Normalized collaboration network
- Three collaboration networks
- Coupling and co-citation
  - Test

Normalized collaboration network

Three collaboration networks

In analysis of collaboration we consider only works with information of all contributing authors - in the DC partition they belong to class 1.

Co1 = t(WA) * WA
n(WA) = diag(1/w) * WA
Co2 = t(WA) * n(WA)
Co3 = t(n(WA)) * n(WA)

Extracting the subnetwork with works of DC-class 1

read the WA network
Network/Create New Network/Transform/Remove/Multiple Lines/Single Line
read DC partition
Partition/Create Constant Partition [75930][2]
select the constant partition as Second
select the DC partition as First
Partitions/Fuse Partitions
Operations/Network+Partition/Extract SubNetwork [Yes][1,2]

Normalization

Network/Create Vector/Centrality/Degree/Output
Network/2-Mode Network/Partition into 2 Modes
Operations/Vector+Partition/Extract Subvector [1]
Vector/Transform/Invert
Operations/Network+Vector/Vector#Network/Output
File/Network/Change Label [Normalized]
File/Vector/Dispose [Yes]
File/Vector/Dispose [Yes]
File/Vector/Change Label [# of authors]

Collaboration 1

select the WA network
Network/2-Mode Network/2-Mode to 1-Mode/Columns
File/Network/Change Label [Collaboration 1]

Collaboration 2

select the WA network as First
select the Normalized network as Second
Network/2-Mode Network/Transpose 2-Mode
Networks/Multiply Networks [Yes]
File/Network/Change Label [Collaboration 2]
select the Transpose network
File/Network/Dispose [Yes]

Collaboration 3

select the Normalized network
Network/2-Mode Network/2-Mode to 1-Mode/Columns
File/Network/Change Label [Collaboration 3]

Self-contribution, Total # of works, Collaborativeness

select the Collaboration 2 network
Network/Create Vector/Get Loops
File/Vector/Change Label [self-contribution]
select the WA network
Network/Create Vector/Centrality/Degree/Input
select the 2-Mode partition
Operations/Vector+Partition/Extract SubVector [2]
File/Vector/Change Label [author's total # of works]
select the self-contribution vector as First
select the author's total vector as Second
Vectors/Divide (First/Second)
File/Vector/Change Label [self-sufficiency]
select the Collaboration 2 network
Vector/Create Constant Vector [OK]
select the self-sufficiency vector as Second
Vectors/Subtract (First-Second)
File/Vector/Change Label [collaborativeness]
select the self-contribution vector
Vector/Make Permutation
Permutation/Mirror Permutation
Operations/Network+Permutation/Reorder Network
File/Network/Change Label [Reordered Collaboration 2]
Operations/Vector+Permutation/Reorder Vector
File/Vector/Change Label [Ordered self-contribution]
select the author's total vector 
Operations/Vector+Permutation/Reorder Vector
File/Vector/Change Label [Ordered total]
select the collaborativeness vector 
Operations/Vector+Permutation/Reorder Vector
File/Vector/Change Label [Ordered collaborativness]

normal.mcr, collaboration.mcr, biblio.zip

Don't forget to sort lines of line values.

k-cores in Collaboration 1 network

select the Collaboration 1 network
Network/Create Partition/k-Core/All
info button: k-core distribution
Operations/Network+Partition/Extract SubNetwork [20-*]
Network/Create New Network/Transform/Sort Lines/Line Values/Ascending
Network/Create Vector/Centrality/Degree/All
Vector/Create Constant Vector [OK]
Operations/Network+Vector/Network*Vector [1]
select the Degree vector as Second
Vectors/Subtract (First-Second)
Vector/Make Partition/by Intervals/Selected Thresholds [0.5]
Partition/Make Cluster/Vertices from selected Cluster [2]
select the Extracting ... partition
Draw/Network+First Partition
Options/Mark Vertices Using/Mark Cluster Only [On]

pS-cores in Collaboration 1 network

select the Collaboration 1 network
Network/Create Vector/Generalized Core/Sum/Input
info button: pS-core distribution
Vector/Make Partition/by Intervals/Selected Thresholds [20]
Operations/Network+Partition/Extract SubNetwork [2]
Network/Create New Network/Transform/Sort Lines/Line Values/Ascending
Network/Create New Network/with Bi-Connected Components ...
Network/Create Vector/Centrality/Degree/All
Vector/Create Constant Vector [OK]
Operations/Network+Vector/Network*Vector [1]
select the Degree vector as Second
Vectors/Subtract (First-Second)
Vector/Make Partition/by Intervals/Selected Thresholds [0.5]
Partition/Make Cluster/Vertices from selected Cluster [2]
select the Bi-Components partition
Draw/Network+First Partition
Options/Mark Vertices Using/Mark Cluster Only [On]

pS-cores in Collaboration 3 network

select the Collaboration 3 network
Network/Create New Network/Transform/Remove/Loops [Yes]
Network/Create Vector/Generalized Core/Sum/Input
Vector/Make Partition/by Intervals/Selected Thresholds [1]
Network/Create New Network/Transform/Sort Lines/Line Values/Ascending
Operations/Network+Partition/Extract SubNetwork [2]
Draw

Coupling and co-citation

Normalized bibliographic coupling network

We first

read the citation network

The corresponding normalized bibliographic coupling network can be determined with:

Network/Create Vector/Centrality/Degree/Output                         outdeg
Vector/Create Constant Vector [n,1] [OK]                               1
select the Output degree vector as the Second vector
Vectors/Max(First,Second)                                              d = max(1,outdeg)
Vector/Transform/Invert                                                D = 1/d
Network/Create New Network/Transform/Transpose 1-Mode [Yes]            t(Cite)
select the original citation network as the First network
select the transposed citation network as the Second network
Networks/Multiply Networks                                             biCo = Cite*t(Cite)
Operations/Network+Vector/Vector#Network/Output                        biC  = D*biCo
File/Network/Change Label [biC]

Network/Create New Network/Transform/Remove/Loops [No]
Network/Create New Network/Transform/Line Values/Power [-1]            1/biC
Network/Create New Network/Transform/Arcs->Edges/Bidirected Only/Sum Values [No]
Network/Create New Network/Transform/Line Values/Add constant [-1]     
Network/Create New Network/Transform/Line Values/Power [-1]            Jaccard = 1/(sum - 1)
File/Network/Change Label [Jaccard]

These commands are stored in macro normBibCoupling.

Trace of computing Jaccard in SN17

Normalized co-citation network

The corresponding normalized co-citation network could be obtained using the relation

coCin(N) = biCon(N^T)

by applying normBibCoupling macro on the transpose of citation network.

Directly it can be determined with the following commands. The first part is the same as for the normalized bibliographic coupling network:

Network/Create New Network/Transform/Transpose 1-Mode [Yes]
select the original citation network as the First network
Network/Create Vector/Centrality/Degree/Output
Vector/Create Constant Vector [n,1] [OK]
select the Output degree vector as the Second vector
Vectors/Max(First,Second)
Vector/Transform/Invert
Operations/Network+Vector/Vector#Network/Output
File/Network/Change Label [Normalized network]

now we have to change the order of networks in the product

select the transpose of citation network as the First network
select the Normalized network as the Second network
Networks/Multiply Networks
Network/Create New Network/Transform/Arcs->Edges/Bidirected Only/Sum Values [Yes]
Network/Create New Network/Transform/Remove/Loops [No]
Network/Create New Network/Transform/Line Values/Multiply by [0.5]
File/Network/Change Label [Normalized co-citation network]

These commands are stored in macro normCoCitation.

Note: In these computations some auxiliary networks and vectors are produced. They can be disposed.

Test

biCo

         1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22  Label
-----------------------------------------------------------------------------------
   1.    2  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  a
   2.    .  4  3  2  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  b
   3.    .  3  6  4  .  1  2  .  1  .  .  .  .  .  .  .  .  .  .  .  .  .  c
   4.    .  2  4  4  .  .  1  .  1  .  .  .  .  .  .  .  .  .  .  .  .  .  d
   5.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  e
   6.    .  .  1  .  .  3  2  .  1  .  .  .  .  .  .  .  .  .  .  .  .  .  f
   7.    .  .  2  1  .  2  5  1  4  .  .  .  .  .  .  .  .  .  .  .  .  .  g
   8.    .  .  .  .  .  .  1  2  2  .  .  .  .  .  .  .  .  .  .  .  .  .  h
   9.    .  .  1  1  .  1  4  2  6  .  .  .  .  .  .  .  .  .  .  .  .  .  i
  10.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  j
  11.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  k
  12.    .  .  .  .  .  .  .  .  .  .  .  1  .  .  .  .  .  .  .  .  .  .  l
  13.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  m
  14.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  n
  15.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  o
  16.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  p
  17.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  r
  18.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  1  .  .  .  s
  19.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  2  .  .  .  t
  20.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  u
  21.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  v
  22.    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  z

A, B	A∩B	A∪B	biCo[A,B]	Jaccard[A,B]
b, d	g, h	e, f, g, h, i, m	2	2/6 = 0.33
c, d	g, h, i, m	f, g, h, i, k, m	4	4/6 = 0.67
c, g	k, m	f, g, h, i, k, l, m, n, o	2	2/9 = 0.22
g, i	l, m, n, o	k, l, m, n, o, p, r	4	4/7 = 0.57
s, t	u	u, v	1	1/2 = 0.50

Jaccard

         1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17   18   19   20   21   22  Label
--------------------------------------------------------------------------------------------------------------------------
   1.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    a
   2.    .    .    .43  .33  .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    b
   3.    .    .43  .    .67  .    .13  .22  .    .09  .    .    .    .    .    .    .    .    .    .    .    .    .    c
   4.    .    .33  .67  .    .    .    .13  .    .11  .    .    .    .    .    .    .    .    .    .    .    .    .    d
   5.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    e
   6.    .    .    .13  .    .    .    .33  .    .13  .    .    .    .    .    .    .    .    .    .    .    .    .    f
   7.    .    .    .22  .13  .    .33  .    .17  .57  .    .    .    .    .    .    .    .    .    .    .    .    .    g
   8.    .    .    .    .    .    .    .17  .    .33  .    .    .    .    .    .    .    .    .    .    .    .    .    h
   9.    .    .    .09  .11  .    .13  .57  .33  .    .    .    .    .    .    .    .    .    .    .    .    .    .    i
  10.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    j
  11.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    k
  12.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    l
  13.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    m
  14.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    n
  15.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    o
  16.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    p
  17.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    r
  18.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .50  .    .    .    s
  19.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .50  .    .    .    .    t
  20.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    u
  21.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    v
  22.    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    z

Networks from allcitiesV4.net (16M).