The recognition for protein complexes based on the PPI network has become one of the most important channels in current research. Detection of protein complexes from PPI networks is an important work in the understanding of biological processes. It is also of great significance for researching mechanisms and developing new drugs. Researchers have put forward a variety of effective methods to recognize protein complexes. The MCODE algorithm chooses a vertex with the maximum weight as the initial cluster, and then recursively searches for the vertices that meet a threshold value to add to the cluster (Bader and Hogue, 2003). The DPClus is a modified algorithm that chooses the vertices with high connectivity with the present cluster iteratively (Altaf-Ul-Amin et al., 2006). Jerarca uses the hierarchical cluster to partition the complexes based on the distance among proteins (Aldecoa and Marín, 2010). RNSC divides the complexes by means of a cost function (King et al., 2004). MCL (Enright et al., 2002) simulates network flow by constructing a similarity matrix, alternately performs expansion and inflation operations, and achieves clustering effect after multiple iterations. But the method is difficult to identify the complexes with little overlap. After that, an improved method was proposed which measured the reliability of PPI based on the annotations of protein function (Cho et al., 2007). SCI-BN and ClusterM combine topology of PPI and biological information of sequences to identify complexes (Qi et al., 2008; Wang et al., 2020).

Although these methods can effectively identify functional modules of proteins, they all ignore the internal structure of the modules. The basic structure of a protein complex is composed of the nucleus of a protein complex and all its subordinate proteins (Gavin et al., 2006). So, a protein complex can be regarded as a subgraph with a nucleus and its subordinate proteins for assisting the nucleus to play a specific role. COACH (Wu et al., 2009) and CORE (Leung et al., 2009) are proposed based on the idea. The F-MCL algorithm combines firefly algorithm and MCL (Lei et al., 2016). ClusterONE is a clustering algorithm guided by cohesion which can identify subgraphs of dense substructure (Nepusz et al., 2012). However, the cohesion formula may lead to deviation in the clustering process. EA (Halim et al., 2015) uses multi-population evolutionary algorithm to cluster the probability map. MNC is a novel clustering model based on multi networks which combines the shared clustering structure in PPI and domain–domain interaction (DDI) networks in order to improve the accuracy of identification (Ou-Yang et al., 2017). IdenPC-CAP recognizes protein complexes from the interaction networks consisting of RNA–RNA interactions, RNA–protein interactions, and PPIs (Wu et al., 2021). CSC uses both topological and biological characteristics to identify protein complexes (Liu et al., 2018; Sharma et al., 2018). DPCMNE detects protein complexes via multilevel network embedding (Meng et al., 2021). PC2P formalizes protein complexes as biclique spanned subgraphs and converts the problem of detecting protein complex to coherent partition (Omranian et al., 2021). A semi-supervised model based on non-negative matrix tri-factorization is also used to detect protein complex (Liu et al., 2021). In the FCAN-PCI, the semantic similarity of proteins and the topology of PPI network are integrated into a fuzzy clustering model (Pan et al., 2021). GECA proposes a model based on the gene expression and core-attachment (Noori et al., 2021). The idenPC-MIIP method modifies the weights of original network by defining mutually important neighbors on the weighted network and then identifies protein complexes using a greedy algorithm (Wu et al., 2021)

For a PPI network N, TSSN computes the edge aggregation coefficient as the topology characteristics of N, makes use of the GO annotation as the biological characteristics of N, and then constructs a weighted network. NNP identifies protein complexes based on this weighted network.

In order to assess the TSSN method, we compare the protein complexes identified by three classical methods, that is, ClusterONE, MCODE, and MCL, respectively, based on the PPI networks with the weight computed by TSSN and the PPI networks without weight. We compare the results of protein complexes predicted by CFinder, ClusterONE, MCODE, MCL, EA, and NNP methods.

In all recorded experimental results, we use CYC2008 as the standard set and set the threshold of OL as 0.2. OL represents the overlap rate between the two complexes. The value of OL being 0.2 indicates that the identified complex is considered correct when the OL with the standard complex reaches 0.2.

Table 1 shows the results. For each method in Table 1, u represents the methods that are used to identify the complexes from the unweighted networks and T represents the methods that are used to identify the complexes from the weighted networks computed by the TSSN. From Table 1, we can see that the precision values for the weighted networks computed by the TSSN method are higher than those for the unweighted networks. So the TSSN method is efficient for computing the weigh values of networks.

The precision results of the NNP algorithm depend on the thresholds of weighted neighbor ratio (WNT). Table 2 shows that F1 values gradually increase with the increase in t values if the thresholds of WNT is (0,0.2), and F1 gradually decreases as a whole if the t values of WNT continue to increase from 0.2. So F1 can reach the maximum 0.42 if values of WNT are (0.2, 0.25). Table 3 shows the precision values of NNP on different thresholds of WNT. When the WNT value is 0.22, the precision is 0.5, which is slightly higher than the other five values. Therefore, it is reasonable for the NNP algorithm to set the threshold of the WNT as 0.22.

Table 4 lists the comparison of the cluster information identified by the six algorithms compared with CYC2008. CYC2008 is selected as the benchmark, and its average size is 4.71; the closer the average size of the cluster identified by a method is to 4.71, the more accurate the method is. Among the six algorithms, the average size of clusters identified by the NNP is 4.54, which is closest to the size of clusters in the standard data. So the recognition result of NNP has high theoretical reliability.

Table 5 shows the results identified by the CFinder, ClusterONE, MCODE, MCL, EA, NNP, and PC2P methods for three complexes randomly selected from DIP. CFI is the mRNA cleavage factor complex with size 5; NEC is the nuclear exosome complex with size 12, and DRC is the DNA-directed RNA polymerase II complex. The table shows that six methods recognize the same proteins as the CYC2008 for the CFI, that is, OL 100%, OL of NNP, and MCL is both 100% for NEC. The OL of PC2P is 83.3%. The OL of EA and that of MCODE are the same, which is 91.7%, ranking second. There is one missed protein: YHR081W. CFinder has two missed proteins and the OL is 84%. The OL of PC2P is 83.3%. So, the accuracy of ClusterONE is low. For DRC, the performance of NNP and ClusterONE is better, while the OL value of EA is 83.3%. There are many omissive and wrong proteins detected by CFinder, MCODE, MCL, and PC2P. The OL of CFinder is 56.3%. The OL of PC2P is only 53.3%.

Table 6 shows the results of six methods. In terms of precision, the value of CFinder is lowest, which is only 26.98%, and the value of NNP is largest compared with other algorithms, reaching 51.07%. The precision of MCODE lists second, reaching 50.1%. Although the precision of MCODE is high, the recall is low, which leads to the low F1 value. From the table, it is obvious that the F1 of NNP is max among all other methods. So NNP has better accuracy in identifying protein complexes than other methods.

Table 7 lists the number of protein complexes identified by CFinder, ClusterONE, MCODE, MCL, EA, NNP, and PC2P from DIP data set, matched with CYC2008. As shown in Table 7, the protein complexes identified by NNP based on the DIP data set are perfectly matched with 17 protein complexes. The MCODE only has six complexes perfectly matched with the standard set. The PC2P has no perfectly matched complex with the standard set. Therefore, compared with other algorithms, the NNP algorithm can accurately and perfectly match more protein complexes on the DIP data set.

Table 8 lists some protein complexes with low p-values identified by the NNP algorithm on the DIP, which can show that the protein complexes identified by the NNP algorithm have significant biological significance. Table 9 lists three protein complexes perfectly matched with DIP and NewMIPS identified by the NNP method.

Considering the topological structure of the PPI network, it introduces the gene ontology in biological information. We propose the methods for computing weight of protein interaction network and the recognizing of protein complexes on the weighted network. By comparing with other algorithms, the TSSN method based on topological features and GO term similarity can filter the noise, which can reduce the impact of noise data. The NNP algorithm can identify the protein complexes. The experimental results show that the NNP is superior to other classical algorithms.

In the future, we will adopt new technologies to detect false-positive edges and predict false-negative edges in the PPI network, thus improving the quality of the PPI network. Machine learning methods will be used to detect protein complexes based on their biological characteristics. Finally, since static PPI networks only contain the interaction between proteins and cannot reflect the dynamic characteristics of proteins interactions over time, we will study how to build a dynamic PPI network and identify protein complexes in the dynamic network.