Advancing Community Detection with Graph Convolutional Neural Networks: Bridging Topological and Attributive Cohesion

1 Introduction

Community Detection (CD) in social networks is an active research area with immense practical implications across numerous fields like marketing, sociology, and public health [Chunaev, 2020; Wu et al., 2020]. Unveiling hidden structures within complex networks drives transformative innovations that help to shape the future of society [Su et al., 2022; He et al., 2021a]. Real-world applications of CD are vast and impactful, including information spreading [Karatas¸ and S¸ahin, 2018], dimensionality reduction, and product recommendation [Moradi et al., 2015].

Many existing methods for CD are mainly based on network topology [Traag et al., 2019; de Silva et al., 2023; Jin et al., 2021]. However, real-world networks often include node attributes that are crucial for identifying meaningful communities. Networks with these attributes are known as attributed networks [Chunaev, 2020; Bhowmick et al., 2024; Xie et al., 2021].

In an attributed network, a community is a group of nodes that are densely connected and share strong attribute similarities [Bhowmick et al., 2024; Zhu et al., 2024; Luo and Yan, 2020]. Such communities capture both topological and attribute cohesiveness, making them meaningful representations of real-world groups where both connections and shared characteristics are important. A set of non-overlapping communities that completely covers the whole attributed network is known as the community structure of the network.

CD in attributed networks has been approached through various methods, including heuristic-based [Combe et al., 2015], evolutionary computation (EC)-based [Guo et al., 2024], and learning-based techniques [Jin et al., 2019; Bhowmick et al., 2024; Ju et al., 2023; He et al., 2022]. Among these, learning-based methods have gained significant attention in recent literature [Sun et al., 2019], with Graph Convolutional Neural Networks (GCNs) emerging as the leading solution. GCNs leverage deep learning to integrate topological and attribute information through layer-wise propagation [Tsitsulin et al., 2023; He et al., 2021b], offering a precise understanding of network topology and providing a comprehensive view of social networks. Despite their strengths, state-of-the-art GCN approaches still face two critical challenges.

The first issue lies in the challenge of directly training GCNs to maximize modularity, which often results in suboptimal community structures [Chunaev, 2020]. Although maximizing modularity effectively promotes topological cohesiveness [Bhowmick et al., 2024; Tsitsulin et al., 2023], the inherent complexity of the modularity function makes gradient-based optimization prone to local optima, leading to poor results. This difficulty in achieving globally optimal solutions highlights the limitations of modularity as a direct training objective and underscores the need to use a different loss function that makes it more straightforward to maximize modularity.

The second issue arises from using human-labeled communities to train GCNs, as these labels are typically based solely on node attributes while overlooking topological cohesiveness. This omission, a critical factor for high-quality community structures, often leads to poorly formed communities with disconnected nodes, significantly reducing modularity. This problem highlights the necessity of integrating topological information with node attributes to enhance GCNs' ability to produce well-formed and cohesive community structures.

To address these issues, we propose a novel Topological and Attributive Similarity-based Community detection (TASCom 1 ). TAS-Com introduces a newly designed loss function to guide GCN training. Our innovative loss function exploits the highly effective and scalable Leiden algorithm [Traag et al., 2019] (see Appendix M for more details) to identify community structures with global optimal modularity. Leiden is further utilized to refine human-labeled communities to ensure connectivity within each community, enabling TAS-Com to detect community structures with desirable trade-offs between modularity and compliance with human labels. The key contributions of this paper are as follows:

• We are the first to address the limitations of directly using human-provided community labels to train GCNs, which often compromise CD due to lack of topological cohesiveness. To overcome this, we propose a novel Leiden-based method to refine human-labeled communities, ensuring they are both cohesive and free from disconnected nodes that degrade CD quality, thereby enhancing their suitability for effective GCN training.
• We are the first to address the limitations of directly training GCNs to maximize modularity. We propose a novel modularity-based similarity loss, enhanced by the Leiden algorithm, to effectively guide GCNs toward discovering community structures with globally optimal modularity. Additionally, we integrate this loss with a refined human-label-based similarity loss, significantly improving the GCN's ability to identify community structures that achieve both high modularity and strong alignment with human-labeled communities.
• We conduct extensive experiments on many real-world attributed benchmark networks. The experiment results confirm that TAS-Com can significantly outperform multiple state-of-the-art approaches for CD across most of these benchmark networks.

2 RelatedWork

CD has traditionally focused on graph topology, but recent research [Chunaev, 2020] started to consider node attributes to improve CD in attributed networks. Heuristic approaches like I-Louvain [Combe et al., 2015] use inertia-based measures for attribute similarity but often fail to find globally optimal structures. EC methods, such as @NetGA [Pizzuti and Socievole, 2018], optimize fitness functions combining attributes and connectivity, while multi-objective algorithms [Li et al., 2017] refine these strategies. However, these approaches rely on manually designed similarity measures, overlooking intrinsic node relationships and highlighting the need for machine learning techniques to learn high-level node embeddings for more accurate CD [Su et al., 2022].

1 The full paper is available at https://arxiv.org/abs/2505.10197, with code at https://github.com/desilanja/TAS-Com

The emergence of advanced Graph Neural Networks (GNNs) has significantly shifted recent research toward learning-based approaches, showcasing the critical importance of leveraging these technologies for more effective CD [Chunaev, 2020; Zhu et al., 2024; Yang et al., 2023; Liu et al., 2022; Xia et al., 2021]. These approaches generally perform CD through two consecutive steps: 1) node representation learning, and 2) node grouping/clustering based on the learned high-level node embeddings [Zhou et al., 2023; Tsitsulin et al., 2023; Bhowmick et al., 2024].

The most commonly used GNNs for CD are Autoencoders (AEs) [Zhu et al., 2024] and GCNs [Bhowmick et al., 2024]. AEs are proficient at extracting node semantic information [Liu et al., 2024; Sun et al., 2020; Kumar et al., 2023]. Notable AE-based approaches include DNR [Yang et al., 2016] and CDBNE [Zhou et al., 2023]. Despite their recent success, AEs are not specifically designed to process graph data. In contrast, GCNs can effectively handle node information at both topological and attribute levels [Zhu et al., 2024].

Most GCN approaches for CD conduct either supervised or semi-supervised learning based on ground truth community labels [Bhowmick et al., 2024]. A few recent studies, like SGCN [Wang et al., 2021] and DMoN [Tsitsulin et al., 2023], further demonstrated the importance of unsupervised learning. For example, Zhu et al. [Zhu et al., 2024] introduced DyFSS, an unsupervised approach that dynamically fuses embeddings from multiple self-supervised tasks with nodespecific weights, effectively balancing attribute and structural information to enhance clustering accuracy and robustness. However, DyFSS's reliance on hyperparameter tuning, such as pseudo-label thresholds, limits its generalizability across diverse graph datasets without extensive adjustments.

Existing unsupervised methods largely focus on optimizing modularity, often neglecting explicit optimization of attribute similarity [Tsitsulin et al., 2023]. While DGCluster [Bhowmick et al., 2024] optimizes both modularity and attribute similarity, its maximization of modularity frequently leads to suboptimal community structures. DGCluster learns directly from human-labeled communities, which often group disconnected nodes based solely on attributes, undermining connectivity cohesiveness. To overcome these challenges, we propose TAS-Com, powered by an innovative loss function that properly integrates topological and attribute information, improves the quality of human-labeled communities, and enables GCNs to discover community structures with optimal modularity and strong alignment with human labels.

3 ProblemDefinition

An attributed network can be modeled as a graph N = (V,E,X), where V is the set of nodes, i.e., V = {v1, v2, ..., vn}. E is the set of edges, i.e., E = {ei,j|ei,j ∈ V × V }. X ∈ Rn×T is the node attributes matrix, where T is the number of attributes for each node.

A community structure CS of an attributed network N is a set of non-overlapping communities, i.e., CS = {C1, C2, ..., Ck} where k ≥ 1 s.t. ∀q ̸= l, Cq ∩ Cl = ∅ and ∪pq=1Cq = V . The main goal of CD in attributed network N is to identify CS that satisfies the following conditions:

• High topological cohesiveness: This implies that intracommunity edge density within any community is higher than the inter-community edge density among different communities [Chunaev, 2020].
• High attribute similarity: Nodes within the same community exhibit strong attribute level similarity. Meanwhile, nodes from different communities are expected to have distinct and dissimilar attributes.

Modularity (Q) is a well-known metric to quantify the quality of different community structures [Newman and Girvan, 2004]. As a quality metric at the topology level, Q with respect to any given community structure CS is defined in Equation (1):

where m is the total number of edges of the social network, ki and kj are the degrees of the nodes vi and vj . Aij is the adjacency matrix where Aij = 1 if an edge exits between nodes vi and vj, otherwise 0. δ(.) is the Kronecker delta function where δ(ci, cj,CS) = 1 if nodes vi and vj are in the same community (i.e., ci = cj with ci and cj being the community labels of node i and j respectively), otherwise 0.

Normalized Mutual Information (NMI) is a widely used metric in existing research to assess how well a community structure C aligns with human-labeled community structure D in a social network N, particularly in terms of attributive similarity [Bhowmick et al., 2024; Chunaev, 2020]. It is defined in Equation (2) below:

where P represents the confusion matrix. Each of its elements Pij refers to the number of nodes of community Ci ∈ C that are also in community Dj ∈ D. The values of i and j span within the range of {1, . . . , n} where n is the number of nodes in N. gC refers to the number of communities in C. gD refers to the number of communities in D. Pi. denotes the sum of the i-th row of P and P.j denotes the sum of the j-th column.

Our Goal: We aim to identify high-quality community structures that can outperform those discovered by other state-of-the-art methods, achieving significantly higher scores in both modularity (indicating topological cohesiveness) and NMI (indicating alignment with human labels).

4 ProposedMethod

This section proposes TAS-Com for CD in attributed networks. Figure 1 illustrates the overall design of TAS-Com. As shown in this figure, the adjacency matrix A, node attribute matrix X, and human-labeled communities CSO are utilized to build the loss function L and to train our GCN model. Specifically, the GCN model first processes A and X to generate the high-level node embedding X(e) . Supported by the Leiden algorithm and our refinement algorithm in Algorithm 1, X(e) is further adopted to calculate respectively the modularity-based loss LM and refined humanlabel-based loss LR to be introduced later in this section. The total loss L is then constructed by combining LM and LR. L subsequently guides the training of the GCN. Finally, based on X(e) produced by the trained GCN, a clustering algorithm named BIRCH [Zhang et al., 1996] is performed to obtain the final community structure CS.

We follow [Bhowmick et al., 2024] to design the architecture of our GCN model. In particular, the message passing rule for the l-th layer, where l = 0, 1, ...,L-1, is defined in Equation (3):

where ˜ A is the normalized adjacency matrix s.t. ˜ A = D- 12 AD 12 . D is the diagonal node degree matrix [Bhowmick et al., 2024]. The embedding output of the l-th layer is denoted by X(l) . W (l) refers to the corresponding learnable weight matrix of this layer. SELU is used as the activation function σ(·) to incorporate the non-linearity for the aggregation of node attributes [Klambauer et al., 2017]. Further, the node embedding matrix X(e) is transformed as in [Bhowmick et al., 2024] to ensure that the embedding is constrained within the positive coordinate space (see Appendix C). The following provides detailed descriptions of the new components introduced in TAS-Com.

4.1 Proposed loss function (L)

In line with the problem formulation in the previous section, we propose a new loss function to train GCNs to jointly maximize the node connectivity strength (modularity optimization) and the node attribute similarity (NMI optimization). The proposed loss function is defined at a high level in Equation (4):

where µ ≥ 0 is a hyperparameter that controls the influence of LR in L. LM refers to the modularity-based similarity loss and LR refers to the refined human-label-based similarity loss. The process of constructing LM and LR are explained in the next two subsections.

Modularity-based similarity loss (LM)

Most existing GNNs were trained directly to optimize the modularity metric (see Equation (1)), resulting frequently in locally optimal community structures with low modularity [Tsitsulin et al., 2023]. In this paper, we employ the Leiden algorithm with proven effectiveness and scalability [Traag et al., 2019; de Silva et al., 2023; de Silva et al., 2022] to identify high-quality community structures with close-to-optimal modularity. Due to the stochastic nature of Leiden, we apply Leiden to a social network 30 times and select the community structure with the highest NMI score out of all runs. Leiden focuses solely on topological information, whereas our problem also concerns about attribute information. Therefore, we select the community structure with the highest NMI from 30 runs, ensuring an ideal balance between topological level and attribute level similarities.

Let H ∈ Rn×n be the pairwise information matrix [Bhowmick et al., 2024]. As an n × n matrix, where n is

Algorithm 1 Refinement of the human-labeled communities

Input: Human-labeled community structure CSO Output: Refined community structure CSR

• 1: for each community Ck in CSO do
• 2: Step 1: Apply Leiden algorithm
• 3: Obtain a sub-network SN that contains nodes in Ck
• 4: CSL ←- CS with highest Q(CSL) after applying Leiden(SN) for n times
• 5: Step 2: Merge sub-communities
• 6: while |CSL| ≥ threshold do
• 7: for each pair of sub-communities Ci and Cj in CSL do
• 8:
• CSnew ←- Merge Ci and Cj
• 9: Calculate Q(CSnew) {Refer Equation (1)}
• 10: end for
• 11: CSL ←-CSnew with the highest Q(CSnew)
• 12: end while
• 13: CSR ←- (CSR \ {Ck}) ∪CSL
• 14: end for
• 15: return CSR

be used to obtain the substitute labels. The pseudo-code of the newly proposed refinement method is presented in Algorithm 1. According to this algorithm, the refinement process consists of two main steps explained below.

1. Apply a topology-based CD algorithm to detect sub-communities in each human-labeled community. Since Leiden can produce topologically connected communities [Traag et al., 2019], we apply Leiden to obtain the connected sub-communities within each humanlabeled community. In practice, any scalable CD algorithm, such as Louvain [Blondel et al., 2008], can replace Leiden for this task. Due to the stochastic nature

the total number of nodes in a social network, each element of H is defined as in Equation (5):

where ci and cj are the community assignments of nodes vi and vj according to Leiden. Specifically, the community structure identified by Leiden can be represented in the form of a one-hot matrix CSL ∈ {0, 1}n×k below:

where k is the total number of communities detected by Leiden. Subsequently, H can be rewritten as follows:

In line with the above, the modularity-based loss LM is designed to minimize the discrepancy between the community assignments obtained by Leiden and the embedding similarity matrix derived from the high-level node embedding X(e) produced by the GCN model, as detailed below:

Refined human-label-based similarity loss (LR)

As pointed out in the introduction, human-labeled communities contain disconnected nodes that seriously hurt the quality of the community structure in terms of modularity (see Appendix D for a concrete example). Hence, we propose a new method to refine human-labeled communities to simultaneously enhance consistency with human labels and connectivity within each community. In practice, if human-labeled communities are unavailable, any scalable CD algorithm can of Leiden, it is executed 10 times in our experiments for each human-labeled community. We then choose the community structure with the highest modularity, i.e., CSL, as described in lines 2-4 of Algorithm 1.

1. Merge sub-communities. In our experiments (see Appendix E), we found that Leiden can sometimes produce many small sub-communities CSL that significantly deviate from human-labeled communities. Hence, GCNs trained based on CSL can exhibit poor NMI performance. To address this issue, we must merge closely connected sub-communities in CSL. For this purpose, we iteratively merge pairs of sub-communities in CSL. Each iteration will select and merge the pair of subcommunities that can produce the highest modularity after merging among all possible merge pairs (see lines 612 in Algorithm 1). This process continues until a specific threshold = |CC(NL)| 2 is reached (see Appendix B), where CC(NL) = {C1, . . . , Ck} refers to the set of connected components of the sub-network NL containing all nodes of network N in CSL.

The community structure obtained from the above two steps is deemed the refined human-label-based community structure, denoted as CSR. CSR is subsequently adopted to train our GCN to maximize NMI. Notably, CSR is consistent with human-labeled communities since each humanlabeled community comprises one or more connected subcommunities in CSR.

Using CSR, we define the refined human-label-based loss LR in Equation (8) below:

In the above, matrix HR follows the definition in Equation (5). It is the pairwise matrix obtained from below:

where CSR is the one-hot matrix (similar to CSL) derived from the community structure obtained from Algorithm 1. According to Equation (8), LR guides our GCN to minimize the discrepancy between HR and the embedding similarity matrix derived from X(e) . This is expected to enable the trained GCN to produce node embedding that closely aligns with human-provided community labels.

Driven by the loss function L designed above, we can finally develop a system to train GCNs through the stochastic gradient descent method. The training process is summarized in Appendix A.

4.2 Community detection based on node embedding

Based on the node embedding produced by the trained GCN model, we utilize the clustering algorithm named Balance Iterative Reducing and Clustering using Hierarchies (BIRCH) [Zhang et al., 1996] to identify the final community structure, following DGCluster [Bhowmick et al., 2024]. The primary benefit of BIRCH is its ability to flexibly construct community structures without determining the number of communities in advance, enabling the algorithm to achieve a desirable trade-off between modularity and NMI.

5 Experiment Design

This section outlines the experimental settings used to examine the performance of TAS-Com.

5.1 Benchmark networks

We conduct experiments on six commonly used attributed social networks with human-provided community labels [Bhowmick et al., 2024; Zhu et al., 2024]. In particular, Cora and Citeseer are citation networks [Sen et al., 2008], Amazon Photo and Amazon PC are co-purchase networks [Shchur et al., 2018], and Coauthor CS [Shchur et al., 2018] and Coauthor Phy [Shchur and G¨unnemann, 2019] are co-authorship networks for computer science and physics respectively. Table 1 summarizes all the benchmark networks.

5.2 Baseline approaches

The effectiveness of TAS-Com is evaluated in comparison to 12 state-of-the-art approaches, categorized into three distinct groups: (1) approaches relying solely on attributive or topological information for CD, including k-m(feat) (i.e., k-means based only on features) and DMoN [Tsitsulin et al., 2023]; (2) approaches that consider node similarities at both the topological and attribute levels, including k-m(DW) [Perozzi et al., 2014], k-means(DGI) [Veliˇckovi´c et al., 2018], DAEGC [Wang et al., 2019], SDCN [Bo et al., 2020], NOCD [Shchur and G¨unnemann, 2019], DyFSS [Zhu et al., 2024], and DGCluster [Bhowmick et al., 2024], and (3) approaches that use graph pooling techniques, including DiffPool [Ying et al., 2018], MinCutPool [Bianchi et al., 2020], and Ortho [Bianchi et al., 2020]. Additional details regarding these approaches are provided in Appendix G, while the performance of the MinCutPool and Ortho approaches is analyzed in Appendix J. Among all competing approaches, DGCluster is the most competitive approach, as it is explicitly designed to maximize both modularity and attribute-level node similarity.

5.3 Performance metrics

We adopt two metrics, namely modularity and NMI introduced in Section 3 to compare the performance of all competing approaches. As explained previously, both metrics are essential to determine the quality of the community structures identified by the trained GCNs [Bhowmick et al., 2024].

5.4 Parameter settings

In the experiments, TAS-Com employs a GCN architecture identical to that proposed in [Bhowmick et al., 2024]. The model uses a GCN with two hidden layers, the Adam optimizer with a learning rate of 0.001, and is trained for 300 epochs. Additional details on the parameter settings of TASCom are provided in Appendix K. In line with existing works [Bhowmick et al., 2024; Tsitsulin et al., 2023], we report the average performance results across 10 independent runs with different random seeds. Furthermore, µ and threshold in Algorithm 1 are two important hyperparameters. Their sensitivity analysis is reported in Appendix B.

6 Results and Discussion

6.1 Performance comparison

Table 2 compares the performance of TAS-Com with 12 stateof-the-art approaches in terms of modularity (Q) and NMI. Most of the results, except DyFSS and DGCluster have been reported previously in [Bhowmick et al., 2024]. The results for DyFSS and DGCluster were reproduced using their published code and original experimental settings. Furthermore, the results of DGCluster are reported in Table 2 based on two settings of the hyperparameter λ (i.e., λ = {0.2, 0.8}), which are the recommended settings in [Bhowmick et al., 2024]. As evidenced in Table 2, TAS-Com achieved the best tradeoff between Q and NMI across all benchmark networks. We have conducted the Wilcoxin rank-sum test. Our test results show that the observed performance gain of TAS-Com is statistically significant (see Appendix H for statistical analysis).

Specifically, while TAS-Com obtained identical NMI value (i.e., 41.0) on the Citeseer network as DGCluster, TASCom significantly improves the quality of the community structure in terms of modularity Q. Although DyFSS attained the highest NMI value for the Citeseer network, its corresponding Q value was notably lower than that of TASCom. Meanwhile, concerning the Amazon PC and Coauthor Phy networks, TAS-Com noticeably improves the quality of the community structures in terms of NMI (i.e., 12% and 11% increase in NMI compared to DGCluster on the two networks respectively) without hurting the modularity Q. For the Coauthor CS network, while TAS-Com doesn't match the best Q value of 74.2 achieved by DGCluster(λ = 0.2), it improves the Q value by 1.1% and matches the NMI value of 82.1 obtained by DGCluster(λ = 0.8).

These results confirm that TAS-Com outperforms in Q and/or NMI without sacrificing either metric. It shows significant performance gains for several benchmark networks, reinforcing its competitiveness for CD in attributed networks.

6.2 Further analysis

We conduct additional analysis to validate the effectiveness of TAS-Com.

Connectivity within communities

We analyze the connectivity within each community identified by TAS-Com, DGCluster, and DyFSS. For this purpose, we check the average number of isolated sub-networks in each community of a community structure CS = {C1, C2, . . . , Ck}, i.e., Oc(CS), as defined below:

where CC(C) refers to the set of isolated sub-networks within community C ∈ CS. Ideally, all nodes with any given community C are expected to be inter-connected, i.e., |CC(C)| = 1. In this case, Oc(CS) reaches its smallest value of 1. Hence, the lower the value of Oc(CS), the better. Figure 2 compares Oc(CS) achieved respectively by TASCom, DGCluster, and DyFSS. For DGCluster, we report the lowest Oc(CS) obtained by either DGCluster(λ = 0.2) or DGCluster(λ = 0.8).

Figure 2 shows that TAS-Com significantly reduces isolated sub-networks compared to DGCluster and DyFSS. While TAS-Com may still produce isolated sub-networks, these can be treated as separate communities in the final CS without reducing modularity Q (see Appendix F). This confirms that using refined human-labeled communities to guide the training of GCNs enhances the effectiveness of CD.

Performance evaluation using additional metrics

To further evaluate the performance of the proposed TASCom, we employ two additional metrics: conductance and F1 score [Bhowmick et al., 2024](see Appendix L). Table 3 compares TAS-Com and the baseline algorithm, DGCluster, in terms of average conductance (Con) and average F1 score (F1) on the benchmark networks Cora and Amazon Photo. The results demonstrate that TAS-Com outperforms DGCluster on these networks, highlighting its superior performance not only in Q and NMI but also in Con and F1. Additional results for all benchmark networks are in Appendix I.

Ablation study

To verify the effectiveness of the loss function proposed in Equation (4), an ablation study has been performed on the Cora network. We specifically consider four variants of TASCom associated with different designs of the loss functions. Figure 3 compares all variants based on both Q and NMI. In this figure, LM indicates that L = LM , LR indicates that L = LR, Q + LR indicates that L = Q + µLR, and LM + NMI indicates that L = LM + µNMI, where NMI refers to the attributive similarity loss with respect to the human-labeled communities (without using Algorithm 1). Finally, LM +LR indicates the proposed loss function in Equation (4).

Figure 3 shows that LM + LR outperforms Q + LR and LM +NMI, confirming the importance of both LM and LR for the overall loss L to be effective. While LM alone yields slightly better Q value than LM + LR, it results in significantly lower NMI. This is because LM focuses only on topological similarity. Similarly, LR achieves a slightly higher NMI but a noticeably lower Q score compared to LM +LR, as it considers only attributive similarity. Hence, it is crucial to balance topological and attributive similarities by including both LM and LR in the overall loss L. This ablation study confirms the effectiveness of the proposed loss function L.

7 Conclusion

In this paper, we developed TAS-Com, a novel GCN-based approach powered by a newly designed loss function to effectively train GCNs to extract high-level node embeddings in attributed social networks. Our new loss function leverages the highly effective and scalable Leiden algorithm to identify community structures with globally optimal modularity (Q). Meanwhile, Leiden refines human-labeled communities, ensuring connectivity within each community and enabling GCNs to effectively learn node similarity at both the topology and attribute levels. Thanks to our new loss function design, the trained GCNs can detect community structures with a desirable balance between topological similarity (i.e., modularity (Q)) and attributive similarity (i.e., NMI). Experiments on multiple benchmark networks with varying sizes and complexities show that TAS-Com significantly outperforms 12 state-of-the-art approaches.

Future work could explore the potential integration of temporal dynamics or multi-view data to enhance the wide applicability of TAS-Com, including dynamic social networks.