A problem we see in psychological network papers is that authors sometimes over-interpret the *visualization* of their data. This pertains especially to the layout and node placement of the graph, for instance: do nodes in the networks cluster in certain communities.

Below I will discuss this problem in some detail, and provide a basic R-tutorial on how to identify communities of items in networks. You can find the data and syntax I use for this tutorial here β feedback is very welcome in the comments section below.

#### Node placement and the Fruchterman-Reingold algorithm

Let’s create an example so we can see what the challenge is. First, we take some data I happen to have lying around, estimate a regularized partial correlation network where the edges between nodes are akin to partial correlations, and plot the network, using the `layout='spring'`

command. This is the default in the psychological network literature, and uses the Fruchterman-Reingold algorithm to create a layout for the nodes in the graph: nodes with the most connections / highest number of connections are put into the center of the graph.

library("graph") load("data.Rda") cormatrix <- cor_auto(data) graph1<-qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data), vsize=7, cut=0, maximum=.45, border.width=1.5) |

`cormatrix`

is simply the correlation matrix of the 20 items, and the `sampleSize`

command tells R how many people we have. The bottom line makes the graph pretty. π

This is the resulting figure:

However, the node placement here is just one of many equally ‘correct’ ways to place the nodes. When there are only 1-3 nodes in a network, the algorithm will always place them in the same way (where the length of the edges between the nodes represent how strongly they are related), and the only degree of freedom the algorithm has is the rotation of the graph. But especially in graphs with many nodes, the placement tells us only a very rough story, and should not be over-interpreted.

Here are two more ways to plot our above network that are equally ‘correct’.

nNode <- 20 set.seed(1) graph2<-qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data), vsize=7, cut=0, maximum=.45, border.width=1.5, layout.par = list(init = matrix(rnorm(nNode*2),nNode,2))) set.seed(2) graph3<-qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data), vsize=7, cut=0, maximum=.45, border.width=1.5, layout.par = list(init = matrix(rnorm(nNode*2),nNode,2))) |

While the edges between items are obviously the same, the placement of the nodes differs considerably.

#### Madhoo & Levine 2016

A new paper by Madhoo & Levine (in press) in *European Neuropsychopharmacology* provides a good example for this challenge. They investigated the networks structure of 14 depression symptoms in about 2500 psychiatric outpatients diagnosed with Major Depression at two timepoints (12 weeks apart). A very cool contribution of the paper is that they examined the change of the network structure over time, in a somewhat different way than we did previously in the same dataset.

Similar to the network example above, they used regularized partial correlation networks to estimate the cross-sectional network models at both timepoints, and plotted the networks using the Fruchterman-Reingold algorithm. They concluded from visually inspecting the graphs that there are 4 symptom clusters present, and that these did not change over time:

“At baseline the network consisted of four symptom groups (Figure 1a) of: Sleep disturbances (items 1β5), cognitive and physical avolition (items 6β9), Affect (items 10β12) and Appetite (items (13β14).

[…]
The endpoint symptoms groupings (in Figure 1b) resembled that at baseline”.”

But these findings and conclusions are merely based on visual inspection of the resulting graphs β and has we have learned above, these should be interpreted with great care. Of note, this visual over-interpretation is pretty common in the psychological network literature, and I really don’t want to call out Madhoo & Levine specifically for their great paper; it just happens to be the most recent example that came across my desk.

Another reason why this stood out to me is that we have analyzed the community structure in the same dataset in a recent paper, and found that the *number* of communities changes over time β which conflicts with the authors’ visual interpretation of the graphs.

#### Data-driven item clustering in R

So what might be a better way to do this, and how can we do it in R? There are numerous possibilities, and I introduce three: one very well-established method from the domain of latent variable modeling (eigenvalue decomposition); one well-established algorithm from network science (spinglass algorithm); and a very new tool that is under development (exploratory graph analysis which uses the walktrap algorithm).

##### Eigenvalue Decomposition

Traditionally, we would want to describe the 20 items above in a latent variable framework, and the question arises: how many latent variables do we need to explain the covariance among the 20 items? A very easy way to do so is to look at the eigenvalues of the components in the data.

plot(eigen(cormatrix)$values, type="b") abline(h=1,col="red", lty = 3) |

This shows us the value of each eigenvalue of each components on the y-axis; the x-axis shows the different components. A high eigenvalue means that it explains a lot of the covariance among the items. The red line depicts the so-called *Kaiser criterion*: a simple rule to decide how many components we need to describe the covariance among items sufficiently (every components with an eigenvalue > 1). There are better ways to do so, such as parallel analysis, which you can also do in R. In any case, depending on the rule we use now, we would probably decide to extract 2-5 components. We do not yet know what item belongs to what component β for that, we need to run, for instance, an exploratory factor analysis (EFA) and look at the factor loadings. And yes, you guessed correctly: you can obviously also do that in R … life is beautiful! π

Why is this related to networks at all? Numerous papers have now shown that latent variable models and network models are mathematical equivalent, which means that the numbers of factors that underlie data may roughly translate to the number of communities you can find in a network.

##### Spinglass Algorithm

A second method is the so-called *spinglass algorithm *that is very well established in network science. For that, we feed the network we estimated above to the *igraph* R-package. The most relevant part is the last line `sgc$membership`

.

library("igraph") g = as.igraph(graph1, attributes=TRUE) sgc <- spinglass.community(g) sgc$membership |

In our case, this results in “5 5 5 5 5 5 5 2 3 1 1 3 3 3 4 4 2 2 3 3”. This means the spinglass algorithm detects 5 communities, and this vector represents to which community the 20 nodes belong (e.g., nodes 1-7 belong to community 5). We can then easily plot these communities in qgraph by, for instance, coloring the nodes accordingly. Note that *iqgraph* is a fantastically versalite package that has numerous other possibilites for community detection apart from the spinglass algorithm, such as the walktrap algorithm. (Thanks to Alex Millner for his input regarding *igraph*; all mistakes here are my mistakes nonetheless, of course).

It is important to note that the spinglass algorithm will often lead to different results every time you run it. This means you should set a seed via `set.seed()`

before you run `spinglass.community`

, unlike I do above. I often run the algorithm 1,000 times, look at the median number of clusters that I obtain, and then find a seed which reproduces this median number of clusters. I use this solution for a paper (noting that solutions look different with a different seed).

It is also crucial to know that there are many dozens of different ways to do community detection. Spinglass is somewhat simplistic because it only allows items to be part of one community β but it could be that items are better described as belonging to several communities at the same time. BarabΓ‘si’s book “Network Science” has an extensive chapter on community detection (thanks to Don Robinaugh for the tip). Spinglass is just one of many opportunities.

##### Exploratory Graph Analysis

The third possibility is using *Exploratory Graph Analysis* via the R-package EGA that is currently under development. This means you really want to check what is happening and make sure you trust the package before you publish a paper using its results, but the preprint looks promising. This package re-estimates a regularized partial correlation network from your data, similar to what we have done above, and then uses the walktrap algorithm to find communities of items in your network. This should lead to identical results compared to *igraph* in case the walktrap algorithm is used.

The advantage of EGA is that β unlike eigenvalue decomposition β it shows you directly what items belong to what clusters. The author of the EGA package is currently testing the performance of different ways to detect communities (see this paper for more details on the topic).

library("devtools") devtools::install_github('hfgolino/EGA') library("EGA") ega<-EGA(data, plot.EGA = TRUE) |

If the method turns out to work well, it’s very easy to use and automatically shows you to which communities your items belong.

Note that at present, EGA takes your data and automatically estimates a Gaussian Graphical Model (that assumes multivariate normal variables). If you have binary data, they do not fulfill the assumptions to estimate such a model. I hope that EGA in the future will be adapted to estimate the Ising Model for binary data which is the appropriate regularized partial correlation model for such data (ref1, ref2).

##### Do EGA and spinglass give us the same results?

Update: I added this section after a comment by KSK below. Now, we want to check our results for robustness: do the *igraph* spinglass algorithm and *EGA* which uses the walktrap algorithm agree in their community detection?

That’s pretty easy to do: let’s plot the two networks next to each other and color the communities accordingly. First, we define the communities based on the *EGA* and *igraph* results, and then plot the networks using the layout of the very first network above.

group.spinglass<- list(c(1:7), c(8,17,18), c(9,12,13,14,19,20), c(10,11), c(15,16)) group.ega<- list(c(1:7), c(8,15,16), c(10,11), c(17,18,20), c(9,12:14,19)) par(mfrow = c(1, 2)) graph4 <- qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.ega, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "green", "blue", "orange", "white"), title="ega walktrap") graph5 <- qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.spinglass, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "orange", "white", "blue", "green"), title="igraph spinglass") |

Intuitively β based on visual inspection β the EGA solution seems to make more sense, where node 8 belongs to the green community instead of the orange one. But, again, this is just a graphical display of complex relationships, and we must be careful with interpretation here.

So let’s plot the same network with a slightly different (random!) layout; again, this layout is not better or worse than the layout above:

par(mfrow = c(1, 2)) set.seed(5) graph4 <- qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.ega, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "green", "blue", "orange", "white"), title="ega walktrap", layout.par = list(init = matrix(rnorm(nNode*2),nNode,2))) set.seed(5) graph5 <- qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.spinglass, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "orange", "white", "blue", "green"), title="igraph spinglass", layout.par = list(init = matrix(rnorm(nNode*2),nNode,2))) |

As you can see now, in this visualization it is unclear whether node 8 should belong to the green or orange communities, and we have no clear intuitive favorite.

#### Conclusions

If you are interested in *statistical *communities among items in your network, please do more than visually inspect your graph. When I do this for papers, I use the three methods described above, and usually they result in very similar findings. Obviously, it may also be that you are more interested in *theoretical* or *conceptual* communities. In that case, you may not need to look at your data at all, and all is well without going through all the above trouble!

Cool! I’d like to add that you can use averageLayout to obtain a layout based on two networks:

Layout <- averageLayout(graph1, graph2)

Which you can then use in qgraph:

qgraph(…, layout = Layout)

It's always advisable to plot two networks of the same nodes with the same layout, to avoid above mentioned interpretation problems.

That’s really cool!!

Nice!

A couple of questions about the EGA results. What is the reason node 8 is getting assigned to the same community as nodes 15 and 16 (rather than the community in green or magenta)? Why isn’t node 9 assigned to the green community instead of the red? I can only imagine that if I would 3D print the relations instead of 2D (so the result would be ballish instead of circleish) that 9 is closer (on average) to the other red dots than to the green dots, although the edges suggest otherwise. In any case, I was wondering if the danger of visually inspecting a 2D graph of higher (n) dimensional relations lies in the n-D to 2-D reduction. If so, what is the benefit of a graphical method over, say, a table of pca factor loadings? Or a path diagrammatical representation of such a table? (feasible with this relatively small number of nodes).

Or did the assignment have to do with the difference between zero-order correlations versus partial correlations? I know you’re a proponent of inspecting partial correlations, so I assumed the plot might be based on partial correlations while the EGA provides information on zero-order correlations or the other way around. Can you clarify the nature of the correlations?

Based solely on my own (lack of) visualization skills I would have clustered differently. But usually I tend to play around with the arguments in qgraph to get an idea of how sensitive or robust the clustering is towards the values of those arguments, including the choice of the algorithm. (so thanks for the averaging tip, Sacha!)

Good points, thanks. I’ll answer here and then maybe edit the post above to clarify.

1) EGA estimates a gaussian graphical model with regularization, using what we believe to be the most reliable defaults at the moment (cor_auto to get the covariance matrix, then GGM with standard regularization tuning parameter of 0.5). This is exactly what I did in the example above, and hence will lead exactly to the same network structure. If I were to take the output from EGA and plot it in qgraph, using the same graphical arguments and layout above, it would be identical.

2) You summed up the problem much better than I did: n-D to 2-D reduction. And yes, multiple people in the last years have actually called for avoiding graphs altogether, and plotting tables instead. I think we should do both, because both provide different answers. Personally, if I have to choose, I’d rather have a visualization of the table when I know how to interpret it, rather than a 20×20 table that has mostly 0s and is rather difficult to figure out by just looking at it.

3) Different clustering: EGA uses the walktrap algorithm and is under development, and it usually gives me slightly different results than igraph with the spinglass algorithm. Let’s check it out in this case, actually.

Not sure how formatting works in comments … let’s see. Here is the rcode. I define groups based on the 2 community analyses outputs:

`# spinglass: 5 5 5 5 5 5 5 2 3 1 1 3 3 3 4 4 2 2 3 3`

sgc$membership

`# ega: 2 2 2 2 2 2 2 4 1 3 3 1 1 1 4 4 5 5 1 5`

ega$wc

`group.spinglass< - list(c(1:7), c(8,17,18), c(9,12,13,14,19,20), c(10,11), c(15,16))`

group.ega< - list(c(1:7), c(8,15,16), c(10,11), c(17,18,20), c(9,12:14,19))

Then we estimate the 2 networks; I simply use the layout of our very first graph.

`graph4 < - qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.ega, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "green", "blue", "orange", "white"))`

`graph5 < - qgraph(cormatrix, graph="glasso", layout="spring", sampleSize = nrow(data),groups=group.spinglass, vsize=7, cut=0, maximum=.45, border.width=1.5, color=c("red", "orange", "white", "blue", "green"))`

Result:

You can see that node 8, again, is somewhat problematic. I would assume that in a factor model, it would either have no loadings on any of the 5 factors, or cross loadings between several.

Now, I played around with different seeds to plot this graph, and after 3 tries I discovered this plot:

Here you see exactly why we should not overinterpret these graphs .. in this 2d renditon of the n-d data, the 2 different community detection algorithms both make equal sense, while they do not in the first plot above.

Good points! I have a few comments:

Personally, I think visually inspecting the result of cluster (or community) detection in networks very insightful. However, I donβt think the visualization per se is the final goal when a person uses, for example, EGA. The goal, or at least my goal, when I use EGA is try to discover the dimensionality of a given instrument. So, if the EGA results in 4 communities, we can verify if this first-order structure fits the data, via confirmatory factor analysis. In the EGA package I have implemented a function, called CFA, that uses the structure suggested by EGA and runs a CFA. My experience shows that, in general, the fit is very good (CFI > .95 and RMSEA < 0.05). So, what are the advantages of investigating dimensionality via EGA and related methods (i.e. via community detection in regularized partial correlation networks)? 1) It shows you which item belong to each dimension, 2) allow an easy inspection of model fit, via CFA, 3) can be used to investigate, for example, the stability of the structure via bootstrap (in the EGA package we have the bootEGA function). One may argue that βnetworks are totally different from latent variable models, so why to use CFA from a structure found via some network strategy?β Wellβ¦ it seems that in some specific cases, network models and latent variable models are two sides of the same coinβ¦

Furthermore, as far as our simulations show (see arxiv.org/abs/1605.02231), using EGA to investigate the dimensionality of an instrument can be as good as, and in some cases, more accurate than traditional methods as parallel analysis, Kaiser-Guttmanβs eigenvalue rule and so on.

Minor freudian typo: “we estimated already to the iqgraph R-package” (and the following code misses a quote mark). Thanks for the post, these tutorials are much needed!

I read through it 5 times and didn’t see it! That’s how often I’ve written “qgraph” in the last years π … thanks for pointing out the 2 mistakes Matti.

Thank your for this tutorial, very useful! I think this way to analyze psychometric tests is promising. I would like to report a problem in the code. Describing the usage of the spinglass algorithm with igraph, you build the function “community.newman”, but you use the function “spinglass.community”.

Thanks for finding this error Davide, the function

`community.newman`

isn’t actually needed, so you can ignore that part of the code (and I’ll delete it from the post and code).Just a brief question: I think it would be a good idea to take the stochastic nature of the spinglass algorithm into account when interpreting its results β they will change from one iteration to the other.

Hi Markus, what do you mean with iteration? The network structure is always the same, just the visualization is different.

Thanks for sharing this Eiko! it was indeed very helpful.

Just a question, and perhaps it is not relevant to your post, but I am trying to use the same layout (nodes at the same position) for three different networks. I have the 1) network of the entire sample, 2) network of the boys only, and 3) network of the girls only. I was wondering if you could so kindly advise what code i should use to generate the same layout for all 3? Many thanks in advance for your help!

Hi Amy.

You estimate the three networks, let’s say

`g1 < - qgraph(data1, layout="spring", ...)`

`g2 < - qgraph(data2, layout="spring", ...)`

`g3 < - qgraph(data3, layout="spring", ...)`

Then:

`L < - averageLayout(getWmat(g1), getWmat(g2), getWmat(g3))`

This averages the layout of the 3 adjacency matrices (the command is slightly different if you have an Ising model instead of a Gaussian Graphical Model).

And then you plot the graphs again with layout=L (either using qgraph() or plot() ).

`plot(g1, layout=L)`

`plot(g2, layout=L)`

`plot(g3, layout=L)`

Let me know if this works for you!

EDIT: there shouldn't be a space between <-, can't get it to work properly on my phone right now sorry.

No worries, thanks so much for the quick reply Eiko!

I just had a try, and it did not work. I applied EBICglasso to the GGM model.

Would that have made things different? here is what i did with EBICglasso for the girls only data as an example (I did the same for boys only and the full data):

graph_girls.m <-EBICglasso(data_girls.cor, n = nrow(data_girls))

graph_girls.g<-qgraph(data_girls.cor, labels=names, directed=FALSE, graph="glasso", layout="spring", legend=TRUE, vsize=5.5, cut=0, maximum=.45, sampleSize = nrow(data_girls), border.width=2, border.color="black", minimum=.03, groups=groups, color=c('#bbbbbb','#a8e6cf', '#dcedc1', '#ffd3b6', '#ff8b94'))

then I followed your coding:

L<-averageLayout(getWmat(graph_facets.g), getWmat(graph_girls.g), getWmat(graph_boys.g))

plot(graph_facets.g, layout=L)

perhaps I did something wrong?

I just wrote this quickly for you. Use this as a template and you will get there. Note also that I use the new estimateNetwork() function from the new package bootnet() that will make your life easier. It looks terrible pasting it here, so I uploaded it here:

http://psych-networks.com/wp-content/uploads/2016/12/amy.txt

Thanks a lot, appreciate your help!

It worked, thanks so much!

Hi Eiko, thanks for this very useful tutorial, I actually managed to get it working after a few trials on my own data and got an almost perfect graph (i.e. in accord with my expectations) to “cluster” patients based on their methylome patterns. It is more informative or at least visually more pleasing than a “phylogenetic tree” approach. I am a total novice to R so please bear w/ me π But how do I delve into the details of this EGA? Specifically, I use identifiers like S102, S405, S250. I noticed that the EGA package shortens them “illegally”, so I am getting S40 and S25 for the last two id-s. How can I fix this, do you know? Thanks!

Hi Hedi, I’m glad this is useful to you. I actually don’t know EGA very well. Its benefit is that it’s really just one line of code, but the disadvantage is that there seem to be few things you can change at present.

What you could try is the following. EGA, under the hood, uses the qgraph package to estimate a gaussian graphical model (a regularized partial correlation network for metric data). You can probably get at the weighted adjacency matrix if you look into the object that EGA estimates. I don’t have R here at the moment, but if you look into the estimated EGA object in RStudio, there should be something like EGA$weiadj or so. You can then use qgraph to plot the network in a different way than EGA does. qgraph really gives you all the options.

e.g.

`network_hedi < - qgraph(EGA$weiadj, xxx)`

Please also note that EGA assumes your data are metric, which is a big problem if you have binary data. In that case, you may want to use spinglass or walktrap and do a bit of magic in qgraph to color your nodes appropriately the way I did it in the tutorial.

You can find all the R-code I used to make the tutorial here.

There you can also find how I color the nodes manually in qgraph using the spinglass/walktrap algorithms. It's not pretty, and there are probably much better ways, but it will help you get your own network done.

Hi Eiko,

Thanks a lot. I did try this and got some error msg:

> network <- qgraph(EGA$weiadj, cormatrix)

Error in EGA$weiadj : object of type 'closure' is not subsettable

I guess I have to look more deeply into R in general. I am amazed how efficient it is!

Hi Hedi, thank you for your interest! To know more about how EGA works, and how accurate it is, give a look here: https://arxiv.org/abs/1605.02231. As Eiko pointed out, I am using qgraph + igraph. So, you can easily set up your node labels. Here we go:

ega1 <- EGA(yourdatahere, plot.EGA = TRUE)

#the glasso matrix is here:

ega1$glasso

#The "clusters" or dimensions of your data is here:

ega1$wc

So, you can use qgraph to adjust the lables as you want:

qgraph(ega1$glasso, layout = "spring", groups = as.factor(ega1$wc), labels = names(yourdatahere))

I hope it helps!

If not, please contact me here: hfgolino@gmail.com

Good luck,

Hudson

Thumbs up Hudson! Thanks!

Cheers, Eiko!

Hi Hudson, Thanks so much for taking the time to respond. The graphs look absolutely fabulous, I mean, as a method to split a network into subnetworks. I did indeed downloaded your paper but I know close to zero about matrix algebra. It is very impressive that you/others use such hard math in psychology, I had no idea. I’ll email you as I still try to get it right.

Hi Eiko & Hudson,

Just wanted to let you know that I finally succeeded with the labels, after studying a bit of R and reading up on glasso. So I had 8+6 columns, for 8 patients and 8 controls. After running EGA as suggested I created a list for each of the participants, as suggested in glasso.

> list1<- list("S1","s2","s3","s4","Samp5","s6","s7","s8","c9","c10","c11","c12","c13","c14")

#Using Hudson's suggestion about plotting the graph:

qgraph(ega$glasso, layout = "spring", groups = as.factor(ega$wc), labels = list1, vsize=9)

#This nicely plotted out the exact names, without abbreviation and increased the font size to 9. As the fog is thinning (in my brain) R is getting more fun! Thanks both π

Hedi, n=16 does not sound like you have enough data to reliable estimate a network structure among multiple items β but maybe I misunderstand what you are doing here.

This is a good starting point for network stability: https://arxiv.org/abs/1604.08462

Hi Eiko, thanks for commenting. I actually have some 20000 rows (i.e. features, them being gene expression values in 15 individuals) and I want to estimate the network structure among the patients, i.e. how similar they are to each other. I got actually 2 subnetworks, i.e. 2 groups of patients/controls. Does this sound reasonable to you? Thanks for the link to the tutorial, I love them!

It does make sense, Hedi! However, as Eiko stated, it is necessary to pay attention to the stability of the dimensionality structure. That’s why I’m suggesting you to use the bootEGA algorithm, which is a bootstrap version of EGA!

That sounds exciting Hedi, what a huge dataset. I’d definitely consider looking at both correlation and regularized partial correlation networks in that case, both seem to provide some sort of interesting information in your case.

By the way, I’d love to see your results if you’re willing to share. Glad this methodology is applied to other fields, we usually model people as rows, you model them as columns.

Hi Eiko, I just generated both graphs (based on simple correlations and EGA). I’ll send them to you and Hudson by email. I have some qualms about justifying why the method works well on such cases but it does. I will appreciate your feedbacks!

Great, looking forward Hedi.

Hedi, I found some literature that may be interesting for you (clustering people similarly to what you are doing):

Karalunas, S. L., Fair, D., Musser, E. D., Aykes, K., Iyer, S. P., & Nigg, J. T. (2014). Subtyping Attention-Deficit/Hyperactivity Disorder Using Temperament Dimensions : Toward Biologically Based Nosologic Criteria. JAMA Psychiatry, 97239(9), 1015β1024. http://doi.org/10.1001/jamapsychiatry.2014.763

Hi Eiko and thanks for the interesting and useful web blog.

I’m following your advice to set.seed() prior to using the spinglass.community command, but I’m not sure I’m doing it correctly. Shouldn’t I see a different computation and graphic output if I set a diffferent seed, because I’m noticing the same output regardless of seed.

rnorm(20)

set.seed(2)

rnorm(20)

#Now if we want the same random numbers

#we can just set the seed to the same thing

set.seed(2)

g = as.igraph(graph1, attributes=TRUE)

sgc <- spinglass.community(g)

Thanks, Rick

Hi Rick, thanks for the comment. In my case, graph1 was the network, estimated via:

`library('qgraph')`

library('IsingFit')

library('bootnet')

library('igraph')

network1 < - estimateNetwork(data1, default="IsingFit")

graph1 < - plot(network1, layout="spring", cut=0, filetype="pdf", filename="network")

I then transferred the network into igraph and ran spinglass 100 times, each time changing the seed.

`g = as.igraph(graph1, attributes=TRUE)`

matrix_spinglass < - matrix(NA, nrow=1,ncol=100)

for (i in 1:100) {

set.seed(i)

spinglass < - spinglass.community(g)

matrix_spinglass[1,i] < - max(spinglass$membership)

}

The results differed from each other, as you can see e.g. from the mean:

`mean(as.vector(matrix_spinglass)) #5.87`

max(as.vector(matrix_spinglass)) #7

min(as.vector(matrix_spinglass)) #5

median(as.vector(matrix_spinglass)) #6

I think this is correct β if there are inconsistencies please do let me know.