@jruths Super helpful video! Is it true that in a configuration model, in the large N-limit, all networks with given degree sequence are sampled approximately uniformly?
Thank you for your nice video. I have a question about the probability that two vertices are connected which you give a formula for p_{i,i} = k_i k_j/(2m-1), is it an approximation ? since if i take the degree distribution K = (3,3,1,1) the graph will have 4 edges, and the probability that node 1 and 2 connected is then p_{1,2} = (3 x 3) / 7 > 1, so it is not a probability.. The probability should simply gives 1. Am I mistaken?
Ah - that degree sequence is not graphical - in a 4 node network if you have two nodes with degree 3, the other two nodes need to have at least degree 2 (making m=5). This would make the probability 3*3/(2*5-1) = 9/9.
They are quite similar. This writeup has a nice description of the differences (see page 11): tuvalu.santafe.edu/~aaronc/courses/3352/csci3352_2019_L3.pdf
@jruths Super helpful video! Is it true that in a configuration model, in the large N-limit, all networks with given degree sequence are sampled approximately uniformly?
Thanks for the video. Just, I have a question. Is the expression Sig(k^2*Pk) equal to at the end of the video?
Hello thank you for the video, do you have the psuedocode for this model?
Thank you! It's very helpful
Thank you for your nice video. I have a question about the probability that two vertices are connected which you give a formula for p_{i,i} = k_i k_j/(2m-1), is it an approximation ? since if i take the degree distribution K = (3,3,1,1) the graph will have 4 edges, and the probability that node 1 and 2 connected is then p_{1,2} = (3 x 3) / 7 > 1, so it is not a probability.. The probability should simply gives 1. Am I mistaken?
Ah - that degree sequence is not graphical - in a 4 node network if you have two nodes with degree 3, the other two nodes need to have at least degree 2 (making m=5). This would make the probability 3*3/(2*5-1) = 9/9.
Hi! i have one question, this model is the same that Chung-Lu Model?
They are quite similar. This writeup has a nice description of the differences (see page 11): tuvalu.santafe.edu/~aaronc/courses/3352/csci3352_2019_L3.pdf