## 3 Results
### Gene Ontology Graph  
Gene ontology has a hierarchical data structure, where each term can have multiple parents and multiple children. A directed acyclic graph (DAG) is commonly used for the GO graph. GO terms and their relationships are expressed by nodes and edges. The primary difficulty in GO graph visualization is displaying a large number of edges. Because GO terms have eight types of different relationships between them, a GO graph displays considerably more edges than a normal graph [28]. In our implementation, we visualize a GO graph that is based on the DAG drawing strategy proposed by AT&T [29]. The strategy proposes minimizing edge crossing by utilizing a heuristic approach.  
The GO graph visualization in DegoViz has diverse properties. Each GO term displays the connections with neighbors with its annotation (see Figure 4). Enriched GO terms are color-coded with their \(p\)-value and display the corresponding DEG collection, which is designated within a circle. If GO terms share the same DEG, then DegoViz provides interactive facilities similar to the heatmap. Users can review detailed information on the specific GO term, including the corresponding DEG list, by simply placing the mouse over it. When the GO term is clicked, all of the parent GO terms between the root GO terms are highlighted and vice versa. This allows the users to easily follow the path of all related terms from the overall graph. We also propose the display controller (on the right side of the window). This allows the display of only those elements set by the user. This facilitates the clear recognition of a complex relationship between GO terms because users can select a certain type of relationship for display. When corresponding GO terms appear on large-scale graph data, it is difficult to display and understand the details from the \"big\" picture. For a more user-friendly data search, we provide a zoom in/out and screen move function, allowing users to easily move to a position on the overall graph and display the specific relationship of the GO terms.  
To consider the relationship between different enriched GO terms that share the same DEG, we introduce two additional visualization tools for the relation between a DEG and corresponding GO terms. The first graph displays how GO terms share their corresponding DEG sets (see Figure 5).  
Figure 4: Visualization of the gene ontology graph.  
Over the enriched gene ontology, the number of corresponding DEGs is assigned in green. A green line between two GO terms means that they share the same genes. The assigned number on the line indicates the number of shared genes. For example, in Figure 5, the graph indicates that two GO terms, \"neuron differentiation\" and \"central nervous system neuron development\", share five DEGs, where each has 13 and five corresponding DEGs. This means that all of the DEGs from the latter are included in the former ontology.  
Another graph indicates how an individual DEG relates to the corresponding GO terms (see Figure 6). It displays specific DEGs that are linked to multiple GO terms. We implement this feature using multidimensional scaling (MDS) [30; 31] in circular space. The MDS method places the DEGs, the green dots in the graph in Figure 6, at the optimal position nearest to the enriched GO terms to which they belong. This allows users to recognize the similarity of the DEG set, which relates to similar GO terms. For example, by reviewing Figure 6, we can observe that the four DEGs located in the center are linked to all of the enriched GO terms, which means that these genes belong to all of the enriched GO terms in the graph. Further, we can observe that all DEGs that belong to ontology \"negative regulation of neuron differentiation\" and \"central nervous system neuron development\" are shared with the three other enriched GO terms. For both graphs, user interaction is available to search for information that is more specific.  
Figure 5: Visualization of the number of DEGs shared between enriched GO terms.