Hi Arlo,

Indeed. Think of these values are the plot positions of the confidence interval in the graph of the paper.

Tore

]]>Thanks very much for your work and code!

I have trouble understanding the statistical significance of the coefficients. With “tnet” function “weighted_richclub_w”, can I say if values in the Y column are outside the intervals created by the corresponding “H95” and “I95” columns, then these values in the Y column are statistically significant? Is this the right interpretation? Thanks!

]]>Kirill,

That’s correct. Link reshuffling implies weight reshuffling unless the origin of the ties are maintained (local).

Have a look at the random network page for details and examples of how the strength distribution can be maintained. https://toreopsahl.com/tnet/weighted-networks/random-networks/

Tore

]]>Thank you for your work and code!

I have a couple of questions about null models. In the article for weighted networks, you use weight & links reshuffling but as far as I understand the function for calculating WRC accept them only separately. Am I right or link reshuffling one implies weight reshuffling? Finally, in the paper, you also say that if richness is defined as the strength (my case), the null model should preserve strength distribution. Can you give a piece of advice on how it can be performed?

Best,

Kirill

Hi Tore,

Well, I must have overlooked or forget the symmetrization process mentioned in the paper. I reran the analysis on the symmetrized edgelist and now the results are looking good and comprehensible :) Thanks for your time and effort.

Best

Drahomir

Hi Drahomir,

There might not sufficient amount of data past s=70. You are correct in symmetrizing the network if it is undirected. Feel free to send me an email and I will have a look at it.

Best,

Tore

Thank you for your response. I would be really thankful if you could explain me the issue I’m having with the results of the analysis.

I have undirected network with n = 248 and m = 2401. The strength values are in the range from 3.26 to 1309. When I ran the analysis, I used “s” as a rich parameter reshuffling weights with NR = 1000 and nbins = 50. The problem I have is that the results show the weighted richclub coefficient (wrc) only up to the prominence level of 70 (i.e. strength = 70). I’m wondering why the stronger nodes weren’t included. I tried to expand the number of bins to 150, but again the maximum prominence value for which wrc is computed is 70. Doesn’t undirected edgelists have to be symmetrised as in the case of computing weighted average shortest paths?

Significant WRC (above 95%-tile of the random counterparts) was detected at the prominence value of 56. If I’m interpreting the results accordingly, then this mean that a significant rich club is forming amongst nodes with strength value 56 or greater. However, in my case this means that rich club consists of almost 55% of the original number of the nodes in the network (I excepted a more prominent rich club). I’m really trying to make sense out of this result, but from visual inspection of the network it is clearly visible that there are much stronger nodes sharing greater weights amongst themselves (which is suggestive of more selective wrc than suggested by the analysis). If I may, I would gladly send you the data and results of my analysis.

Thank you for your patience and help

Best,

Drahomir

Hi Drahomir,

Glad you’re finding the work useful.

The prominence is not reclaculated as the rich-club becomes more selective.

Best,

Tore

Thank you for your great and fascinating work.

I’m currently conducting a network analysis where i’m trying to identify core structure that controls the prominent portion of information flow within the network.

I had one question regarding the computations of strenghts at certain levels of prominence. In my case the prominence is represented by weighted degree (or strength). As the strength is calculated as a sum of adjacent edges to the node, is strength recalculated for each selected rich-club?

Lets say i have prominence level of strength 80 (units doesn’t matter) at which i detected significant formation of a rich-club. If i understood the algorithm right, this means that all the nodes not meeting this level of strength (prominence) have been removed. That is, the strengths of remaining nodes is 80 or greater, but this is the recalculated strength after removal of nodes not meeting this requirment. I mean something simillar to k-core (based on degrees) or s-core (based on strengths) decomposition of the network, which iterativelly removes nodes starting from minimum value recalculating the selected parameter each time a node is removed.

Thank you for your response

Best regards

Drahomír

Thank you for taking an interest in my work, Rodrigo.

You are correct: the x-axis represents the prominence vector (e.g., a value of 20 means that nodes with s >= 20 (if prominence is s) forms the rich-club). The y-axis shows the rich-club coefficient (ratio of the observed and the random) for the select nodes in the rich-club.

Good luck!

Tore

Sorry, I misunderstood the results. I thought that x was the observed phi, when actually I realized that the x is the cutting point of richness, is that correct?

Thank you for letting your work available.

Kind Regards,

Rodrigo

]]>Before all, congratulations by your work. I have read the articles and follow the resourceful blog. It is all really interesting!

I have one doubt about the results of this function. Would each bin be the distribution of prominence? Then, in order to retrieve the level of prominence used in the calculations (s >= prominence) at bin 20, is just necessary to see the limits of the weight distribution of the network at the bin 20, for instance?

Thank you in advance.

Best,

Rodrigo

]]>Hi A.W.Mahesar,

Thanks for taking an interest in my work. How is the prominence-object defined? It needs to be a single character that is either “k” or “s” for binary degree or weighted degree, respectively. See code example above.

Hope this helps,

Tore

Kindly if possible can you please tell me why I’m getting this error when I’m finding rich club effect on my data set.

weighted_richclub_w(ProjectedStates,prominence)

Error in weighted_richclub_w(ProjectedStates, prominence) :

The rich-parameter is not properly specified; only k and s.

In addition: Warning messages:

1: In if (rich == “k”) { :

the condition has length > 1 and only the first element will be used

2: In if (rich == “s”) { :

the condition has length > 1 and only the first element will be used

Further, when I apply weighted_richclub_tm on my 2mode network it is not giving appropriate results.

I’ll remain thankful for your concern.

Kind regards

A.W.Mahesar

]]>Rose,

You can use degree_w to find the distribution of your prominence metric, and then calculate the distribution.

Hope this helps,

Tore

So i know that as x value increases a smaller set of agents are included in that club and then the y value represents average value. There are 30 rows in the output. But how do i restrict to a percentile of nodes only? Thanks for clarifying.

]]>Hi Rose,

All the numbers in the diagrams are scores for the whole network, but at various cut-off of defining prominence. You could look at a percentile of nodes (e.g., only the top 10% are prominent / rich).

Best,

Tore

Hi David,

Are you using 100 or more random networks? I think I set confidence ranges only to be computed for 100+ random networks — perhaps the values should be set to NA instead when the sample is small.

Best,

Tore

OK, I had wondered about the 95% CIs as mine are all 0:

x y l99 l95 h95 h99

1 0.999990 1.000000 0 0 0 0

2 1.117379 1.078395 0 0 0 0

3 1.248549 1.078395 0 0 0 0

4 1.395117 1.078395 0 0 0 0

5 1.558890 1.078395 0 0 0 0

6 1.741889 1.078395 0 0 0 0

7 1.946370 1.078395 0 0 0 0

8 2.174856 1.175318 0 0 0 0

9 2.430163 1.175318 0 0 0 0

10 2.715441 1.175318 0 0 0 0

11 3.034208 1.205826 0 0 0 0

12 3.390395 1.205826 0 0 0 0

13 3.788396 1.205826 0 0 0 0

14 4.233117 1.245198 0 0 0 0

15 4.730045 1.245198 0 0 0 0

16 5.285307 1.411366 0 0 0 0

17 5.905752 1.411366 0 0 0 0

18 6.599031 1.411366 0 0 0 0

19 7.373695 1.479959 0 0 0 0

20 8.239296 1.479959 0 0 0 0

21 9.206511 1.545667 0 0 0 0

22 10.287268 1.545667 0 0 0 0

23 11.494896 1.545667 0 0 0 0

24 12.844287 1.598236 0 0 0 0

25 14.352084 1.598236 0 0 0 0

26 16.036883 1.871658 0 0 0 0

27 17.919460 1.886792 0 0 0 0

28 20.023034 2.649007 0 0 0 0

29 22.373548 2.649007 0 0 0 0

30 24.999990 2.649007 0 0 0 0

Does that mean there CIs have no size?

David

]]>Hi David,

The average value is present in the y-column, and the confidence intervals are listed. However, there are no direct way to get all the scores out. If you look into the weighted_richclub_w-function, the rphi-object contains the scores. Altering the function to return/save this object would enable you to make the histograms on this page.

Best,

Tore

How do you extract the values for the random networks from the weighted_richclub_w function?

Cheers,

David

]]>Apologies. There was a spelling mistake (now corrected). Node F has no choice in shifting its attention between prominent and non-prominent nodes, and as such, gets a score of 1.

]]>