## 3 Results
### Candidate Network and Sub-Networks  
With our predicted associations, we focused on the pairs containing at least one candidate gene. Among these pairs, some were known to be associated, while others were not known to be associated. In addition, some of these genes were known to be ASD-related genes, while others were novel candidate genes. We have demonstrated these complex relationships with a graph. Figure 6 shows the network of candidate genes and their connecting genes. Through this network, we discovered interesting sub-groups of genes, and this prompted us to conduct a further analysis of the network using ClusterViz [48], a plugin software for CytoScape [49] based on the EAGLE clustering algorithm [50]. With this algorithm, we applied a clique size threshold of 3 and a complex size threshold of 2. The results revealed three sub-networks, and these are shown in Figure 7.  
Figure 4: Results of KEGG pathway enrichment analysis.  
Figure 7a shows a sub-network consisting of 53 genes and 87 associations. Among them, the top three genes with high degree values, _CUL3_, _MECP2_, and _TOP1_ (with degree values of 33, 31, and 18, respectively) stood out. _CUL3_ and _MECP2_ are known ASD-related genes. Hence, DNA Topoisomerase I (_TOP1_) is an interesting candidate gene in this sub-network due to its connections to several known ASD-related genes, including _AP3B2_, _CCT4_, _CUL3_, _MEPC2_, and _SLC12A5_. Some of these links were already known associations found in the database. It has been reported that _TOP1_ inhibition reduces the expression of long genes linked to synapses and autism [14; 15]. Additionally, this sub-network revealed other genes of interest that were connected to known ASD-related genes, including _RBMI7_, _RPL3_, _SNRPN_, and _UBC_.  
Figure 5: Results of Reactome pathway enrichment analysis.  
Figure 6: The network of candidate genes. The red nodes represent known ASD-related genes and the green nodes represent new candidate genes. The bold lines represent known associations and the dashed lines represent unknown associations.  
Figure 7b shows a sub-network comprised 33 genes and 60 associations. _RBFOX1_ and _TSC1_ had the highest degree values (30 and 29, respectively). However, these two genes were already known to be ASD-related genes. General Transcription Factor IIIC Subunit 3 (_GTF3C3_) is an intriguing gene in this sub-network. This gene exhibited a slightly higher betweenness centrality value (0.0625) than the other genes in the sub-network. Interestingly, _GTF3C3_ was connected to two known ASD-related genes, _SDC2_ and _RBFOX1_. The protein encoded by _GTF3C3_ is a part of the TFIIIC2 complex, which is involved in the recruitment of RNA polymerase III. _GTF3C3_ has been identified as a potential ASD gene [48].  
The sub-network shown in Figure 7c contains 64 genes and 124 associations. _CTNNB1_ and _TOP3B_ were the two genes with the highest degree values (62). Nevertheless, these two genes were already known to be ASD-related genes. _CTNNB1_ has two known associations (to _DDB1_ and _SIRTI_), while _TOP3B_ exhibited known associations with _CLTC_, _PTPRK_, _HCFC1_, _FXR1_, _EEF2K_, _ALDH19A1_, _SYMPK_, and _DGKZ_. These connecting genes could potentially be candidates for ASD. All information regarding the associations, association statuses, and gene statuses of all the sub-networks is provided in Supplementary Table S6.