. The relation between the KNN-based ML approach's accuracy and the HEA interaction network is finding the nearest neighbors in the network for phase prediction. Figure 4 is an example. Suppose that a new compound is introduced that is not available in the dataset, and its phase is unknown. The phase prediction process is such that first, the compound location is found in the interaction network to identify its connections with its neighbors. Then, the phase is predicted by KNN-based analysis. Assume that ZrHfTiCuNi in Figure 4 is a compound with an unknown phase. The compound ZrHfTiCuNi has four neighbors which are listed as follows: ErTbDyNiAl by weight 0.8192, TiZrCuNiBe by weight 0.9998, PdPtCuNiP by weight 0.8191, and ZrHfTiCuCo by weight 0.8498. The node's neighbors list is sorted in descending order of their connection weight. It selects three of the nearest neighbors in dark blue. The proposed approach correctly predicts the ZrHfTiCuNi phase as Amorphous. Figure 4 shows the stronger connections of each compound with thicker lines, and the compound with the largest circle has more neighbors. Figure 3: The probability distribution of the degree of a node in an HEA network is the distribution of connections it has to other nodes which is called degree distribution. Figure 2: A portion of the HEA interaction network with Fruchterman Reingold layout. Nodes with a larger circle have more neighbors, which indicates a stronger relationship. The accuracy of 88.88% was achieved using the \(k\)-fold random subsampling method. Model performance was used for 27 compounds in the testing set, of which, the phase of 18 compounds was correctly predicted, and 9 compounds were not correctly predicted based on the confusion matrix. The proposed approach predicts the phase of unseen data. It was compared with six other methods, as shown in Figure 5. The Fast Large Margin model has one-fifth of the accuracy of the proposed approach, which had the worst accuracy in phase prediction. The Support Vector Machine (SVM) and Naive Bayes model perform the prediction with equal accuracy, which is about twice that of the Fast Large Margin model. The SVM performed classification and regression in supervised learning.