Thanks for your data and code.

It seems that you are getting the warnings because you have disconnected components. All the components are fully connected except for the ones with node 31 and 42. In these two components, the two nodes sits between others, and hence gets a betweenness score when the alpha is set to 0.

Hope this helps,
Tore

Thanks for using tnet. Could you send me a copy of your data and code that you are using?

Best,
Tore

I was wondering if you could help me with an error message that i’m getting? I’m doing some simple analysis with a weighted network and have calculated degree and closeness values fine, but the betweenness_w function is throwing up an error message:

> warnings()
Warning messages:
1: In get.shortest.paths(g, from = i, to = V(g)[V(g) > i]) :
At structural_properties.c:4277 :Couldn’t reach some vertices

I’m using the same edgelist for this as for the degree and closeness values that worked fine.

Thanks for any help that you can give me!

Nicola

The above code should work for other cases; however, you should change the line starting with “reg <- lm(" to a regression function that suits your dependent variable.

Let me know if you have any issues,
Tore

You are the best!

I read this post with interest … would the same work if the dependent variable was a factorial measure? In my case it would be animal disease status as the dependent variable – either positive or negative, and seeing which value of alpha was most appropriate to infer whether the number of animals you are connected to (an alpha value closer to 0) or the weighting – the amount of time that you spend in contact with those animals (an alpha value closer to 1) was more important in terms of predicting whether individuals would be infected or not?

Thanks for your help,

Nicola

Your data sounds ideal for finding the “optimal” value of alpha. My understanding of ridge models are limited, but here is a suggestion of how it can be done using OLS. Note that the example data is not ideal as there are only 32 observations, the dependent variable is not normally distributed, and there are no control variables etc, but it shows how it can be implemented.

# Load tnet and data
library(tnet)
data(Freemans.EIES)

# Define output data frame
out <- data.frame(alpha=seq(from=0, to=2, by=0.1), y=NaN)

# Get independent variables
for(i in 1:nrow(out)) {
  # Compute centrality measure
  tmp <- degree_w(net=Freemans.EIES.net.3.n32, measure="alpha", alpha=out[i,"alpha"])
  # Extract just centrality scores
  tmp <- tmp[,"alpha"]
  # Regress (add control variables etc)
  reg <- lm(Freemans.EIES.node.Citations.n32 ~ tmp)
  # Instead of a nice way of doing it: Extract the t-statistic
  tmp <- eval(parse(text=as.character(summary(reg))[4]))
  tmp <- matrix(data=tmp, nrow=(length(tmp)/4), ncol=4)
  tmp <- abs(tmp[nrow(tmp),3])
  out[i,"y"] <- tmp
}
# Plot alpha values and the corresponding significance obtained
plot(out, type="b", ylab="Significance of centrality measure")

The last command produces the following plot, which suggests that for this limited data, the optimal point is close to 0. Please do not base any conclusions on this data due to the limitations listed above.

Hope this helps,
Tore

I have a question again,

I want to study how alpha value helps predict a continuous variable.

My database capture a communication network and I want to find what value of alpha helps to explain a continuous variable (for example, to predict the number of words used by each node using weighted out degree). Ridge-regression method can be a good choice ?

Sincerely, Victor

The values are:
-degree: number of ties
-output: sum of tie weights (aka node strength)
-alpha: the second generation weighted measure that combines degree and output, see the paper.

You can also find this by typing ?degree_w in R.

Best,
Tore

Forgive me if this is an ignorant question, but I was just wondering what exactly the values in the output meant in terms of the values given for “degree”, “output” and “alpha”?

Thanks for your help.

The degree_w-function uses the outgoing ties by default. To calculate the measures for the incoming ties, you should define type=”in”.

degree_w(net, measure=c("degree", "output", "alpha"), alpha=0.5, type="in")

For an undirected network, the type parameter is irrelevant as the outbound and incoming ties are identical. For example:

> # Load tnet
> library(tnet)

> # Load network
> net <- cbind(
> i=c(1,1,2,2,2,2,3,3,4,5,5,6),
> j=c(2,3,1,3,4,5,1,2,2,2,6,5),
> w=c(4,2,4,4,1,2,2,4,1,2,1,1))
>
> # Calculate degree centrality
> degree_w(net, measure=c("degree", "output", "alpha"), alpha=0.5)
     node degree output    alpha
[1,]    1      2      6 3.464102
[2,]    2      4     11 6.633250
[3,]    3      2      6 3.464102
[4,]    4      1      1 1.000000
[5,]    5      2      3 2.449490
[6,]    6      1      1 1.000000
>
> degree_w(net, measure=c("degree", "output", "alpha"), alpha=0.5, type="in")
     node degree output    alpha
[1,]    1      2      6 3.464102
[2,]    2      4     11 6.633250
[3,]    3      2      6 3.464102
[4,]    4      1      1 1.000000
[5,]    5      2      3 2.449490
[6,]    6      1      1 1.000000

Best,
Tore

I want to calculate degree_w. I know that for out degree I need to write..

degree_w(net, measure=c("degree", "output", "alpha"), alpha=0.5)

But, I dont know how to write the instruction for calculate in degree.

degree_w(net, measure=c("degree", "in", "alpha"), alpha=0.5).

It’s correct or not the second one.

May I have your help.

Have a good day,

Sincerely, Victor

xingqin

I am uncertain what you are referring to when you are using inverse weights in the degree_w-function, and also what closeness() is. Please send me an email with the commands and data you are using.

Best,
Tore

Sorry for ‘spamming’, I forgot to ask another question that puzzels me: I am using closeness_w, but if I dont use weights (set them all to 1, just to check), I do not get the same result for node closeness as when using closeness() in an unweighted network. Why is this? Am I doing something wrong?

Kirsten

One more quesiton… concerning degree_w, is there a way to calculate the degree_w per node using the inverse weights with tnet?

Best,
Kirsten

All the clustering_w-function is the global clustering coefficient, while the clustering_w_local-function is the local clustering coefficient that produces a score for each node (see Barrat et al., 2004). These functions are just different aggregations of the triplets in the network with the global one aggregating all triplets and the local one being an intermediate step.

The measure-parameter (“am” “gm” “ma” “mi” “bi”) controls how triplets are valued. This could, for example, be the regular mean (arithmetic mean; “am”) of the two tie weighs that make up the triplet, or the geometric mean (“gm”). The main difference between these two is that the geometric mean discounts the tie weight if there is variation (e.g., tie weights of 2 and 2 would be am=2 and gm=2, and tie weights 3 and 1 would be am=2 and gm=sqrt(3)~1.73.

Hope this helps,
Tore

Thank you for the quick response. I will have to think about this… :)
Just to make sure that I get your other function right, – the clustering_w “gm” would be a transitivity measure for the overall weighted graph, right?

Best,
Kirsten

Thank you for using the site and tnet!

Normalisation of node centrality scores is, to my opinion, adding a bias to the data instead of removing one. In fact, I have stayed clear of standardising the measures due to what I believe was misleading in the original measures, let alone generalised ones. My main concern with the original ways of standardising/normalising node centrality measures (i.e., n-1) is that these scale linearly with the number of nodes. Specifically, I believe that none of the main three node centrality measures scales linearly. First, it has been argued that the average degree in networks does not change as a network grows. Hence, no scaling (i.e., use the average degree to compare networks). Second, closeness centrality is based on shortest distances. In small world networks, shortest distances does not scale linearly with the number of nodes, but rather logarithmically (i.e., divide farness scores by log(N) if your network is a “small world”). Third, betweenness is based on n*(n-1) shortest paths, so it could be argued that it scales n-squared. Given these issues with the original measures, I have not given much thought/effort to normalise the generalised ones. Let me know if you figure out a way of doing it!

Best,
Tore

Great site, and great software :)
One question regarding degree_w and closeness_w. The output I get is an array, however I am interested in the overall degree(strength) centralization of the weighted network, not for each individual node. Is there a way to do this with tnet?

Best,
Kirsten

Thanks. When I have the analysis, I will contact you again. Maybe, I made a good discovery with your idex. Let me try!!!

Sincerelly,

Vicktor

Thank you for taking an interest in my work, and reading the future research section carefully!

The “optimal” (read: what high performers have)-level of the centrality measures could be probed by using a performance variable as the dependent variable and a centrality variable as an independent variable along with controls. If you ran multiple regressions each with a different alpha for the centrality parameter (e.g., 0, 0.1, 0.2, 0.3 etc), then if you could plot the attained z-scores of the centrality variable (y-axis) against the alpha (x-axis). This should give you an inverse u-shaped curve. The optimal-level is where the maxium z-score is attained.

Hope this helps,

Tore

Hi,

I have a doubt. In his article states that could make a regression analysis to find an optimal level of alpha. For example, if I have a binary variable to explain, how you might proceed in the analysis?. You could provide guidance for compare different and found and optimal alpha. I use SPSS for analysis.

Thanks!

Victor Hugo

I am not aware of any general literature on this topic. You could have a look at the Fernandez and Gould-paper that does something similar with brokerage measures. They define – based on directionality, which your data should have – various roles based on ego networks.

Best,
Tore

Do u think i can just assign roles based on three centrality? for example,
make the one with big centralites as a leader. Centrality can be the measure of influence within the community?

Thanks in advance,
MJ