# Gene coexpression network inference

# Introduction

To date, several packages have been developed to infer gene coexpression networks from expression data, such as WGCNA (Langfelder and Horvath 2008), CEMiTool (Russo et al. 2018) and petal (Petereit et al. 2016). However, network inference and analysis is a non-trivial task that requires solid statistical background, especially for data preprocessing and proper interpretation of results. Because of that, inexperienced researchers often struggle to choose the most suitable algorithms for their projects. Besides, different packages are required for each step of a standard network analysis, and their distinct syntaxes can hinder interoperability between packages, particularly for non-advanced R users. Here, we have developed an all-in-one R package that uses state-of-the-art algorithms to facilitate the workflow of biological network analysis, from data acquisition to analysis and interpretation. This will likely accelerate network analysis pipelines and advance systems biology research.

# Installation

    if(!requireNamespace('BiocManager', quietly = TRUE))
      install.packages('BiocManager')

    BiocManager::install("BioNERO")

    # Load package after installation
    library(BioNERO)
    set.seed(123) # for reproducibility

# Data loading and preprocessing

For this tutorial, we will use maize (Zea mays) gene expression data normalized in TPM. The data were obtained from Shin et al. (2020) and were filtered for package size issues. For more information on the data set, see `?zma.se`. The data set is stored as a SummarizedExperiment object.1

The input expression data in `BioNERO` can be both a SummarizedExperiment object or a gene expression matrix or data frame with genes in rows and samples in columns. However, we strongly recommend using SummarizedExperiment objects for easier interoperability with other Bioconductor packages.

    data(zma.se)

    # Take a quick look at the data
    zma.se
    ## class: SummarizedExperiment
    ## dim: 10802 28
    ## metadata(0):
    ## assays(1): ''
    ## rownames(10802): ZeamMp030 ZeamMp044 ... Zm00001d054106 Zm00001d054107
    ## rowData names(0):
    ## colnames(28): SRX339756 SRX339757 ... SRX2792103 SRX2792104
    ## colData names(1): Tissue
    SummarizedExperiment::colData(zma.se)
    ## DataFrame with 28 rows and 1 column
    ##                    Tissue
    ##               <character>
    ## SRX339756       endosperm
    ## SRX339757       endosperm
    ## SRX339758       endosperm
    ## SRX339762       endosperm
    ## SRX339763       endosperm
    ## ...                   ...
    ## SRX2792107 whole_seedling
    ## SRX2792108 whole_seedling
    ## SRX2792102 whole_seedling
    ## SRX2792103 whole_seedling
    ## SRX2792104 whole_seedling

## Step-by-step data preprocessing

This section is suitable for users who want to have more control of their data analysis, as they can inspect the data set after each preprocessing step and analyze how different options to the arguments would affect the expression data. If you want a quick start, you can skip to the next section (Automatic, one-step data preprocessing).

Step 1: Replacing missing values. By default, `replace_na()` will replace NAs with 0. Users can also replace NAs with the mean of each row (generally not advisable, but it can be useful in very specific cases).

    exp_filt <- replace_na(zma.se)
    sum(is.na(zma.se))
    ## [1] 0

Step 2: Removing non-expressed genes. Here, for faster network reconstruction, we will remove every gene whose median value is below 10. The function’s default for `min_exp` is 1. For other options, see `?remove_nonexp`.

    exp_filt <- remove_nonexp(exp_filt, method = "median", min_exp = 10)
    dim(exp_filt)
    ## [1] 8529   28

Step 3 (optional): Filtering genes by variance. It is reasonable to remove genes whose expression values do not vary much across samples, since we often want to find genes that are more or less expressed in particular conditions. Here, we will keep only the top 2000 most variable genes. Users can also filter by percentile (e.g., the top 10% most variable genes).

    exp_filt <- filter_by_variance(exp_filt, n = 2000)
    dim(exp_filt)
    ## [1] 2000   28

Step 4: Removing outlying samples. There are several methods to remove outliers. We have implemented the Z.K (standardized connectivity) method (Oldham et al. 2012) in `ZKfiltering()`, which is a network-based approach to remove outliers. This method has proven to be more suitable for network analysis, since it can remove outliers that other methods (such as hierarchical clustering) cannot identify. By default, BioNERO considers all samples with ZK < 2 as outliers, but this parameter is flexible if users want to change it.

    exp_filt <- ZKfiltering(exp_filt, cor_method = "pearson")
    ## Number of removed samples: 1
    dim(exp_filt)
    ## [1] 2000   27

Step 5: Adjusting for confounding artifacts. This is an important step to avoid spurious correlations resulting from confounders. The method was described by Parsana et al. (2019), who developed a principal component (PC)-based correction for confounders. After correction, the expression data are quantile normalized, so every gene follows an approximate normal distribution.

    exp_filt <- PC_correction(exp_filt)

## Automatic, one-step data preprocessing

Alternatively, users can preprocess their data with a single function. The function `exp_preprocess()` is a wrapper for the functions `replace_na()`, `remove_nonexp()`, `filter_by_variance()`, `ZKfiltering()` and `PC_correction()`. The arguments passed to `exp_preprocess()` will be used by each of these functions to generate a filtered expression data frame in a single step.2

    final_exp <- exp_preprocess(
        zma.se, min_exp = 10, variance_filter = TRUE, n = 2000
    )
    ## Number of removed samples: 1
    identical(dim(exp_filt), dim(final_exp))
    ## [1] TRUE

    # Take a look at the final data
    final_exp
    ## class: SummarizedExperiment
    ## dim: 2000 27
    ## metadata(0):
    ## assays(1): ''
    ## rownames(2000): ZeamMp030 ZeamMp092 ... Zm00001d054093 Zm00001d054107
    ## rowData names(0):
    ## colnames(27): SRX339756 SRX339757 ... SRX2792103 SRX2792104
    ## colData names(1): Tissue

# Exploratory data analysis

`BioNERO` includes some functions for easy data exploration. These functions were created to avoid having to type code chunks that, although small, will be used many times. The idea here is to make the user experience with biological network analysis as easy and simple as possible.

Plotting heatmaps: the function `plot_heatmap()` plots heatmaps of correlations between samples or gene expression in a single line. Besides the arguments users can pass to parameters in `plot_heatmap()`, they can also pass additional arguments to parameters in `ComplexHeatmap::pheatmap()` to have additional control additional on plot aesthetics (e.g., hide/show gene and sample names, activate/deactivate clustering for rows and/or columns, etc).

    # Heatmap of sample correlations
    p <- plot_heatmap(final_exp, type = "samplecor", show_rownames = FALSE)
    p

    # Heatmap of gene expression (here, only the first 50 genes)
    p <- plot_heatmap(
        final_exp[1:50, ], type = "expr", show_rownames = FALSE, show_colnames = FALSE
    )
    p

Principal component analysis (PCA): the function `plot_PCA()` performs a PCA and plots whatever pair of PCs users choose (PC1 and PC2 by default), as well the percentage of variance explained by each PC.

    plot_PCA(final_exp)

# Gene coexpression network inference

Now that we have our filtered and normalized expression data, we can reconstruct a gene coexpression network (GCN) with the WGCNA algorithm (Langfelder and Horvath 2008). First of all, we need to identify the most suitable \(\beta\) power that makes the network satisfy the scale-free topology. We do that with the function `SFT_fit()`. Correlation values are raised to a power \(\beta\) to amplify their distances and, hence, to make the module detection algorithm more powerful. The higher the value of \(\beta\), the closer to the scale-free topology the network is. However, a very high \(\beta\) power reduces mean connectivity, which is not desired. To solve this trade-off, we pick the lowest \(\beta\) power above a certain threshold (by default in `SFT_fit()`, 0.8). This makes the network close to the scale-free topology without dramatically reducing the mean connectivity.

    sft <- SFT_fit(final_exp, net_type = "signed hybrid", cor_method = "pearson")
    ##    Power SFT.R.sq  slope truncated.R.sq mean.k. median.k. max.k.
    ## 1      3    0.220 -0.218          0.178   278.0    303.00  598.0
    ## 2      4    0.416 -0.382          0.272   196.0    199.00  472.0
    ## 3      5    0.573 -0.468          0.462   145.0    136.00  381.0
    ## 4      6    0.675 -0.536          0.584   110.0     95.70  312.0
    ## 5      7    0.748 -0.584          0.676    86.3     70.00  259.0
    ## 6      8    0.791 -0.653          0.735    68.8     51.90  221.0
    ## 7      9    0.803 -0.717          0.761    55.8     38.60  191.0
    ## 8     10    0.815 -0.775          0.790    45.8     29.90  167.0
    ## 9     11    0.821 -0.828          0.815    38.1     22.90  147.0
    ## 10    12    0.838 -0.874          0.850    32.0     17.90  130.0
    ## 11    13    0.847 -0.913          0.876    27.2     14.30  116.0
    ## 12    14    0.856 -0.943          0.893    23.2     11.80  104.0
    ## 13    15    0.875 -0.973          0.913    20.0      9.79   93.0
    ## 14    16    0.892 -0.997          0.937    17.3      8.00   83.9
    ## 15    17    0.897 -1.020          0.941    15.1      6.75   76.0
    ## 16    18    0.891 -1.070          0.948    13.3      5.79   69.7
    ## 17    19    0.888 -1.100          0.950    11.7      4.96   64.2
    ## 18    20    0.888 -1.130          0.957    10.4      4.27   59.4
    sft$power
    ## [1] 9
    power <- sft$power

As we can see, the optimal power is 9. However, we strongly recommend a visual inspection of the simulation of different \(\beta\) powers, as WGCNA can fail to return the most appropriate \(\beta\) power in some cases.3 The function `SFT_fit()` automatically saves a ggplot object in the second element of the resulting list. To visualize it, you simply have to access the plot.

    sft$plot

Now, we can use the power calculated by `SFT_fit()` to infer the GCN. The function `exp2gcn()` infers a GCN and outputs a list of 7 elements, each of which will be used by other functions in the analysis pipeline.

    net <- exp2gcn(
        final_exp, net_type = "signed hybrid", SFTpower = power,
        cor_method = "pearson"
    )
    ## ..connectivity..
    ## ..matrix multiplication (system BLAS)..
    ## ..normalization..
    ## ..done.
    names(net)
    ## [1] "adjacency_matrix"    "MEs"                 "genes_and_modules"
    ## [4] "kIN"                 "correlation_matrix"  "params"
    ## [7] "dendro_plot_objects"

The function `exp2gcn()` saves objects in the last element of the resulting list that can be subsequently used to plot common figures in GCN papers. The figures are publication-ready and display i. a dendrogram of genes and modules; ii. heatmap of pairwise correlations between module eigengenes.

    # Dendro and colors
    plot_dendro_and_colors(net)

    # Eigengene networks
    plot_eigengene_network(net)

Let’s see the number of genes per module.

    plot_ngenes_per_module(net)

# Gene coexpression network analysis

Now that we have our coexpression network, we can start exploring some of its properties.

## Assessing module stability

The function `module_stability()` allows users to check if the identified coexpression modules are stable (i.e., if they can resist removal of a particular sample). This function will resample the data set and rerun the module detection algorithm n times (default: 30) and return a PDF figure displaying a gene dendrogram and colors representing modules identified in each run. By looking at the figure, you can detect if a particular module is only found in a very small fraction of the runs, which suggests instability. Here, we will perform only 5 resampling runs for demonstration purposes.4

    module_stability(final_exp, net, nRuns = 5)
    ##  ...working on run 1 ..
    ##  ...working on run 2 ..
    ##  ...working on run 3 ..
    ##  ...working on run 4 ..
    ##  ...working on run 5 ..
    ##  ...working on run 6 ..

## Module-trait associations

The function `module_trait_cor()` can be used to calculate module-trait correlations. This analysis is useful to identify modules that are positively or negatively correlated with particular traits, which means that their gene expression levels go up or down in these conditions. Here, tissues will be considered traits, so we want to identify groups of genes whose expression levels are inhibited or induced in particular tissues. Alternatively, one can use continuous variables (e.g., metabolite content, protein concentration, height) or discrete variables (e.g., disease index) as traits.5

    MEtrait <- module_trait_cor(exp = final_exp, MEs = net$MEs)
    head(MEtrait)
    ##        ME          trait          cor    pvalue  group
    ## 1 MEblack      endosperm -0.166480994 0.4065715 Tissue
    ## 2 MEblack         pollen  0.213691004 0.2845053 Tissue
    ## 3 MEblack whole_seedling -0.020227505 0.9202318 Tissue
    ## 4 MEbrown      endosperm  0.003843583 0.9848197 Tissue
    ## 5 MEbrown         pollen -0.020729547 0.9182584 Tissue
    ## 6 MEbrown whole_seedling  0.012815311 0.9494147 Tissue

Next, you can use the function `plot_module_trait_cor()` to visualize the output of `module_trait_cor()` as follows:

    plot_module_trait_cor(MEtrait)

## Visualizing module expression profile

The heatmap above shows that genes in the yellow module are negatively correlated with endosperm samples. We can visually explore it with `plot_expression_profile()`.

    plot_expression_profile(
        exp = final_exp,
        net = net,
        plot_module = TRUE,
        modulename = "yellow"
    )

## Enrichment analysis

After identifying modules that are inhibited or enhanced in particular tissues, users would likely want to find to which biological processes (e.g., GO biological process) or pathways (e.g., Reactome, KEGG, MapMan) these genes are related. This can be done with enrichment analyses, which can uncover terms that are found more than expected by chance in a module.

The easiest way to accomplish this is to use the function `module_enrichment()`, which performs enrichment analysis for all modules at once. To illustrate it, we will scan coexpression modules for enriched protein domains using all genes in the network as background. The Interpro annotation was downloaded from the PLAZA 4.0 Monocots database (Van Bel et al. 2018).

    # Enrichment analysis for conserved protein domains (Interpro)
    data(zma.interpro)
    interpro_enrichment <- module_enrichment(
        net = net,
        background_genes = rownames(final_exp),
        annotation = zma.interpro
    )
    ## Enrichment analysis for module black...
    ## Enrichment analysis for module brown...
    ## Enrichment analysis for module darkgreen...
    ## Enrichment analysis for module darkolivegreen...
    ## Enrichment analysis for module greenyellow...
    ## Enrichment analysis for module lightyellow...
    ## Enrichment analysis for module midnightblue...
    ## Enrichment analysis for module paleturquoise...
    ## Enrichment analysis for module violet...
    ## Enrichment analysis for module yellow...

    # Print results without geneIDs for better visualization
    interpro_enrichment[, -6]
    ##                                        term genes all         pval         padj
    ## 184                      Histone H2A/H2B/H3    43  44 2.155952e-09 4.840112e-07
    ## 185                             Histone H2B    14  14 6.217795e-04 3.489738e-02
    ## 186                       Histone H3/CENP-A    15  15 3.659921e-04 2.347578e-02
    ## 187                              Histone H4    15  15 3.659921e-04 2.347578e-02
    ## 188                            Histone-fold    58  60 1.083394e-11 4.864438e-09
    ## 326           Ribosomal protein L2 domain 2    18  18 7.448332e-05 6.688602e-03
    ## 395     Translation protein SH3-like domain    22  22 8.872064e-06 1.327852e-03
    ## 396 Translation protein, beta-barrel domain    26  27 1.235834e-05 1.387224e-03
    ## 299                   Protein kinase domain     5  18 1.202246e-04 2.699043e-02
    ## 448         Zinc finger, RING/FYVE/PHD-type     5  18 1.202246e-04 2.699043e-02
    ## 46                    Aquaporin transporter     3   5 9.644015e-05 4.330163e-02
    ##        category       module
    ## 184 Description        black
    ## 185 Description        black
    ## 186 Description        black
    ## 187 Description        black
    ## 188 Description        black
    ## 326 Description        black
    ## 395 Description        black
    ## 396 Description        black
    ## 299 Description  lightyellow
    ## 448 Description  lightyellow
    ## 46  Description midnightblue

As we can see, two modules are enriched in genes with particular protein domains. We could get the same result with the function `enrichment_analysis()`, which performs enrichment analysis for a user-defined gene set instead of all modules. 6

## Hub gene identification

Hub genes are often identified using two different metrics: module membership (MM) (i.e., correlation of a gene to its module eigengene) and degree (i.e., sum of connection weights of a gene to all other genes in the module). Some researchers consider the top 10% genes with the highest degree as hubs, while others consider those with MM > 0.8. To avoid false positives, `BioNERO`’s algorithm combines both metrics and defines hub genes as the top 10% genes with highest degree that have MM > 0.8. Hubs can be identified with the function `get_hubs_gcn()`.

    hubs <- get_hubs_gcn(final_exp, net)
    head(hubs)
    ##             Gene Module  kWithin
    ## 1 Zm00001d033147  black 188.3864
    ## 2 Zm00001d049790  black 181.4522
    ## 3 Zm00001d005649  black 180.7062
    ## 4 Zm00001d045448  black 180.6744
    ## 5 Zm00001d008203  black 178.7147
    ## 6 Zm00001d023340  black 177.7553

## Extracting subgraphs

Subgraph extraction can be particularly useful to visualize specific modules, and it can be done with the function `get_edge_list()`. The function returns the subgraph as an edge list. Users can also extract an edge list for a particular gene set instead of a module.

    edges <- get_edge_list(net, module="midnightblue")
    head(edges)
    ##              Gene1          Gene2    Weight
    ## 45  Zm00001d001857 Zm00001d002384 0.9401886
    ## 89  Zm00001d001857 Zm00001d002690 0.9675345
    ## 90  Zm00001d002384 Zm00001d002690 0.9185426
    ## 133 Zm00001d001857 Zm00001d003962 0.7178340
    ## 134 Zm00001d002384 Zm00001d003962 0.6534956
    ## 135 Zm00001d002690 Zm00001d003962 0.6840004

The function `get_edge_list()` returns a fully connected subgraph for the specified module or gene set. However, filtering weak correlations is desirable and can be accomplished by setting the argument `filter = TRUE`, which will remove edges based on one of optimal scale-free topology fit (default), p-value, Z-score, or an arbitrary minimum correlation coefficient. 7 For more details details, check `?get_edge_list()`.

    # Remove edges based on optimal scale-free topology fit
    edges_filtered <- get_edge_list(net, module = "midnightblue", filter = TRUE)
    ## The correlation threshold that best fits the scale-free topology is 0.7
    dim(edges_filtered)
    ## [1] 588   3

    # Remove edges based on p-value
    edges_filtered <- get_edge_list(
        net, module = "midnightblue",
        filter = TRUE, method = "pvalue",
        nSamples = ncol(final_exp)
    )
    dim(edges_filtered)
    ## [1] 921   3

    # Remove edges based on minimum correlation
    edges_filtered <- get_edge_list(
        net, module = "midnightblue",
        filter = TRUE, method = "min_cor", rcutoff = 0.7
    )
    dim(edges_filtered)
    ## [1] 588   3

## Network visualization

As we now have an edge list for a module, let’s visualize it with the function `plot_gcn()`. By default, this function only labels the top 5 hubs (or less if there are less than 5 hubs). However, this can be customized according to the user’s preference (see `?plot_gcn` for more information).

    plot_gcn(
        edgelist_gcn = edges_filtered,
        net = net,
        color_by = "module",
        hubs = hubs
    )

Networks can also be visualized interactively by setting `interactive = TRUE` in `plot_gcn`.

    plot_gcn(
        edgelist_gcn = edges_filtered,
        net = net,
        color_by = "module",
        hubs = hubs,
        interactive = TRUE,
        dim_interactive = c(500, 500)
    )

## Network statistics

Finally, the function `net_stats()` can be used to calculate the main network statistics (or properties, or indices), namely: connectivity, scaled connectivity, clustering coefficient, maximum adjacency ratio, density, centralization, heterogeneity, diameter, betweenness (optional), and closeness (optional).

Depending on your system capacities and network size, this may take a very long time. Hence, if you are willing to calculate network statistics for your data set, grab a cup of coffee, because the waiting may be long.

# Session information

This vignette was created under the following conditions:

    sessionInfo()
    ## R version 4.6.0 (2026-04-24)
    ## Platform: x86_64-pc-linux-gnu
    ## Running under: Ubuntu 24.04.4 LTS
    ##
    ## Matrix products: default
    ## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
    ## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
    ##
    ## locale:
    ##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
    ##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
    ##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
    ##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
    ##  [9] LC_ADDRESS=C               LC_TELEPHONE=C
    ## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
    ##
    ## time zone: Etc/UTC
    ## tzcode source: system (glibc)
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] BioNERO_1.20.0   BiocStyle_2.40.0
    ##
    ## loaded via a namespace (and not attached):
    ##   [1] RColorBrewer_1.1-3          ggdendro_0.2.0
    ##   [3] sys_3.4.3                   rstudioapi_0.18.0
    ##   [5] jsonlite_2.0.0              shape_1.4.6.1
    ##   [7] NetRep_1.2.10               magrittr_2.0.5
    ##   [9] farver_2.1.2                rmarkdown_2.31
    ##  [11] GlobalOptions_0.1.4         vctrs_0.7.3
    ##  [13] memoise_2.0.1               base64enc_0.1-6
    ##  [15] htmltools_0.5.9             S4Arrays_1.12.0
    ##  [17] dynamicTreeCut_1.63-1       SparseArray_1.12.0
    ##  [19] Formula_1.2-5               sass_0.4.10
    ##  [21] bslib_0.10.0                htmlwidgets_1.6.4
    ##  [23] plyr_1.8.9                  impute_1.86.0
    ##  [25] cachem_1.1.0                networkD3_0.4.1
    ##  [27] buildtools_1.0.0            igraph_2.3.0
    ##  [29] lifecycle_1.0.5             ggnetwork_0.5.14
    ##  [31] iterators_1.0.14            pkgconfig_2.0.3
    ##  [33] Matrix_1.7-5                R6_2.6.1
    ##  [35] fastmap_1.2.0               MatrixGenerics_1.24.0
    ##  [37] clue_0.3-68                 digest_0.6.39
    ##  [39] colorspace_2.1-2            patchwork_1.3.2
    ##  [41] AnnotationDbi_1.74.0        S4Vectors_0.50.0
    ##  [43] GENIE3_1.34.0               Hmisc_5.2-5
    ##  [45] GenomicRanges_1.64.0        RSQLite_2.4.6
    ##  [47] labeling_0.4.3              httr_1.4.8
    ##  [49] abind_1.4-8                 mgcv_1.9-4
    ##  [51] compiler_4.6.0              withr_3.0.2
    ##  [53] bit64_4.8.0                 doParallel_1.0.17
    ##  [55] htmlTable_2.5.0             S7_0.2.2
    ##  [57] backports_1.5.1             BiocParallel_1.46.0
    ##  [59] DBI_1.3.0                   intergraph_2.0-4
    ##  [61] MASS_7.3-65                 DelayedArray_0.38.0
    ##  [63] rjson_0.2.23                tools_4.6.0
    ##  [65] foreign_0.8-91              nnet_7.3-20
    ##  [67] glue_1.8.1                  nlme_3.1-169
    ##  [69] grid_4.6.0                  checkmate_2.3.4
    ##  [71] cluster_2.1.8.2             reshape2_1.4.5
    ##  [73] generics_0.1.4              sva_3.60.0
    ##  [75] gtable_0.3.6                preprocessCore_1.74.0
    ##  [77] sna_2.8                     data.table_1.18.2.1
    ##  [79] WGCNA_1.74                  XVector_0.52.0
    ##  [81] BiocGenerics_0.58.0         ggrepel_0.9.8
    ##  [83] foreach_1.5.2               pillar_1.11.1
    ##  [85] stringr_1.6.0               limma_3.68.0
    ##  [87] genefilter_1.94.0           circlize_0.4.18
    ##  [89] splines_4.6.0               dplyr_1.2.1
    ##  [91] lattice_0.22-9              survival_3.8-6
    ##  [93] bit_4.6.0                   annotate_1.90.0
    ##  [95] tidyselect_1.2.1            locfit_1.5-9.12
    ##  [97] ComplexHeatmap_2.28.0       maketools_1.3.2
    ##  [99] Biostrings_2.80.0           knitr_1.51
    ## [101] gridExtra_2.3               IRanges_2.46.0
    ## [103] Seqinfo_1.2.0               edgeR_4.10.0
    ## [105] SummarizedExperiment_1.42.0 RhpcBLASctl_0.23-42
    ## [107] stats4_4.6.0                xfun_0.57
    ## [109] Biobase_2.72.0              statmod_1.5.1
    ## [111] matrixStats_1.5.0           stringi_1.8.7
    ## [113] statnet.common_4.13.0       yaml_2.3.12
    ## [115] minet_3.70.0                evaluate_1.0.5
    ## [117] codetools_0.2-20            data.tree_1.2.0
    ## [119] tibble_3.3.1                BiocManager_1.30.27
    ## [121] cli_3.6.6                   rpart_4.1.27
    ## [123] xtable_1.8-8                jquerylib_0.1.4
    ## [125] network_1.20.0              Rcpp_1.1.1-1.1
    ## [127] coda_0.19-4.1               png_0.1-9
    ## [129] fastcluster_1.3.0           XML_3.99-0.23
    ## [131] parallel_4.6.0              ggplot2_4.0.3
    ## [133] blob_1.3.0                  scales_1.4.0
    ## [135] crayon_1.5.3                GetoptLong_1.1.1
    ## [137] rlang_1.2.0                 KEGGREST_1.52.0

# References

Langfelder, Peter, and Steve Horvath. 2008. “WGCNA: an R package for weighted correlation network analysis.” BMC Bioinformatics 9 (1): 559. https://doi.org/10.1186/1471-2105-9-559.
Love, Michael I., Wolfgang Huber, and Simon Anders. 2014. “Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2.” Genome Biology 15 (12): 1–21. https://doi.org/10.1186/s13059-014-0550-8.
Oldham, Michael C., Peter Langfelder, and Steve Horvath. 2012. “Network methods for describing sample relationships in genomic datasets: application to Huntington’s disease.” BMC Systems Biology 6 (1): 1. https://doi.org/10.1186/1752-0509-6-63.
Parsana, Princy, Claire Ruberman, Andrew E. Jaffe, Michael C. Schatz, Alexis Battle, and Jeffrey T. Leek. 2019. “Addressing confounding artifacts in reconstruction of gene co-expression networks.” Genome Biology 20 (1): 94. https://doi.org/10.1186/s13059-019-1700-9.
Petereit, Juli, Sebastian Smith, Frederick C. Harris, and Karen A. Schlauch. 2016. “petal: Co-expression network modelling in R.” BMC Systems Biology 10 (S2): 51. https://doi.org/10.1186/s12918-016-0298-8.
Russo, Pedro S. T., Gustavo R. Ferreira, Lucas E. Cardozo, et al. 2018. “CEMiTool: a Bioconductor package for performing comprehensive modular co-expression analyses.” BMC Bioinformatics 19 (1): 56. https://doi.org/10.1186/s12859-018-2053-1.
Shin, Junha, Harald Marx, Alicia Richards, et al. 2020. “A network-based comparative framework to study conservation and divergence of proteomes in plant phylogenies.” Nucleic Acids Research, 1–23. https://doi.org/10.1093/nar/gkaa1041.
Van Bel, Michiel, Tim Diels, Emmelien Vancaester, et al. 2018. “PLAZA 4.0: An integrative resource for functional, evolutionary and comparative plant genomics.” Nucleic Acids Research 46 (D1): D1190–96. https://doi.org/10.1093/nar/gkx1002.

1. NOTE: In case you have many tab-separated expression tables in a directory, `BioNERO` has a helper function named `dfs2one()` to load all these files and combine them into a single data frame.↩︎

2. NOTE: Here, we are using TPM-normalized data. If you have expression data as raw read counts, set the argument `vstransform = TRUE` in `exp_preprocess()`. This will apply DESeq2’s variance stabilizing transformation (Love et al. 2014) to your count data.↩︎

3. PRO TIP: If your \(\beta\) power is too low (say below 6), look at the plot as a sanity check.↩︎

4. NOTE: The calculations performed by this function may take a long time depending on the your network size. Use it only if you have some reason to suspect that the modules are highly dependent on a particular set of samples.↩︎

5. NOTE: The function `gene_significance()` works just like `module_trait_cor()`, but it correlates individual genes (not the whole module) to traits. This function is very useful if you have a set of candidate genes and you want to find which of them are more associated with the trait of interest. See `?gene_significance()` for more details.↩︎

6. NOTE: The functions `module_enrichment()` and `enrichment_analysis()` can be parallelized with `BiocParallel` to increase speed. The default parallel back-end is SerialParam(), but this can be modified in the argument `bp_param`.↩︎

7. PRO TIP: Generally, we advise you to filter by optimal scale-free topology fit (default). However, if you want to specify your own correlation filter for some reason (e.g., visualization), we strongly recommend using the function `check_SFT()` to check if your resulting graph satisfies the scale-free topology. If it does not, then your graph does not resemble real biological networks and, hence, one cannot trust it for biological interpretations.↩︎