Definition of `e_weight` leads to incorrect values of `v_reg_sum`

[yinyee]

In line 366, the values of e_weight are set to (1/w if w>0 else 1) for w in authorwt. Why?

Assuming that the w values in authorwt correspond to edge degrees, it seems to lead to an incorrect computation of v_reg_sum.

Using this hypergraph as an example:

(Changing the indices from 1-based to 0-based)

authorwt = [ 2 , 4 , 1 ]

paper_author[0] = [ 0 , 0 ]
paper_author[1] = [ 1 , 0 ]
paper_author[2] = [ 1 , 1 ]
paper_author[3] = [ 2 , 1 ]
paper_author[4] = [ 3 , 1 ]
paper_author[5] = [ 3 , 2 ]
paper_author[6] = [ 4 , 1 ]

Following line 366

e_weight[0] = 0.5
e_weight[1] = 0.25
e_weight[2] = 1

Assuming alpha_v = 1, the results of line 382 should be:

e_reg_weight[0] = 0.5
e_reg_weight[1] = 0.5
e_reg_weight[2] = 0.25
e_reg_weight[3] = 0.25
e_reg_weight[4] = 0.25
e_reg_weight[5] = 1
e_reg_weight[6] = 0.25

And paper2sum in line 383 should be:

paper2sum[0] = [0.5]
paper2sum[1] = [0.5, 0.25]
paper2sum[2] = [0.25]
paper2sum[3] = [0.25, 1]
paper2sum[4] = [0.25]

Then in line 393, v_reg_sum should be:

v_reg_sum[0] = 0.5
v_reg_sum[1] = 0.75
v_reg_sum[2] = 0.25
v_reg_sum[3] = 1.25
v_reg_sum[4] = 0.25

But according to the definition of the normalisation denominator in the the paper:

the denominator matrix should be:

     [0]   [1]   [2]   [3]   [4]
[0]   2     0     0     0     0
[1]   0     2+4   0     0     0
[2]   0     0     4     0     0
[3]   0     0     0     4+1   0
[4]   0     0     0     0     4

By setting the values of e_weight in line 366 to w instead, we get:

e_weight[0] = 2
e_weight[1] = 4
e_weight[2] = 1

Then the results of line 382 should become:

e_reg_weight[0] = 2
e_reg_weight[1] = 2
e_reg_weight[2] = 4
e_reg_weight[3] = 4
e_reg_weight[4] = 4
e_reg_weight[5] = 1
e_reg_weight[6] = 4

And paper2sum in line 383 should become:

paper2sum[0] = [2]
paper2sum[1] = [2, 4]
paper2sum[2] = [4]
paper2sum[3] = [4, 1]
paper2sum[4] = [4]

Then in line 393, v_reg_sum should be:

v_reg_sum[0] = 2
v_reg_sum[1] = 6
v_reg_sum[2] = 4
v_reg_sum[3] = 5
v_reg_sum[4] = 4

which corresponds to the definition given in the paper. Ditto for v_weight and e_reg_sum.