# A Special Structural Based Weighted Network Approach for the Analysis of Protein Complexes
## 5 Results and Discussion
### Function Enrichment Analysis  
We investigated the biological significance of our detected protein complexes to confirm the effectiveness of our WECALM approach because the reference complexes were incomplete. Each identified complex has a \(p\)-value calculated by Equation (36) for enrichment analysis. A complex is considered biologically significant if its \(p\)-value is less than \(p\leq 10^{-2}\) after being detected using a wide range of methods. A complex with a lower \(p\)-value has a statistically significantly greater biological significance. Using SGD's GO Term Finder web service [83], we validated the functional relationships and cellular mechanism of the detected complexes based on biological process terms. In this case, the smallest  
Figure 7: The effect of \(\omega\) on the performance of WECALM based on Recall, Precision, F-measure, CR, and MMR matrices. is a predefined core structural similarity threshold. **(A)**: The performance on BioGRID based on NewMIPS. **(B)**: The performance on DIP based on NewMIPS. **(C)**: The performance on BioGRID based on CYC2008. **(D)**: The performance on DIP based on CYC2008. The precision and F-measure are maximum when \(\omega=0.8\) and \(\omega=0.4\), respectively, on both NewMIPS and CYC2008. \(p\)-value across all gene ontology terms represents the functional homogeneity of each identification complex. We also evaluated the protein complexes identified by WECALM and calculated the \(p\)-value of protein complexes identified by MCL, COACH, Core, CALM, EWCA, CFinfer, Core, CALM, GMFTP, ClusterONE, CMC, and ProRank+ whose sizes were \(\geq\) 3 Table 4 shows the \(p\)-value test results for MCL, COACH, Core, CALM, EWCA, CFinfer, GMFTP, ClusterONE, CMC, ProRank+, and WECALM. To compare the biological significance of protein complexes identified by different algorithms, we computed the number of detected complexes, the total number of detected complexes, and the percentage of detected complexes in different \(p\)-value ranges. We discovered on the one hand that the majority of algorithms only consider the percentage of detected complexes. The \(p\)-values of identified protein complexes, on the other hand, are proportional to their size [22; 23; 84; 85]. When analyzing the function enrichment of identified protein complexes, it is essential to consider both the quantity and the proportion of the identified complexes. On the BioGRID dataset, as shown in Table 4, WECALM detected 97.45% of the significant new protein complexes, slightly less than ProRank+, which recorded the highest significant score (97.59%). The size of the protein complexes identified by WECALM is typically larger than that of other algorithms such as ProRank+, which is most likely why. WECALM detects far more protein complexes than ProRank+. MCL, COACH, Core, CALM, EWCA, CFinfer, GMFTP, ClusterONE, and CMC is 107, 161, 1035, 463, 1341, 269, 449, 210, 832, and 728 protein complexes in the BioGRID dataset, respectively. We also observe that WECALM has detected a maximum of 1376 protein complexes, significantly better than ProRank+. On the DIP dataset, WECALM detected 96.17% of significant protein complexes, compared to ProRank+'s 93.79%, an increase of about 3%. At the same time, WECALM also identified the most protein complexes. In the DIP dataset, there were 113, 144, 315, 603, 869, 272, 350, 235, 146, and 319 protein complexes identified by MCL COACH, Core, CALM, EWCA, CFinfer, GMFTP, and CMC, respectively. In general, as the percentage of detected protein complexes decreases, the proportion of significant protein complexes increases. COACH,