*igraph* allows you to quickly generate a graph object and search for communities (clusters) of related nodes / vertices. For one, *igraph* is utilised in the R implementation of the popular Phenograph clustering algorithm.

This tutorial will allow you to:

- create graph and spanning tree objects from a data-frame or -matrix of numerical data
- identify community structure in your graph and tree objects
- perform some basic downstream analyses on the tree objects

For simple testing, we'll use the estrogen microarray data-set in R and follow the tutorial from Rob Gentleman and Wolfgang Huber. This dataset was looking at genes that respond to estrogen stimulation.

**NB - the method can be applied to any type of numerical data, be it microarray, RNA-seq, metabolomics, qPCR, etc.**

# Step 1: read in, normalise, and identify genes with significant effects

`NB - IF YOU ALREADY HAVE YOUR OWN DATA, PROCEED TO STEP 2`

```
library(affy)
library(estrogen)
library(vsn)
library(genefilter)
datadir <- system.file("extdata", package="estrogen")
dir(datadir)
setwd(datadir)
# Read in the phenotype data and the raw expression 'CEL' files
pd <- read.AnnotatedDataFrame("estrogen.txt", header=TRUE, sep="", row.names=1)
a <- ReadAffy(filenames=rownames(pData(pd)), phenoData=pd, verbose=TRUE)
# Normalise the data
x <- expresso(
a,
bgcorrect.method="rma",
normalize.method="constant",
pmcorrect.method="pmonly",
summary.method="avgdiff")
# Remove control probes
controlProbeIdx <- grep("^AFFX", rownames(x))
x <- x[-controlProbeIdx,]
# Identify genes of significant effect
lm.coef <- function(y) lm(y ~ estrogen * time.h)$coefficients
eff <- esApply(x, 1, lm.coef)
effectUp <- names(sort(eff[2,], decreasing=TRUE)[1:25])
effectDown <- names(sort(eff[2,], decreasing=FALSE)[1:25])
main.effects <- c(effectUp, effectDown)
# Filter the expression set object to include only genes of significant effect
estrogenMainEffects <- exprs(x)[main.effects,]
```

We now have the top 25 genes showing statistically significant effects in both directions and have filtered our expression object to include only these genes. The object that we'll use for further analysis is *estrogenMainEffects*

```
head(estrogenMainEffects)
low10-1.cel low10-2.cel high10-1.cel high10-2.cel low48-1.cel
36785_at 4257.2678 4127.1452 5783.745 4888.527 5936.3714
39755_at 699.1178 658.3222 2026.508 1869.705 468.5581
151_s_at 1517.0178 1378.5044 2892.287 2852.310 1372.7407
32174_at 441.2678 416.9485 1442.827 1253.596 257.8186
39781_at 536.2678 508.1147 1590.378 1340.251 472.4352
1985_s_at 750.1178 643.6604 1612.051 1406.858 306.4513
```

# Step 2: create the graph and tree objects

In this example, we now have our data-frame/-matrix stored as *estrogenMainEffects* and will construct a graph adjacency object from this. *estrogenMainEffects* can be any numerical data-frame/-matrix from you own experiment(s).

```
library(igraph)
# Create a graph adjacency based on correlation distances between genes in pairwise fashion.
g <- graph.adjacency(
as.matrix(as.dist(cor(t(estrogenMainEffects), method="pearson"))),
mode="undirected",
weighted=TRUE,
diag=FALSE
)
```

**NB - if you have trouble creating the correlation matrix due to its size, take a look at 2 (b), here: R functions for parallel processing**

**NB - Euclidean distances can also be used instead of correlation, but this changes the tutorial slightly:**

```
#g <- graph.adjacency(
# as.matrix(dist(estrogenMainEffects, method="euclidean")),
# mode="undirected",
# weighted=TRUE,
# diag=FALSE
#)
# Simplfy the adjacency object
g <- simplify(g, remove.multiple=TRUE, remove.loops=TRUE)
# Colour negative correlation edges as blue
E(g)[which(E(g)$weight<0)]$color <- "darkblue"
# Colour positive correlation edges as red
E(g)[which(E(g)$weight>0)]$color <- "darkred"
# Convert edge weights to absolute values
E(g)$weight <- abs(E(g)$weight)
# Change arrow size
# For directed graphs only
#E(g)$arrow.size <- 1.0
# Remove edges below absolute Pearson correlation 0.8
g <- delete_edges(g, E(g)[which(E(g)$weight<0.8)])
# Assign names to the graph vertices (optional)
V(g)$name <- V(g)$name
# Change shape of graph vertices
V(g)$shape <- "sphere"
# Change colour of graph vertices
V(g)$color <- "skyblue"
# Change colour of vertex frames
V(g)$vertex.frame.color <- "white"
# Scale the size of the vertices to be proportional to the level of expression of each gene represented by each vertex
# Multiply scaled vales by a factor of 10
scale01 <- function(x){(x-min(x))/(max(x)-min(x))}
vSizes <- (scale01(apply(estrogenMainEffects, 1, mean)) + 1.0) * 10
# Amplify or decrease the width of the edges
edgeweights <- E(g)$weight * 2.0
# Convert the graph adjacency object into a minimum spanning tree based on Prim's algorithm
mst <- mst(g, algorithm="prim")
# Plot the tree object
plot(
mst,
layout=layout.fruchterman.reingold,
edge.curved=TRUE,
vertex.size=vSizes,
vertex.label.dist=-0.5,
vertex.label.color="black",
asp=FALSE,
vertex.label.cex=0.6,
edge.width=edgeweights,
edge.arrow.mode=0,
main="My first graph"
)
```

Note that layout can be modified to various other values, including:

- layout.fruchterman.reingold
- layout.kamada.kawai
- layout.lgl
- layout.circle
- layout.graphopt

For further information, see Graph layouts

# Step 3: identify communities in the tree object based on 'edge betweenness'

```
mst.communities <- edge.betweenness.community(mst, weights=NULL, directed=FALSE)
mst.clustering <- make_clusters(mst, membership=mst.communities$membership)
V(mst)$color <- mst.communities$membership + 1
par(mfrow=c(1,2))
plot(
mst.clustering, mst,
layout=layout.fruchterman.reingold,
edge.curved=TRUE,
vertex.size=vSizes,
vertex.label.dist=-0.5,
vertex.label.color="black",
asp=FALSE,
vertex.label.cex=0.6,
edge.width=edgeweights,
edge.arrow.mode=0,
main="My first graph"
)
plot(
mst,
layout=layout.fruchterman.reingold,
edge.curved=TRUE,
vertex.size=vSizes,
vertex.label.dist=-0.5,
vertex.label.color="black",
asp=FALSE,
vertex.label.cex=0.6,
edge.width=edgeweights,
edge.arrow.mode=0,
main="My first graph"
)
```

Other community identification methods, including *fastgreedy.community*, can be found at Detecting Community Structure.

# Step 4: further analyses

```
# Check the vertex degree, i.e., number of connections to each vertex
degree(mst)
# Output information for each community, including vertex-to-community assignments and modularity
commSummary <- data.frame(
mst.communities$names,
mst.communities$membership,
mst.communities$modularity
)
colnames(commSummary) <- c("Gene", "Community", "Modularity")
options(scipen=999)
commSummary
Gene Community Modularity
1 39755_at 2 -0.027161612
2 151_s_at 3 -0.006790403
3 32174_at 4 0.014033499
4 39781_at 2 0.034631055
5 1985_s_at 5 0.055454957
....
# Compare community structures using the variance of information (vi) metric (not relevant here)
# Community structures that are identical will have a vi=0
compare(mst.communities, mst.communities, method="vi")
[1] 0
```

Other metrics that one can observe include (check the *igraph* documentation):

- hub score
- closeness centrality
- betweenness centrality

In a case-control study, a useful approach is to generate separate networks for cases and controls and then compare the genes in these based on these metrics.

Suggestion: add

`microarray`

tag? Also include that in the title? Or are you using the microarray data only becuase it is easily available?Thanks genomax. I've added

microarrayandrna-seq. Technically, the method can be applied to any type of data though. I originally pieced together the pipeline on metabolomics data.Thanks @ Kevin.

Dear @Kevin Blighe, Hi and thank you. Can I use

igraphfor myTrinityde novo RNA-seq assembly? I have assembled my reads then performed DEG analysis using Trinity. which file I can use as input ofigraph? Thanks again.Dear Farbod,

All that you require is a data-frame or data-matrix of numerical data, preferably binomial distributed, as the method is based on Pearson correlation.

If your data-frame/-matrix is

MyData, then the starting point is:You can also use Euclidean distances instead of correlation, with:

Thank you

Trinity produces several kind of matrix. for example the first line of "Trans_counts.TMM.EXPR.matrix" is as:

can I use that ?

It looks fine.

The code in the tutorial above can be used in very diverse ways and the meaning/significance of the graph will change depending on the data that you provide. If you are supplying it data from Trinity, then I presume that it is

de novotranscriptome assembly transcripts? The graph of these would then show transcripts whose expression is highly positively or inversely correlated.Yes it is

de novobutPlease tell me what do you mean by "ranscripts whose expression is highly positively or inversely correlated"? are you telling me that the result graph would have some sort of skew or error? or it would be just a great candidate for my data?

Hey Farbod, the tutorial first generates a square correlation matrix of your data. It answers the question: '

Which genes are highly correlated with each other?' The graph object is then created from this correlation matrix. Thus, the edges in your graph will connect genes that are highly positively or inversely correlated. Closely related genes will also be grouped together in the same community.You should probably ask yourself this question: why do you want to perform network analysis on your data and what do you believe it will add to your project?

In the example that I provide in the tutorial, I first filter the example dataset to include

onlygenes that are statistically significantly related to treatment group and time (n=50). The resulting plot, then, shows the potential relationships between just these significant genes.Thank you Kevin, I got some errors in step1 data normalization

normalization: vsn

PM/MM correction : pmonly

expression values: medianpolish

try loading library "vsn" (

`library(vsn)`

)Hi Mike, did you install the

vsnpackage? - Does`library(vsn)`

return an error?If you already have your own data, then you can start from the second step '

Create the graph and tree objects'yes I installed vsn and loaded

`library(vsn)`

then I check normalize.AffyBatch.vsn, but I couldnt get it...

normalize.AffyBatch.vsn package:vsn R Documentation

Wrapper for vsn to be used as a normalization method with expresso

Description:

The normalisation method is not too important just for the tutorial. Could you try:

Thank you very much, Kevin

Then watch out for the control probes step!

Use this instead of the original line:

Hi again Mike, I now remove those control probes just after normalisation. So, they shouldn't be a problem. I also added a note about VSN possibly not working.

Thanks for your feedback!

Hi, I have used it on my whole Trinity matrix file just for test and I received the following error:

is it some separator issues?

You may have to read the file 'home/trans_counts.TMM.EXPR.matrix' into a data-frame? Something like

Thank you, there is another "x" and "numeric" issue:

Try

`as.matrix(as.dist(cor(t(data.matrix(MyData)), method="pearson")))`

Hi, it seems that it is a problem with huge matrix file so I did it simple and just put 100 lines in the matrix. I want to know by which command I can create the plot? is it just

`plot()`

?(sorry for simple questions)Yes, it will be difficult to produce a network of a large data-matrix because it has to compute a squared distance/correlation matrix. For example, if you tried it on a transcriptome of 20,000 protein-coding genes, you would have to generate a distance matrix of 400,000,000 data points.

You can generate a quick plot with just the base R

`plot()`

function, which will interpret the graph object.`plot.igraph`

should also work. However, between the graph adjacency object and actually plotting the graph, there are many other important steps (as you can see above in the tutorial)What is the significance of the Modularity column in the final commSummary data frame? To my understanding, modularity is a singular value that speaks to the entire network - why is each node assigned its own value?

In this context, it relates to the community structure, not the entire graph. Also, based on the fact that I have used edge.betweenness.community() for the purpose of identifying community structure in this tutorial, the modularity score relates to the maximum score achieved for each node when identifying the community structures.

[source: http://igraph.org/r/doc/cluster_edge_betweenness.html]Does that help? - hope so.

Thank you very much for the code!

I have two very basic questions. 1. Why do you use as input the four conditions in "estrogenMainEffects"? 2. Don´t you should use just one condition to find the "transcription modules" in that particular scenario?

Thank you again for your contribution! Regards, Luis

Hey Luis! This is really just a simple tutorial to show one way of constructing a network / minimum spanning tree. It would indeed be interesting to construct the network separately for each of the 4 conditions, and to then compare the networks between these. There are many diverse ways to conduct a network analysis.

Very awesome code and tutorial! I've been thinking how can I investigate the network overlap and/or uniqueness? For example, for time-course study, that'll be very interesting if looks at network "hand-shake" between two continuous time point, e.g Day3 has own network and Day4 has its own network, in the same plot, but also shows some interactions (maybe gene expressed in both days, or the subnetwork btw two days because some genes have correlations). Do you have any idea of how to achieve that? Thanks.

Hey Joseph. Thank you! I have not included that type of functionality in this tutorial, and other network analysis tools neither have sufficiently tackled this issue.

My recommendation would be to compare genes by the following metrics:

You can also directly compare 2 networks by the '

variance of information' (vi) metric (not relevant here). Identical graphs will have a vi=0get error info as: Error in i_compare(comm1, comm2, method) : (list) object cannot be coerced to type 'double'

I don't understand what's the problem.

Oh, my apologies. The compare() function is to compare community structures, like:

This just outputs a single number, though. If the community structures are identical, the value is 0.0.

Thanks! That sounds only indicates either identical or discrepancy without any further details. I wonder, we can make to networks, g1 and g2, the genes A, B, and C appear in both networks. Can we let them "cross-talk" vis the genes A, B, and C in the Cytoscape? or how to make two networks connected? Any comment?

Cytoscape

NetworkAnalyzerplugin allows you to do many extra things like that. I believe you can export your igraph objects to Cytoscape with`toCytoscape(igraphobj)`

, fromcyRESTpackageHi, I tried "Step 2 Create the graph and tree objects" with my own microarray data. But values such as edgeweights and vSizes are all NA, and therefore I cannot get a plot with the error message of "need finite 'xlim' values. My own data is 182 obs. of 661 variables. Is there anything that I should check to solve my problem? Thanks.

Was the

`graph.adjacency()`

function successfully run?Thank you Kevin, when I run graph.adjacency(), there was no error message. Although I viewed the list "g", it was difficult for me to know whether it was successful or not. Could you please let me know how to check the output of graph.adjacency()?

Hey, if you just type

`g`

at the console, it should display some textual information about the graph object.Can you show the exact command that you used for

`graph.adjacency()`

?Your input data may also contain NAs somewhere. What is the source of your data?

Hi Kevin, the command for graph.adjacency and the output of typing "g" at the console is as below. I found that there are 196 NAs in my data. My data is normalized microarray data of blood from 661 human subjects. When there are NAs, do I need to add specific argument? I also found that when I entered " g <- simplify(g, remove.multiple=TRUE, remove.loops=TRUE)", there was an error message with "Error in simplify(g, remove.multiple = TRUE, remove.loops = TRUE) : unused arguments (remove.multiple = TRUE, remove.loops = TRUE)"

Thank you so much.

g <- graph.adjacency( as.matrix(as.dist(cor(t(datExpr_LG5), method="pearson"))), mode="undirected", weighted=TRUE, diag=FALSE )

If there are NAs in the data, then I am not sure how it manages to successfully produce the

`g`

object. The`cor()`

function (with default settings) applied to data with missing values will throw an error. Perhaps it is producing a corrupt g object.The key may be in the '

`use`

' parameter, which is passed to`cor()`

.You could try

Thanks! I tried the command as you suggested, but in the next step of "g <- simplify(g, remove.multiple=TRUE, remove.loops=TRUE)", I still get the error message with "Error in simplify(g, remove.multiple = TRUE, remove.loops = TRUE) : unused arguments (remove.multiple = TRUE, remove.loops = TRUE)". Could you please suggest any other method? I appreciate your help.

I have never seen that error for that function in the past. If you skip this step, are you able to produce the graph?

Other things to try:

`simplify`

?`g <- igraph::simplify(g, remove.multiple=TRUE, remove.loops=TRUE)`

It works with your suggestion "g <- igraph::simplify(g, remove.multiple=TRUE, remove.loops=TRUE)". Thanks! Before you suggested the new graph.adjacency command, all values of both edgeweights and vSizes were NA. After I used your new graph.adjacency command, edgeweights are not NA. But all vSizes are still NA. I cannot produce the graph. Could you please suggest any other method in this situation?

Okay, that indicates that there is a namespace issue, i.e., there is some other package that is loaded in your R session that shares the same function names as those functions used by

igraphpackage. You may consider saving your R session via`save.image("MySession.rdata")`

, restarting R, loading just`igraph`

package, and then loading your data with`load("MySession.rdata")`

(and then trying the commands again).Yes, the original "simplify" command works well when I load igraph only. However, vSizes are still NA. Maybe it is caused by NA in my data, as you suggested earlier. Could you let me know the method to deal with NA problem? Thanks!

For vSizes, you have to specify your original dataframe into the command. So, yours would be:

You can also just skip this part and specify your vertex sizes manually when calling the

`plot()`

function, eg:Sure, I specified my original dataframe into the command. But it does not work. However, as you suggested, when I skipped that part and specified vertex sizes manually, it worked! Thank you so much. By the way, two thirds of my nodes don't have any edges. Could you let me know how to delete nodes without edges?

Great!

The nodes / vertices that have no edges are the ones whose original edge values fell below your chosen threshold for correlation. You can remove them using this function: http://igraph.org/r/doc/delete_vertices.html

OK, thank you very much for your kind help! I wish you success and happiness.

And you too, of course!

Thank you so much for this tutorial. I have applied it to my data and it works fantastic. I would like to ask about something though. I followed your directions exactly in creating a pearson correlation distance:

and the rest of the tutorial; however, I run into issues when I get to this command:

It generates the following error:

If I read this correctly, this is saying that this command is not appropriate for weighted edges bc the edges are weighted and the command treats them as distances instead, so the groups you end up with in your graph may not be biologically relevant or even correct.

I have found this link explaining the issue as well: https://github.com/igraph/igraph/issues/1040

Do you happen to know a work-around for this? I have tried to set the

`weighted = NULL`

but I don't end up with any edges, just a bunch of balls floating in space.Thank you so very much!!

That is a conundrum indeed! I read through the GitHub issue and it seems that there was no consensus on how to deal with this situation where edges are weighted and a user attempts to identify communities via edge betweenness. Well, the consensus appears to be to just issue a warning, which was not issued in the previous version of

igraphon which I had built the tutorial.The way around it (to make it through this tutorial at least) is is to just specify

`weights=NULL`

, which you tried for your own data. If you ended up with just the vertices and no edges, you may try to reduce the threshold that you use for`delete_edges()`

. Perhaps your network is simply not very well connected.There are many other community identification metrics, though. One quick and easy one is 'fast greedy':

That, when run with the subsequent commands on the tutorial data, produces:

One would have to look through each method and decide whether it is suitable for the underlying data. Some of the community identification methods are explained here: https://stackoverflow.com/questions/9471906/what-are-the-differences-between-community-detection-algorithms-in-igraph

Hi Kevin,

If I understand this correctly. I take my counts data and normalize it first e.g use rlog of the counts. Then I need to find the genes that have a significant effect as the code below. However, I am bit confuse of what I should input in where is says: "y ~ estrogen *time.h" . Is this meant to be one of my conditions?

Thanks

Oh, you just need to start at Step 2. From that step, your rlog data should slot into the code where

estrogenMainEffectsis used. For this network analysis, though, you will struggle to work with 1000s of genes - it is mostly designed for smaller datasets. With your RNA-seq data, you would have to filter down based on variance on differential expression.Hi Kevin, I have a very fundamental question about how to pre-processing the time course data. In your demonstration, you have several time points, my study is also time-course data. I'm very seriously considering should we subtract the baseline (e.g. 0hr, Day0 et al) from subsequent time points prior to construct the network. The major differences are if we take give time point expression value, that value number maybe around 10+ (as example), but if we use the expression data of DayX-Day0, the intensity value may go to 0.1, 0.5 et al and even with negative values. I don't know how that can impact on the network construction. However, the baseline value certainly influenced the latter time points. The variance from baseline would mislead us in the understanding of the network?

My preference would be to perform unbiased / unsupervised network construction separately at each time point (if possible), and then compare hub scores, vertex degrees, and module (community) memberships. These will likely differ across the different time-points.

For now, I have not worked specifically on time-course data in the context of network analysis.

Thank you, Kevin. In order to gain separate networks at each time point, will you suggest to use DayX-Day0 as input?

Yes:

When I run the code

I get this error:

Error in data.frame(mst.communities$names, mst.communities$membership, : arguments imply differing number of rows: 290, 288