 Research
 Open Access
 Published:
Clustering analysis of tumor metabolic networks
BMC Bioinformatics volume 21, Article number: 349 (2020)
 The Correction to this article has been published in BMC Bioinformatics 2020 21:494
Abstract
Background
Biological networks are representative of the diverse molecular interactions that occur within cells. Some of the commonly studied biological networks are modeled through proteinprotein interactions, gene regulatory, and metabolic pathways. Among these, metabolic networks are probably the most studied, as they directly influence all physiological processes. Exploration of biochemical pathways using multigraph representation is important in understanding complex regulatory mechanisms. Feature extraction and clustering of these networks enable grouping of samples obtained from different biological specimens. Clustering techniques separate networks depending on their mutual similarity.
Results
We present a clustering analysis on tissuespecific metabolic networks for single samples from three primary tumor sites: breast, lung, and kidney cancer. The metabolic networks were obtained by integrating genome scale metabolic models with gene expression data. We performed network simplification to reduce the computational time needed for the computation of network distances. We empirically proved that networks clustering can characterize groups of patients in multiple conditions.
Conclusions
We provide a computational methodology to explore and characterize the metabolic landscape of tumors, thus providing a general methodology to integrate analytic metabolic models with gene expression data. This method represents a first attempt in clustering large scale metabolic networks. Moreover, this approach gives the possibility to get valuable information on what are the effects of different conditions on the overall metabolism.
Background
Biological data produced by high throughput experiments, and in particular by Next Generation Sequencing technologies are being accumulated in publicly available databases. Multiyear research projects, such as The Cancer Genome Atlas (TCGA) [1], are producing petabytes of data. Besides this type of initiatives, there are many research projects focused on extracting knowledge from experiments, and they are storing resulting metadata in knowledgebased repositories. One of these projects is the Human Metabolic Atlas (HMA) [2], which has been accumulating genomescale metabolic models for different healthy and cancer tissues. Such models describe in analytic format the knowledge about specific tissues metabolism. From the integration of such different sources, it is possible to obtain a knowledgebased characterization of patients with different cancer subtypes.
In the case of Genome Scale Metabolic (GSM) models, this integrative approach has been used in several studies [3–5]. It usually involves gene expression data and metabolic models, to compare two conditions (e.g., healthy vs diseased), highlighting an average behaviour of a group of patients with respect to another. In order to overcome this limit, we decided to model patients separately, obtaining a network model for each of them. Starting from this representation of the cohort, we proposed a supervised learning technique to produce predictive mathematical models to classify diseases and their subtypes [6].
Following these ideas, we decided to devise a clustering technique for network data. Again, each patient is represented in form of a network integrating gene expression data and a GSM model. We obtain a representation of the networks based on a probability distribution of their shortest paths, and an adhoc distance based on ShannonJensen divergence is used to compute their pairwise distances. Since the number of nodes in such networks is in the order of thousands, we explored a simplification technique [7, 8] that helps in reducing the computational time needed for the distance computation. Using the mutual distances among networks, it is natural to represent them in a similarity matrix, on which spectral clustering [9] can be used to characterize the classes of patients. There are two main advantages of this solution. First, modeling each sample in the dataset using data from both a metabolic model and a gene expression experiment, provides more information. Then, representing the data in the form of networks permits to obtain a quantitative model that retains information about the crosstalk existing among the different pathways and modules of the human metabolism.
The overall workflow used in the present study is schematically shown in Fig. 1. Its main four main steps are detailed in the “Materials and methods” section.
Materials and methods
Data
Gene expression data of breast cancer from microarray experiments are publicly available in the NCBI Gene Expression Omnibus database [10] (GSE78958). Raw CEL files were imported, corrected, transformed, and normalized using GEOquery [11] and Affy [12] R packages. Probe ids were mapped to relative gene symbols using the annotation file “hgu133a2.db”. RNA sequencing data of breast cancer (Project TCGABRCA), lung cancer (Projects TCGALUSC and TCGALUAD), and kidney cancer (Projects TCGAKIRC and TCGAKIRP) collected into the Genomic Data Commons Data Portal (https://portal.gdc.cancer.gov) were downloaded in the form of FPKM normalized read counts. As summarized in Table 1, the Breast Microarray dataset contains 418 samples of four intrinsic molecular subtypes based on BreastPRS [13, 14]: Basallike (99 samples), HER2enriched (50 samples), Luminal A (226 samples), and Luminal B (43 samples). The Breast RNAseq dataset contains 401 samples of two intrinsic molecular subtypes based on PAM50 [15]: Luminal A (200 samples), and Luminal B (201 samples). The Lung dataset contains 337 samples divided into three groups: Adenocarcinoma (159 samples), Squamous carcinoma (150 samples), and Solid tissue normal (28 samples). The Kidney dataset contains 299 samples divided in three groups: 159 samples of clear cell Renal Cell Carcinoma (ccRCC or KIRC), 90 samples of Papillary Renal Cell Carcinoma (PRCC or KIRP), and 50 samples of Solid tissue normal.
For each type of cancer under study, the corresponding metabolic network was downloaded from the HMA database [2] in the compressed Systems Biology Markup Language (SBML) format [16]: breast cancer INIT model [17], lung tissue, and kidney tissue models [18]. The metabolic models were imported, and the relative stoichiometric matrices were extracted in the R environment using the sybilSBML package.
Raw expression data are considered as basic data for comparison. They are a subset of the whole gene expression data obtained by selecting the metabolic genes. We refer to these data with the term “Expression” in the experimental results.
Network construction
The graphs (throughout the paper, we will use the terms graph and network interchangeably) were generated considering the metabolites as nodes, with edges connecting metabolites involved in the same reaction, one as a reagent and the other one as the product, as illustrated in Fig. 2. Given the metabolic model (Fig. 2a), for each reaction and each gene/enzyme catalyzing it, we consider all the (source, target) couples of involved metabolites. (Figure 2b). The network for the metabolic model is obtained by linking each node representing a source metabolite with the node representing the corresponding target metabolite, with as many links as there are enzymes catalyzing the reaction (Fig. 2c. Data for each patient is given by the relative gene expression values of the sample Fig. 2d), that are used for weighting the corresponding edges (Fig. 2e). The obtained multigraphs (i.e., graphs where two nodes may be linked by more than one edge) are finally reduced to simple graphs (referred to as “Whole graph” in the results), where weights are computed by averaging the gene expression values in the same reaction and adding these means in the case of different reactions (Fig. 2f). In general, the mapping of enzymes to the reactions represents a difficult task since it is not a onetoone association, as multiple enzymes can catalyze the same reaction as well as one enzyme can catalyze multiple reactions. We assumed that the weights of multiple enzymes catalyzing the same reaction can be simplified by averaging the expression values of their corresponding genes. Some of them work in complexes and some others are alternative catalysts, but we considered all their expressions equally important for the regulation of the connection between a substrate and a product. Instead, the relationship between genes catalyzing different reactions and linking the same metabolites can be considered as a Boolean OR, as the path from one metabolite to the other is alternatively defined by one reaction OR the other, and thus simplified by summing their values, as suggested in [19].
The same metabolite can have more than one cellular compartment localization fulfilling different functions; thus, we considered it as a different metabolite in each compartment Reactions not catalyzed by any enzyme were not considered and disconnected nodes were excluded as well. Indeed, networks representing different patients differ only for the weights of their links, and this information would be absent in both the above cases.
The recurrent metabolites (such as H2O and CO2; see Additional file 1 for a complete list) were excluded from the network. Indeed, they are functional groups, cofactors, and carriers for electrons transferring, and cannot be intrinsically considered compounds; therefore, their connections would give rise to an unrealistic definition of the paths and their lengths, as suggested in [20]. The metabolitebased networks were generated through an inhouse R script, giving rise to 3254, 3380, 3959, and 4022 nodes for the Breast Microarray, Breast RNAseq, Lung, and Kidney networks, respectively. The networks are then partially processed using igraph R package [21]. Further details concerning the data networks are reported in Table 2.
Network summarization
Given a network \(\mathcal {G} = (V,E,W)\), where V and E are the set of all nodes and edges in \(\mathcal {G}\), respectively, and W is the weight matrix, its summarization into supernodes was obtained as described in [7]. Briefly, given a partition of the l nodes of the network \(\mathcal {G}\) into k clusters, a matrix Q=[q_{1},q_{2},...,q_{k}]∈R^{l×k} is considered, consisting of a set of indicator vectors q_{j} that represent the membership relationship for cluster j,j=1,…,k (i.e., q_{j}=(q_{1,j},…,q_{l,j})^{T}, where, for all i, q_{i,j}=1 if node i is in cluster j and q_{i,j}=0 otherwise). The summarized network \(\mathcal {G}_{s} = {\left (V_{s},E_{s},W_{s}\right)}\) is formed by merging the nodes in each of the k clusters into a supernode; the weight matrix W_{s} is obtained by W_{s}=Q^{T}WQ. Further details are given by the authors in [7].
In our approach, network summarization is applied to the largest connected component of each network (see Table 2), having experienced that the other disconnected components contained too few nodes, less than 1% of the largest connected component (see Additional file 2). For computing the initial partition of each network into k clusters, we adopted spectral clustering; a well know algorithm used for cluster analysis [9]. It uses a representation of the dataset in terms of mutual distances among the samples, and therefore is well suited for networks.
Spectral clustering uses as a main tool the Laplacian matrix\(\mathcal {L}=\mathcal {D}A\) of a graph \(\mathcal {G}\), where A is the adjacency matrix of \(\mathcal {G}\) and \(\mathcal {D}\) is a diagonal matrix, where \(\mathcal {D}_{i,i}\) is the degree of node i,i=1,…,l. The eigenvectors x and eigenvalues λ of \(\mathcal {L}\) are obtained by solving \(\mathcal {L}x = {\lambda }x\). Finally, the eigenvectors of the graph Laplacian \(\mathcal {L}\) that correspond to the k smallest eigenvalues are used as features for a clustering algorithm, where each row of that matrix is a representation of the corresponding sample in the dataset.
In our implementation, we used the spectral.clustering function of the fcd (Fused community detection) package in R [22]. For each dataset, clustering was performed on the unweighted adjacency matrix of its graphs, that is common to all of them (all the networks within a dataset have the same nodes and edges; only the edge weights change, based on gene expression values that are different for each sample).
Distance and clustering
The final step of our approach involves the calculation of distances between the summarized networks, in order to cluster the patient samples. In [23], we represented networks using a set of metrics obtained by computing distances between probability distributions of network topological properties, which were an extension of the definitions introduced in [24–26]. In this study, we use the distances calculated between transition matrices\(\mathcal {T}^{r}\) of different networks \(\mathcal {G}_{r}\), whose element \(\mathcal {T}^{r}_{i}(j)\) is the probability of node i to be reached in one step by a random walker located in node j. Therefore, \(\mathcal {T}^{r}\) is the adjacency matrix of \(\mathcal {G}_{r}\) rescaled by the degree of each node and contains local information about the connectivity of \(\mathcal {G}_{r}\).
Given two networks \(\mathcal {G}_{p}\) and \(\mathcal {G}_{q}\), let their transition matrices be \(\mathcal {T}^{p}\) and \(\mathcal {T}^{q}\), respectively. Averaging over all k supernodes of the summarized networks, we defined the network distance \(\mathcal {M}^{2}\):
where d_{JS} is a metric known as JensenShannon distance [27], defined as the square root of the JensenShannon divergence \(\mathcal {J}\) of the two distributions [28]. Using the distance in Eq. (1), each network in the dataset can be represented by the vector containing the distances from all other elements.
The square matrix containing in each row the vector representing a sample from the dataset is usually called the Gram matrix or distance matrix.
For obtaining the final clustering results of the proposed approach, we applied spectral clustering from the sklearn package in Python [29] to the distance matrices computed for the summarized networks.
Results and discussion
Analysis of summarized networks
The summarization of the whole network through spectral clustering and supernodes collapse gave rise to different sized networks, depending on the number k of clusters that were set (Fig. 1 step 3). Inspired by [8], we chose six values of k, ranging between 50 and 300, which is approximately less than 10% of the nodes of the whole graphs, and evaluated the clustering performance on the distance matrices (see Additional file 3). A range tighter than the one in [8] was set to better analyze small differences. The best performance was obtained using 300 supernodes for all the datasets except the kidney, which shows the best results with 250 supernodes.
As an example of possible evaluation of the clusters from a biological point of view, in Fig. 3, we show the KEGG pathways enriched by the enzymes from the edges of all pairs of interacting nodes (metabolites) present in each of the 50 clusters of the kidney metabolic network (see Additional File 4 for details). The figure shows that the clustering of the whole network gives rise to communities of nodes and relative edges which have a defined biological function. The enriched terms containing the highest number of enzymes enriching a pathway are shown for the top 28 clusters, according to nodes number. Most of the terms are enriched by a single cluster or few of them, suggesting that almost each of the obtained clusters has a specific biological meaning. Some of the bigger clusters enriched terms as “Metabolism of xenobiotics by cytochrome P450” and “Chemical carcinogenesis”, which are well known to be involved in tumor metabolism and particularly in renal injuries. The kidney is the organ responsible for the elimination of drugs from the body, but it is also involved in drug metabolism through activity of cytochrome P450 (CYP) enzyme group and crosstalk with the liver [30]. Furthermore, due to its functions of filtering and reabsorption, the exposure to carcinogenic substances is much higher than other organs [31]. The most abundant cluster (692 nodes) enriches “Purine metabolism” pathway. Purines are involved in many biological processes, including immune responses and host–tumor interaction, and their metabolism changes continuously in response to cell demands; thus, it is a consequence that the alteration of the enzymes involved in this pathway, organized in dynamic multienzyme complexes called “purinosome”, occurs in severe diseases. In particular, purine metabolism involvement and nucleotide imbalance in tumorigenic processes has been largely demonstrated [32–34].
Performance results
Several metrics exist for clustering. In the experiments, we consider an extended set of metrics often adopted for clustering evaluation [29, 35–38], to allow easier comparison with existing and newly proposed methods. They are described in detail in the Additional file 5 and summarized in Table 3, where we report their name (column Name), abbreviation (column Acronym), definition (column Computed as), possible values (column Codomain), and whether they should be minimized (↓) or maximized (↑) to have more accurate results (column Better if). Matlab scripts used for clustering evaluation are provided as Additional file 6.
Performance results for the four datasets are reported in Table 4. Here, “Expression” refers to results achieved by spectral clustering applied to the gene expression data obtained in the first step of the proposed approach, “Whole graph” refers to results obtained by spectral clustering on the distance matrices of the networks constructed in the second step, and “Summarized graph” refers to the results achieved by the proposed simplified approach.
For the Breast Microarray dataset, we observe that clustering gene expression data leads to poor overall performance. Indeed, RI values below 50% reveal very low accuracy and negative ARI values reveal that accuracy is even lower than the one that could be obtained by a random partitioning. At the same time, more than 50% of the times the wrong decision is taken (MR=52.72%). Similarly, all the other metrics confirm poor performance. This can be ascribed to the microarray technology used to quantify the gene expression, which is known to be less sensible for slight differences in expression measurements compared to the RNAseq method used for the other datasets. Moreover, Bartlet et al. [39] investigated the classification of breast cancer into intrinsic molecular subtypes, showing that the classifications obtained using different tests were discordant in 40.7% of the studied cases. This could also justify the poor results obtained for clustering the raw expression data from the Breast RNAseq dataset. On the other side, we observe fairly improved performance for the Breast Microarray dataset when using both whole and summarized graph data. This may mean that considering metabolic interactions, rather than raw data, can help in capturing the differences between breast cancer subtypes.
This also holds true for the case of the Breast RNAseq dataset, even though with a small improvement as compared to the case of gene expression data.
For the Lung and Kidney datasets, clustering of raw data leads to quite high performance, as witnessed by low values of MR and high values for all the other performance metrics. Comparable performance is achieved using whole graphs, slightly better than using summarized graphs.
For all the datasets, the execution times for computing the distance matrices for summarized graphs strongly decrease (≈ 35 times less of the execution times for whole graphs).
Therefore, we can conclude that the proposed simplification proves to be beneficial for clustering “difficult” highthroughput data (e.g., those coming from imprecise technologies or having rather uncertain ground truth classification) and only minimally detrimental in the other cases. In all cases, it allows a strong reduction in execution times, making it feasible for big data analyses.
Visual exploratory analyses
Tdistributed Stochastic Neighbor Embedding (tSNE) is a nonlinear dimensionality reduction technique that allows embedding of highdimensional data for visualization in a lowdimensional space [40]. It models each highdimensional sample by a two or threedimensional point in such a way that similar samples are modeled by nearby points and dissimilar samples are modeled by distant points with high probability. It is capable of retaining the local structure of the highdimensional data, while also revealing some important global structure, such as the presence of clusters at several scales.
Figure 4 provides visual representations of the Kidney data mapped into the 2D Euclidean space by tSNE. Data are colored to reflect the ground truth classification (left column) and the clustering results (right column).
The top row of Fig. 4 reports the visual representation for the gene expression data. Here, three clusters are obtained, basically consistent with the ground truth classification (left column). Only a few embedded points corresponding to ccRCC appear close to the PRCC cluster and vice versa. Moreover, a small of group of embedded points from the two carcinoma classes appears close to the solid tissue normal class. These few visual anomalies also reflect in the clustering results (right column), where the three clusters appear more uniform that the ground truth (i.e., no red point in the center of the blue cluster and no blue points in the center of the red cluster), consistently with the visual judgement.
The middle row provides the visual representation for the whole graph data. Here, the two carcinoma clusters are spatially contiguous, without marked separation (left column). The same can be said for the clustering results (right column), where most of the misclassified points appear spatially close to the cluster they are deemed to belong to (i.e., no blue point in the rightmost border of the red cluster and no blue points in the lower border of the green cluster). This shows that spectral clustering on these data fails like we would fail in judging based on the tSNE visual representation.
The bottom row reports the visual representation for the summarized graphs. Similarly to the case of gene expression data, three spatially separated clusters can be identified, corresponding to the three different classes (left column). Only few carcinoma samples lye in an ambiguous region of the plane, at the intersection of the three clusters. Clustering assigns almost all of these few samples to the ccRCC class (right column), predicting the ambiguous plane region as belonging to this class.
The above analysis of visual representations obtained using tSNE suggests that the proposed simplification leads to clusters that are better separated than in the whole graph case, and similarly to the gene expression case, thus confirming the comparable performance achieved. Analogous analyses carried out for all the considered datasets (see Additional file 7) confirm the achieved performance results.
The heatmap in Fig. 5 is a colorbased representation of the distance matrix obtained by the calculation of the \(\mathcal {M}^{2}\) metric between the summarized graphs created for the Kidney project patients. The patients are ordered according to distance values. The labels from ground truth classification and from spectral clustering are shown. In both cases, three clusters are clearly visible, representing the three classes: PRCC (blue), ccRCC (red), and solid tissue normal (green). In particular, the two disease classes form two welldefined clusters for most of the patients, but some of them appear to be mixed. Some of these mixed samples are differently assigned by spectral clustering compared to ground truth labels. Looking at the heatmap, these samples seem to not belong to any of the present classes and show a big heterogeneity among themselves as well. A certain grade of heterogeneity is also shown by the normal samples, but not enough to not assign them to the same cluster. Heatmaps for the remaining datasets are provided in Additional file 8.
Conclusions
In this paper, we describe a methodological approach for clustering of biological networks obtained by the integration of genomescale metabolic models with gene expression data. Each sample in a dataset is described by a network, whose nodes are metabolites connected by an edge when involved in the same reaction. The edge weights are derived by the abundance of the enzymes catalyzing the associated reaction. The networks are then simplified, summarizing them into supernodes, to reduce the computational complexity of the clustering algorithm, which uses an adjacency matrix containing the distances between all pairs of networks. We show that the performance of this approach on literature data is competitive with the clustering of raw data, with the advantage of highlighting the crosstalk between different metabolic modules and pathways. Future work will be performed to extract biological information linked to the connection between the supernodes which define the differences among the classes. Furthermore, given the heterogeneity of tumors, clinical information and further subclasses annotations will be exploited in networks analysis.
Availability of data and materials
The data used in the present study are publicly available and have been downloaded from three main public data repositories. In detail: the gene expression microarray data are available at the Gene Expression Omnibus portal (https://www.ncbi.nlm.nih.gov/gds) under the accession number GSE78958; gene expression RNAseq data are available at the Genomic Data Commons Data Portal (https://portal.gdc.cancer.gov) under the cancer projects indicated in the “Data” paragraph of Materials and Methods; the metabolic models can be retrieved from the HMA database at http://www.metabolicatlas.org.
Change history
02 November 2020
An amendment to this paper has been published and can be accessed via the original article.
Abbreviations
 TCGA:

The cancer genome atlas
 HMA:

Human metabolic atlas
 GSM:

Genome scale metabolic model
 TCGABRCA:

The cancer genome atlas breast invasive carcinoma
 LUSC:

Lung squamous cell carcinoma
 LUAD:

Lung adenocarcinoma
 KIRC:

Kidney renal clear cell carcinoma
 KIRP:

Kidney renal papillary cell carcinoma
 ccRCC:

Clear cell renal cell carcinoma
 PRCC:

Papillary renal cell carcinoma
 SBML:

Systems biology markup language
 tSNE:

Tdistributed stochastic neighbor embedding
 RI:

Rand’s index
 ARI:

Adjusted rand’s index
 MR:

Misclassification rate
 F1:

FMeasure
 FMI:

FowlkesMallows index
 CA:

Cluster accuracy
 NMI:

Normalized mutual information
 AMI:

Adjusted mutual information
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Acknowledgements
The work was carried out within the activities of L. Maddalena as members of the INdAM Research group GNCS. The early stage investigator fellowship of Ichcha Manipur has been supported by the INCIPIT program cofunded by Horizon 2020  COFUND Marie Sklodowska Curie Actions. The work of Mario R. Guarracino was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE). The authors would like to thank G. Trerotola for the technical support.
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This article has been published as part of BMC Bioinformatics Volume 21 Supplement 10, 2020: Proceedings from the 13th Bioinformatics and Computational Biology International Conference  BBCC2018. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral.com/articles/supplements/volume21supplement10.
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Publication costs are funded by the MIUR project DM23492 for the publicprivate Laboratory for Genomics, Transcriptomics and Proteomics (LABGTP).
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MRG, IM, and IG conceived the project, LM investigated clustering evaluation and tSNE visual representation, IM and IG carried out all experiments. All authors drafted and revised the manuscript, as well as read and approved the final manuscript.
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Additional file 1
List of recurrent metabolites removed from the network. The file AdditionalFile1.xlsx contains a list of all the recurrent metabolites which were removed during network construction.
Additional file 2
Connected components size. The file AdditionalFile2.xlsx provides tables showing number of connected components and relative nodes from the four datasets networks.
Additional file 3
Clustering Results. The file AdditionalFile3.pdf provides spectral clustering results with different numbers k of supernodes for network summarization.
Additional file 4
KEGG term enrichment from the 50 clusters of the Kidney metabolic network. The file AdditionalFile4.xlsx provides the list of KEGG terms enriched from the enzymes belonging to the different clusters in the kidney metabolic network.
Additional file 5
Clustering metrics. The file AdditionalFile5.pdf provides an in depth description of all the metrics adopted for clustering evaluation.
Additional file 6
Matlab scripts for clustering evaluation. The file AdditionalFile6.zip provides a (zipped) set of Matlab scripts, used for clustering evaluation.
Additional file 7
tSNEbased visual representations. The file AdditionalFile7.pdf provides the tSNE visual representations for expression, whole graph, and summarized graph data in Breast Microarray, Breast RNAseq, and Lung datasets.
Additional file 8
Heatmap representations. The file AdditionalFile8.pdf provides the heatmap representations for summarized graphs in Breast Microarray, Breast RNAseq, and Lung datasets.
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Manipur, I., Granata, I., Maddalena, L. et al. Clustering analysis of tumor metabolic networks. BMC Bioinformatics 21, 349 (2020). https://doi.org/10.1186/s12859020035649
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Keywords
 Metabolic networks
 Network simplification
 Networks clustering