# NodeVector: A Novel Network Node Vectorization with Graph Analysis and Deep Learning
## 3 Materials and Methods
### Node Similarities  
Networks exhibit uncertain topologies for various reasons [30]. This means that the connections and relationships in these networks are subject to false positives and false negatives. These false positive and false negative interactions can arise due to various general factors such as data collection limitations, noise in the data, privacy concerns, or network-specific factors such as the dynamic nature of social interaction networks or the inherent uncertainty in biological processes for biological networks. The occurrence of false positives and false negatives poses a significant challenge in network analysis, with a high prevalence in numerous networks such as social or biological networks. Research has shown that in protein interaction networks, the data often contain a significant number of false positive and false negative interactions. Specifically, it has been reported that the rates of false positive and false negative interactions can exceed half of the total network [31]. Network edge enrichment is a method for improving the accuracy of prediction by adding similarity-inferred edges to networks. This is achieved by first identifying pairs of nodes that are similar, and then adding an edge between these pairs if they do not already have one. The resulting enriched network is then used for the prediction task. Network edge enrichment has successful results in network analysis such as social network analysis [32] and PPI network analysis [33]. In social network analysis tasks, identifying communities and predicting future interactions can be examples of application, and in protein interaction network analysis tasks such as prediction of protein functions can be named. Results are typically more accurate than those obtained from the original network. Based on these literature results, we developed the hypothesis that network enrichment methods can increase the representation ability of network node embedding methods. To test and validate our hypothesis, we developed network enrichment methods that can be used with our new node encoding algorithm and examined their effects on the results. As a result of our hypothesis, we consider that the use of network enrichment instead of a high percentage of negative samples affects the estimation results positively and that the network enrichment methods we develop are preferable to reduce the negative sample rate. To process network nodes by computational methods such as measuring similarity between nodes or to use machine learning algorithms, at least a simple numerical representation of the nodes is required. Since nodes are considered independent units, the one-hot encoding method is the most commonly used representation type in the literature. Unlike in the literature, we use an alternative encoding approach for representing network nodes, departing from the commonly used one-hot encoding method. While one-hot encoding is widely employed, it has limitations in terms of capturing interaction information and can lead to a loss of important contextual details during subsequent operations. To address these limitations, in this study, the row belonging to the relevant node in the adjacency matrix is improved and used as a multi-label one-hot encoding for the initial node representation. For the mathematical representation of network nodes, we define the leveled neighborhood matrix representation. The level corresponds to the shortest path distance measurement between nodes. From this definition, for source node n, \(L_{1}\) level representation includes nodes that can be accessed with at most 1 edge, while \(L_{2}\) level representation includes nodes that can be accessed with at most 2 edges. Similarly, \(L_{k}\) representation contains nodes accessible with at most \(k\) edges. In the neighborhood matrix representation, unlike the original representation, a self-loop is added to each node. In this way, it is ensured that the node itself is included in the representation.