Introduction to the GraphExperiment class

Fabricio Almeida-Silva1 and Yves Van de Peer1

1VIB-UGent Center for Plant Systems Biology, Ghent University, Ghent, Belgium

Contents

1 Introduction

Networks (or graphs) have become widely used data representations in biology, as they can efficiently encode node-node interactions and neighborhoods. In high-throughput, quantitative omics data (e.g., transcriptomics, proteomics, metabolomics, epigenomics, etc), widely used network representations include gene coexpression, protein-protein interaction, gene regulatory, and co-abundance networks. While data structures to store quantitative data and associated metadata exist (e.g., SummarizedExperiment, SingleCellExperiment, SpatialExperiment, etc), support for networks describing how features relate to each other is currently missing. GraphExperiment is an S4 class that extends SingleCellExperiment (Amezquita et al. 2020) to include an additional container for networks associated with assay features (graphs representing columns, such as samples and cells, are not supported by this package).

Of note, trees are an alternative way of representing how assay features are related to each other. Users interested in tree representations of assays rows/columns can use the TreeSummarizedExperiment package. Trees are essentially a kind of graph (i.e., all trees are graphs, but not all graphs are trees). Here, we chose to use a more general graph representation (namely igraph objects) to provide users and developers with more flexibility.

2 Installation

GraphExperiment can be installed from Bioconductor with the following code:

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

BiocManager::install("GraphExperiment")

# Load package after installation
library(GraphExperiment)

set.seed(777) # for reproducibility

3 Anatomy of a GraphExperiment object

Since the GraphExperiment class extends the SingleCellExperiment class, all SingleCellExperiment slots are present in GraphExperiment, including:

• assays: list of matrices with primary (e.g., counts) and transformed (e.g., log-normalized counts, TPM, etc) data, with features in rows and observations in columns.
• colData: a data frame with column (observation) metadata, such as sample ID, condition, batch ID, genotype, etc.
• rowData: a data frame with row (feature) metadata, such as gene ID, genomic coordinates, functional annotation, etc.
• reducedDims: list of data frames with reduced dimensions, such as PCA, t-SNE, and UMAP embeddings.

Compared to SingleCellExperiment objects, GraphExperiment provides an additional container:

• graphs: list of igraph objects containing graphs, including (but optional) node and edge attributes. Graphs are used to represent how features (rows, not columns) relate to each other.111 Note on software design: if you’re familiar with SingleCellExperiment objects, you probably know that it offers a rowPairs slot to store pairwise relationships between rows of assays. In theory, some of the data stored in graphs (of a GraphExperiment object) could be stored in rowPairs (of a SingleCellExperiment). However, we chose to implement a dedicated slot with igraph objects to guarantee (i) seamless interoperability with other packages, given that igraph is the de facto standard class for graphs in R; and (ii) convenience in methods (e.g., subsetting, integration with rowData, integration across multiple graphs, etc).

Figure 1: The GraphExperiment class

The igraph data class from the igraph package is the standard data structure for graph representation in R. If you are unfamiliar with igraph objects, you can learn more about it by reading the igraph vignettes.

4 Building a GraphExperiment object

GraphExperiment objects can be created from scratch using the constructor function GraphExperiment(). Below we will simulate a scRNA-seq count matrix with some gene (row) and cell (column) metadata, and create a graph based on gene-gene correlations.

# Simulate parts of a `GraphExperiment` object
## Assays
gene_ids <- paste0("gene", seq_len(200))
cell_ids <- paste0("cell", seq_len(100))
mat <- matrix(rpois(20000, 5), ncol = 100, dimnames = list(gene_ids, cell_ids))
mat[1:5, 1:5]
#>       cell1 cell2 cell3 cell4 cell5
#> gene1     6     7     5     5     6
#> gene2     5     3     6     3     5
#> gene3     4     5     9     7     2
#> gene4    12     4     5     9     3
#> gene5     6     6     5     2     8

## rowData
rdata <- data.frame(
    row.names = gene_ids,
    pathway = sample(c("P1", "P2"), size = length(gene_ids), replace = TRUE),
    coding = sample(c(TRUE, FALSE), size = length(gene_ids), replace = TRUE)
)
head(rdata)
#>       pathway coding
#> gene1      P1  FALSE
#> gene2      P1   TRUE
#> gene3      P2   TRUE
#> gene4      P1  FALSE
#> gene5      P1   TRUE
#> gene6      P1  FALSE

## colData
cdata <- data.frame(
    row.names = cell_ids, 
    cell_type = sample(c("ct1", "ct2"), size = length(cell_ids), replace = TRUE)
)
head(cdata)
#>       cell_type
#> cell1       ct2
#> cell2       ct2
#> cell3       ct2
#> cell4       ct1
#> cell5       ct2
#> cell6       ct1

## Graph (with node attribute `degree`)
g <- graph_from_adjacency_matrix(
    cor(t(mat)), mode = "undirected", weighted = TRUE
)
g <- set_vertex_attr(g, "degree", value = strength(g))
g
#> IGRAPH ffe8272 UNW- 200 20096 -- 
#> + attr: name (v/c), degree (v/n), weight (e/n)
#> + edges from ffe8272 (vertex names):
#>  [1] gene1--gene1  gene1--gene2  gene1--gene3  gene1--gene4  gene1--gene5 
#>  [6] gene1--gene6  gene1--gene7  gene1--gene8  gene1--gene9  gene1--gene10
#> [11] gene1--gene11 gene1--gene12 gene1--gene13 gene1--gene14 gene1--gene15
#> [16] gene1--gene16 gene1--gene17 gene1--gene18 gene1--gene19 gene1--gene20
#> [21] gene1--gene21 gene1--gene22 gene1--gene23 gene1--gene24 gene1--gene25
#> [26] gene1--gene26 gene1--gene27 gene1--gene28 gene1--gene29 gene1--gene30
#> [31] gene1--gene31 gene1--gene32 gene1--gene33 gene1--gene34 gene1--gene35
#> [36] gene1--gene36 gene1--gene37 gene1--gene38 gene1--gene39 gene1--gene40
#> + ... omitted several edges

To create a GraphExperiment object from the constructor function, you would run:

# Create a `GraphExperiment` object
ge <- GraphExperiment(
    assays = list(counts = mat),
    rowData = rdata,
    colData = cdata,
    graphs = list(cor = g)
)
ge
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(3): pathway coding cor__degree
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(1): cell_type
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(1): cor

If you’re familiar with SummarizedExperiment and SingleCellExperiment objects, you will certainly recognize nearly everything you see in ge. Compared to SingleCellExperiment objects, the only difference here is in the last row, which indicates that this object contains a graph named ‘cor’.

Importantly, since nodes of graphs are always in sync with rownames, feature IDs in rownames and graph node names need to be the same. For example, attempting to create a GraphExperiment object with some features from rownames missing would lead to an error:

# Remove 'gene1' to 'gene10' from the graph and try to recreate object
g2 <- delete_vertices(g, paste0("gene", 1:10))
GraphExperiment(
    assays = list(counts = mat),
    rowData = rdata,
    colData = cdata,
    graphs = list(cor = g2)
)
#> Error in `validObject()`:
#> ! invalid class "GraphExperiment" object: 
#>     10 feature(s) in 'rownames' are missing from graph 'cor'.

Alternatively, you can create a GraphExperiment object by coercing from an existing (Ranged)SummarizedExperiment or SingleCellExperiment object. For example:

# Coercing from `SummarizedExperiment`
se <- SummarizedExperiment(list(counts = mat))
ge1 <- as(se, "GraphExperiment")
ge1
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(0):
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(0):
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(0):

Note that the graphs container is still there, but empty. To access the names of all graphs, you will use the graphNames() function.

# Get graph names
graphNames(ge)      # 'cor'
#> [1] "cor"
graphNames(ge1)     # empty (NULL)
#> NULL

5 Accessing graphs and rowData (a.k.a. ‘getters’)

To access graphs in graphs, you can use one of two getter functions:

• graphs(x): retrieves all graphs as a simple list of igraph objects.
• graph(x, i): retrieves only graph \(i\) from the list. Note that \(i\) can be a numeric scalar (index) or a character scalar (name).

The design here is equivalent to assays() versus assay() for SummarizedExperiment objects.

# Get graphs
graphs(ge)
#> List of length 1
#> names(1): cor

# Get first graph by index
graph(ge, 1)
#> IGRAPH ffe8272 UNW- 200 20096 -- 
#> + attr: name (v/c), degree (v/n), pathway (v/c), coding (v/l), weight
#> | (e/n)
#> + edges from ffe8272 (vertex names):
#>  [1] gene1--gene1  gene1--gene2  gene1--gene3  gene1--gene4  gene1--gene5 
#>  [6] gene1--gene6  gene1--gene7  gene1--gene8  gene1--gene9  gene1--gene10
#> [11] gene1--gene11 gene1--gene12 gene1--gene13 gene1--gene14 gene1--gene15
#> [16] gene1--gene16 gene1--gene17 gene1--gene18 gene1--gene19 gene1--gene20
#> [21] gene1--gene21 gene1--gene22 gene1--gene23 gene1--gene24 gene1--gene25
#> [26] gene1--gene26 gene1--gene27 gene1--gene28 gene1--gene29 gene1--gene30
#> [31] gene1--gene31 gene1--gene32 gene1--gene33 gene1--gene34 gene1--gene35
#> + ... omitted several edges

# Get first graph by index (alternative)
graphs(ge)[[1]]
#> IGRAPH ffe8272 UNW- 200 20096 -- 
#> + attr: name (v/c), degree (v/n), pathway (v/c), coding (v/l), weight
#> | (e/n)
#> + edges from ffe8272 (vertex names):
#>  [1] gene1--gene1  gene1--gene2  gene1--gene3  gene1--gene4  gene1--gene5 
#>  [6] gene1--gene6  gene1--gene7  gene1--gene8  gene1--gene9  gene1--gene10
#> [11] gene1--gene11 gene1--gene12 gene1--gene13 gene1--gene14 gene1--gene15
#> [16] gene1--gene16 gene1--gene17 gene1--gene18 gene1--gene19 gene1--gene20
#> [21] gene1--gene21 gene1--gene22 gene1--gene23 gene1--gene24 gene1--gene25
#> [26] gene1--gene26 gene1--gene27 gene1--gene28 gene1--gene29 gene1--gene30
#> [31] gene1--gene31 gene1--gene32 gene1--gene33 gene1--gene34 gene1--gene35
#> + ... omitted several edges

# Get graph by name
graph(ge, "cor")
#> IGRAPH ffe8272 UNW- 200 20096 -- 
#> + attr: name (v/c), degree (v/n), pathway (v/c), coding (v/l), weight
#> | (e/n)
#> + edges from ffe8272 (vertex names):
#>  [1] gene1--gene1  gene1--gene2  gene1--gene3  gene1--gene4  gene1--gene5 
#>  [6] gene1--gene6  gene1--gene7  gene1--gene8  gene1--gene9  gene1--gene10
#> [11] gene1--gene11 gene1--gene12 gene1--gene13 gene1--gene14 gene1--gene15
#> [16] gene1--gene16 gene1--gene17 gene1--gene18 gene1--gene19 gene1--gene20
#> [21] gene1--gene21 gene1--gene22 gene1--gene23 gene1--gene24 gene1--gene25
#> [26] gene1--gene26 gene1--gene27 gene1--gene28 gene1--gene29 gene1--gene30
#> [31] gene1--gene31 gene1--gene32 gene1--gene33 gene1--gene34 gene1--gene35
#> + ... omitted several edges

Careful readers will notice that this igraph object has node attributes that were not present in the original graph: ‘pathway’ and ‘coding’. This is because graphs()/graph() automatically extract rowData variables (if any) and add them to node attributes. The same happens in the other direction: the rowData() method for GraphExperiment objects automatically adds node attributes (if any) to rowData variables.

# `graphs` and `rowData` are always in sync!
rowData(ge)
#> DataFrame with 200 rows and 3 columns
#>             pathway    coding cor__degree
#>         <character> <logical>   <numeric>
#> gene1            P1     FALSE    3.125219
#> gene2            P1      TRUE    4.454433
#> gene3            P2      TRUE    0.873847
#> gene4            P1     FALSE    1.511270
#> gene5            P1      TRUE    0.568855
#> ...             ...       ...         ...
#> gene196          P1      TRUE    0.773387
#> gene197          P2     FALSE    0.857870
#> gene198          P1      TRUE    1.591484
#> gene199          P1      TRUE    2.324144
#> gene200          P1     FALSE   -0.887166

Variables ‘pathway’ and ‘coding’ were in the original data frame we used as rowData, but variable ’cor__degree’ was added by extracting the degree attribute of nodes in graph cor.

6 Modifying GraphExperiment objects (a.k.a. ‘setters’)

Like in the SummarizedExperiment and SingleCellExperiment classes, all getter methods specific to GraphExperiment objects have a corresponding setter method. Such methods allow users to modify elements by adding <- after the getter method. For example, to add or replace a particular graph, you would use the graph<- method as follows:

# Create a new graph without correlations between -0.4 and 0.4
fg <- graph(ge, "cor") |> 
    delete_vertex_attr("pathway") |>
    delete_vertex_attr("degree") |>
    delete_vertex_attr("coding")

todelete <- abs(E(fg)$weight) <0.4
fg <- delete_edges(fg, which(todelete))
fg
#> IGRAPH cb99d1a UNW- 200 202 -- 
#> + attr: name (v/c), weight (e/n)
#> + edges from cb99d1a (vertex names):
#>  [1] gene1 --gene1  gene2 --gene2  gene3 --gene3  gene4 --gene4  gene5 --gene5 
#>  [6] gene6 --gene6  gene7 --gene7  gene8 --gene8  gene9 --gene9  gene10--gene10
#> [11] gene11--gene11 gene12--gene12 gene13--gene13 gene14--gene14 gene15--gene15
#> [16] gene16--gene16 gene17--gene17 gene18--gene18 gene19--gene19 gene20--gene20
#> [21] gene21--gene21 gene22--gene22 gene23--gene23 gene24--gene24 gene25--gene25
#> [26] gene26--gene26 gene27--gene27 gene28--gene28 gene29--gene29 gene30--gene30
#> [31] gene31--gene31 gene32--gene32 gene33--gene33 gene34--gene34 gene35--gene35
#> [36] gene36--gene36 gene37--gene37 gene38--gene38 gene39--gene39 gene40--gene40
#> + ... omitted several edges

# Add filtered graph a new graph named `fcor`
graph(ge, "fcor") <- fg
ge
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(5): pathway coding cor__degree cor__pathway cor__coding
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(1): cell_type
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(2): cor fcor

If you’d like to replace all graphs at once, you could use the graphs<- setter. For example, let’s add a few graphs to the GraphExperiment object we created before by coercing from SummarizedExperiment:

# Taking a quick look (note: nothing in `graphs`)
ge1
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(0):
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(0):
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(0):

# Adding graphs from `ge`
graphs(ge1) <- graphs(ge)
ge1
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(5): cor__degree cor__pathway cor__coding fcor__pathway
#>   fcor__coding
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(0):
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(2): cor fcor

Lastly, you can also rename graphs by updating graphNames as follows:

# Rename graphs
graphNames(ge1) <- c("correlations", "correlations_filtered_0.4")
ge1
#> class: GraphExperiment 
#> dim: 200 100 
#> metadata(0):
#> assays(1): counts
#> rownames(200): gene1 gene2 ... gene199 gene200
#> rowData names(5): correlations__degree correlations__pathway
#>   correlations__coding correlations_filtered_0.4__pathway
#>   correlations_filtered_0.4__coding
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(0):
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(2): correlations correlations_filtered_0.4

7 Subsetting GraphExperiment objects

In SummarizedExperiment objects, subsetting rows and columns (using square brackets, [) automatically subsets rowData and colData besides the assays. The same is true for SingleCellExperiment objects: subsetting columns automatically subsets colData and reducedDims.

Since graphs in GraphExperiment objects are linked to rows, subsetting rows of a GraphExperiment object automatically subsets rows of the assays, rowData, and all graphs in graphs. For example:

# Subsetting `GraphExperiment` object
ge_subset <- ge[1:10, ]

ge_subset
#> class: GraphExperiment 
#> dim: 10 100 
#> metadata(0):
#> assays(1): counts
#> rownames(10): gene1 gene2 ... gene9 gene10
#> rowData names(7): pathway coding ... fcor__pathway fcor__coding
#> colnames(100): cell1 cell2 ... cell99 cell100
#> colData names(1): cell_type
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
#> graphs(2): cor fcor
graph(ge_subset, "cor")
#> IGRAPH 60a7d51 UNW- 10 55 -- 
#> + attr: name (v/c), degree (v/n), pathway (v/c), coding (v/l), weight
#> | (e/n)
#> + edges from 60a7d51 (vertex names):
#>  [1] gene1--gene1 gene1--gene2 gene2--gene2 gene1--gene3 gene2--gene3
#>  [6] gene3--gene3 gene1--gene4 gene2--gene4 gene3--gene4 gene4--gene4
#> [11] gene1--gene5 gene2--gene5 gene3--gene5 gene4--gene5 gene5--gene5
#> [16] gene1--gene6 gene2--gene6 gene3--gene6 gene4--gene6 gene5--gene6
#> [21] gene6--gene6 gene1--gene7 gene2--gene7 gene3--gene7 gene4--gene7
#> [26] gene5--gene7 gene6--gene7 gene7--gene7 gene1--gene8 gene2--gene8
#> [31] gene3--gene8 gene4--gene8 gene5--gene8 gene6--gene8 gene7--gene8
#> + ... omitted several edges

Session information

This document was created under the following conditions:

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References

Amezquita, Robert, Aaron Lun, Etienne Becht, Vince Carey, Lindsay Carpp, Ludwig Geistlinger, Federico Marini, et al. 2020. “Orchestrating Single-Cell Analysis with Bioconductor.” Nature Methods 17: 137–45. https://www.nature.com/articles/s41592-019-0654-x.