WKl
Multiplying KK = t(WK)*WK we get a symmetrical directed network. KK[i,j] = KK[j,i]. Both values are equal to the number of co-appearances of keywords i and j. In transformation arcs -> edges we select MIN.
In KK'' = t(n(WK))*n(WK), the meaning of KK''[i,j] is the fractional contribution of i to j. In transformation arcs -> edges we select SUM.
==============================================================================
Info on 2-Mode Network 1. C:\Mail.Ru Cloud\ANR HSE\ANR Projects\SNA Vlado Batagelj\Comparison\LietzSN\WKl.net [2-Mode] (48787)
==============================================================================
Number of vertices (n): 48787
----------------------------------------------------------
Arcs Edges
----------------------------------------------------------
Total number of lines 202181 0
----------------------------------------------------------
Number of loops 0 0
Number of multiple lines 0 0
----------------------------------------------------------
2-Mode Network: Rows=25760, Cols=23027
Density [2-Mode] = 0.00034085
Average Degree = 8.28831451
Indegree
==============================================================================
9. Input Degree of N1 (48787)
==============================================================================
Dimension: 48787
The lowest value: 0.0000
The highest value: 3091.0000
Highest values:
Rank Vertex Value Id
--------------------------------------------------------
1 28832 3091.0000 COMMUNITY
2 47810 2806.0000 USER
3 44894 2239.0000 SOCIAL_NETWORK_ANALYSIS
4 44532 1681.0000 SOCIAL_CAPITAL
5 33154 1598.0000 FRIEND
6 45181 1452.0000 SOCIAL_SUPPORT
7 35952 1310.0000 INTERNET
8 40285 1185.0000 OPPORTUNITY
9 47381 1170.0000 TRUST
10 48304 993.0000 WEB
11 44787 940.0000 SOCIAL_INTERACTION
12 40381 908.0000 ORGANIZATIONAL
13 35422 872.0000 INNOVATION
14 28519 848.0000 COLLABORATION
15 39497 824.0000 NETWORK_STRUCTURE
16 32319 742.0000 EVOLVE
17 32521 738.0000 FACEBOOK
18 26967 733.0000 AVERAGE
19 29612 728.0000 COOPERATION
20 47962 728.0000 VARIETY_OF
21 29077 715.0000 COMPLEX_NETWORK
22 45092 679.0000 SOCIAL_RELATIONSHIP
23 44991 650.0000 SOCIAL_NETWORK_SITE
24 45173 649.0000 SOCIAL_STRUCTURE
25 33170 613.0000 FRIENDSHIP
26 39215 611.0000 NETWORK_ANALYSIS
27 40487 599.0000 ORGANIZE
28 40134 598.0000 ONLINE_SOCIAL_NETWORK
29 25761 573.0000
30 27912 555.0000 CENTRALITY
--------------------------------------------------------
Sum (all values): 202181.0000
WKl
Transpose, choose as 1st netw
WKl - choose as 2nd
Multiply
KK
==============================================================================
3. Multiplying N2 * N1 [1-Mode] (23027)
==============================================================================
Number of vertices (n): 23027
----------------------------------------------------------
Arcs Edges
----------------------------------------------------------
Number of lines with value=1 998879 0
Number of lines with value#1 230216 0
----------------------------------------------------------
Total number of lines 1229095 0
----------------------------------------------------------
Number of loops 23027 0
Number of multiple lines 0 0
----------------------------------------------------------
Density [loops allowed] = 0.00231799
Average Degree = 106.75250793
Loops are the same as WK indegree
Arcs to Edges -- Bidirected only, MIN -- Remove loops
KK_regL
Reduction: Look at line values
==============================================================================
5. KK_regL (23027)
==============================================================================
Lowest value of line: 1.00000000
Highest value of line: 434.00000000
Line Values Frequency Freq% CumFreq CumFreq%
---------------------------------------------------------------------------------------------------
( ... 1.0000] 494109 81.9372 494109 81.9372
( 1.0000 ... 23.7895] 107527 17.8310 601636 99.7682
( 23.7895 ... 46.5790] 1005 0.1667 602641 99.9348
( 46.5790 ... 69.3684] 210 0.0348 602851 99.9697
( 69.3684 ... 92.1579] 85 0.0141 602936 99.9837
( 92.1579 ... 114.9474] 34 0.0056 602970 99.9894
( 114.9474 ... 137.7368] 20 0.0033 602990 99.9927
( 137.7368 ... 160.5263] 10 0.0017 603000 99.9944
( 160.5263 ... 183.3158] 10 0.0017 603010 99.9960
( 183.3158 ... 206.1053] 5 0.0008 603015 99.9968
( 206.1053 ... 228.8947] 4 0.0007 603019 99.9975
( 228.8947 ... 251.6842] 5 0.0008 603024 99.9983
( 251.6842 ... 274.4737] 0 0.0000 603024 99.9983
( 274.4737 ... 297.2632] 0 0.0000 603024 99.9983
( 297.2632 ... 320.0526] 3 0.0005 603027 99.9988
( 320.0526 ... 342.8421] 3 0.0005 603030 99.9993
( 342.8421 ... 365.6316] 1 0.0002 603031 99.9995
( 365.6316 ... 388.4211] 1 0.0002 603032 99.9997
( 388.4211 ... 411.2105] 0 0.0000 603032 99.9997
( 411.2105 ... 434.0000] 2 0.0003 603034 100.0000
---------------------------------------------------------------------------------------------------
Total 603034 100.0000
Remove lines with values lower then (70)
Got the network of 87 nodes
Islands [2, 100]
Got 135 islands
==============================================================================
15. Canonized [Decreasing frequencies] C14 (23027)
==============================================================================
Dimension: 23027
The lowest value: 0
The highest value: 135
Frequency distribution of cluster values:
Cluster Freq Freq% CumFreq CumFreq% Representative
----------------------------------------------------------------
0 22627 98.2629 22627 98.2629
1 100 0.4343 22727 98.6972 ACQUAINTANCE
2 7 0.0304 22734 98.7276 ACETYL_CHOLINE_ESTERASE
3 5 0.0217 22739 98.7493 BRIDGE_DECK
4 4 0.0174 22743 98.7667 HEADQUARTERS
5 4 0.0174 22747 98.7840 GAP_OF2SUBSPACE
6 4 0.0174 22751 98.8014 ACYLASE_LIPASE
7 4 0.0174 22755 98.8188 ATRIAL_FIBRILLATION
8 4 0.0174 22759 98.8361 COMPLETE_RESIDUATED_LATTICE
9 4 0.0174 22763 98.8535 CHAIN_REFERRAL_SAMPLE
10 3 0.0130 22766 98.8665 DIRECT&INDIRECT_TIE
11 3 0.0130 22769 98.8796 GIDDEN
12 3 0.0130 22772 98.8926 DUP
13 3 0.0130 22775 98.9056 COMPLETE_INFLUENCE
14 3 0.0130 22778 98.9187 CORPORATE_SOCIAL_RESPONSIBILITY
15 3 0.0130 22781 98.9317 AEROASSISTED_SPACE_RENDEZVOUS
16 3 0.0130 22784 98.9447 AZEOTROPE
17 3 0.0130 22787 98.9577 INJECTION_DRUG_USE
18 3 0.0130 22790 98.9708 DELAY_TOLERANT_NETWORK
19 3 0.0130 22793 98.9838 ACTOR_NETWORK
20 3 0.0130 22796 98.9968 CANDECOMP
21 3 0.0130 22799 99.0099 BURNE_MOUTH_DISORDER
Others are pairs
Main island = 100 nodes
Other islands > 2 = 72 nodes
WK.net
Play macro norm2.mcr (25,760) - Normalized network
Normalized network -- Transpose 2-mode
Transposed normalized as first
Normalized as second
Multiply networks
==============================================================================
13. Multiplying N12 * N11 [1-Mode] (23027)
==============================================================================
Number of vertices (n): 23027
----------------------------------------------------------
Arcs Edges
----------------------------------------------------------
Number of lines with value=1 11 0
Number of lines with value#1 1229084 0
----------------------------------------------------------
Total number of lines 1229095 0
----------------------------------------------------------
Number of loops 23027 0
Number of multiple lines 0 0
----------------------------------------------------------
Density [loops allowed] = 0.00231799
Average Degree = 106.75250793
Arcs to Edges -- Bidirected only, MIN
KKnorm network
Get Loops + 30
==============================================================================
10. Loops from N14 (23027)
==============================================================================
Dimension: 23027
The lowest value: 0.0012
The highest value: 573.0000
Highest values:
Rank Vertex Value Id
--------------------------------------------------------
1 1 573.0000
2 19421 163.0826 SOCIAL_SUPPORT
3 19134 105.6536 SOCIAL_NETWORK_ANALYSIS
4 3072 73.7967 COMMUNITY
5 18772 50.1255 SOCIAL_CAPITAL
6 7394 45.9935 FRIEND
7 22050 43.5851 USER
8 19413 35.8713 SOCIAL_STRUCTURE
9 2152 27.3791 CENTRALITY
10 9662 26.0541 INNOVATION
11 21621 25.9971 TRUST
12 14621 25.7954 ORGANIZATIONAL
13 19332 25.7138 SOCIAL_RELATIONSHIP
14 19027 24.8978 SOCIAL_INTERACTION
15 14525 23.4166 OPPORTUNITY
16 10192 22.8595 INTERNET
17 13737 21.7220 NETWORK_STRUCTURE
18 1207 21.2707 AVERAGE
19 7410 19.9492 FRIENDSHIP
20 19426 19.3222 SOCIAL_SUPPORT_NETWORK
21 22544 18.9125 WEB
22 11604 17.5033 LONELINESS
23 13455 16.9493 NETWORK_ANALYSIS
24 19328 16.8651 SOCIAL_RELATION
25 3317 16.6638 COMPLEX_NETWORK
26 19359 16.2166 SOCIAL_SCIENCE
27 19453 15.7832 SOCIAL_TIE
28 22202 14.6690 VARIETY_OF
29 3544 14.5803 CONNECTIVITY
30 3852 13.9333 COOPERATION
--------------------------------------------------------
Sum (all values): 5524.7835
Remove loops
KK_normL
Reduction: Line values
==============================================================================
15. KK_normL (23027)
==============================================================================
Lowest value of line: 0.00104058
Highest value of line: 5.58040447
Line Values Frequency Freq% CumFreq CumFreq%
---------------------------------------------------------------------------------------------------
( ... 0.0010] 0 0.0000 0 0.0000
( 0.0010 ... 0.2947] 601598 99.7619 601598 99.7619
( 0.2947 ... 0.5883] 1046 0.1735 602644 99.9353
( 0.5883 ... 0.8820] 209 0.0347 602853 99.9700
( 0.8820 ... 1.1756] 96 0.0159 602949 99.9859
( 1.1756 ... 1.4693] 33 0.0055 602982 99.9914
( 1.4693 ... 1.7629] 12 0.0020 602994 99.9934
( 1.7629 ... 2.0566] 5 0.0008 602999 99.9942
( 2.0566 ... 2.3503] 14 0.0023 603013 99.9965
( 2.3503 ... 2.6439] 4 0.0007 603017 99.9972
( 2.6439 ... 2.9376] 1 0.0002 603018 99.9973
( 2.9376 ... 3.2312] 4 0.0007 603022 99.9980
( 3.2312 ... 3.5249] 4 0.0007 603026 99.9987
( 3.5249 ... 3.8185] 1 0.0002 603027 99.9988
( 3.8185 ... 4.1122] 2 0.0003 603029 99.9992
( 4.1122 ... 4.4058] 1 0.0002 603030 99.9993
( 4.4058 ... 4.6995] 0 0.0000 603030 99.9993
( 4.6995 ... 4.9931] 1 0.0002 603031 99.9995
( 4.9931 ... 5.2867] 2 0.0003 603033 99.9998
( 5.2867 ... 5.5804] 1 0.0002 603034 100.0000
---------------------------------------------------------------------------------------------------
Total 603034 100.0000
Line cut at 1 = 84 nodes
Islands [2, 100] -- 426 islands
Cluster Freq Freq% CumFreq CumFreq% Representative
----------------------------------------------------------------
0 21919 95.1883 21919 95.1883
1 100 0.4343 22019 95.6225 ACQUAINTANCE
2 7 0.0304 22026 95.6529 ACETYL_CHOLINE_ESTERASE
3 5 0.0217 22031 95.6746 DIPTERA
4 5 0.0217 22036 95.6964 JOINT_ATTENTION
5 5 0.0217 22041 95.7181 EXCHANGE_NETWORK
6 5 0.0217 22046 95.7398 CONTEXTUALIZED_RESEARCH
7 5 0.0217 22051 95.7615 ENERGY_INFRASTRUCTURE
8 5 0.0217 22056 95.7832 ATPG
9 5 0.0217 22061 95.8049 BRIDGE_DECK
10 5 0.0217 22066 95.8266 COLLECTIVENESS
11 5 0.0217 22071 95.8484 NEUPAL_NETWOPK
of size 4 -- islands 12-39 of size 3 -- islands 40-109 of size 2 -- islands 100-426
Main island = 100 nodes
Multiplied networks
Arcs to Edges -- Bidirected only -- SUM
Get loops -- Loops are the same
Remove loops
KK_normLsum
Reduction: Line values
==============================================================================
33. KK_normLsum (23027)
==============================================================================
Lowest value of line: 0.00208117
Highest value of line: 11.16080895
Line Values Frequency Freq% CumFreq CumFreq%
---------------------------------------------------------------------------------------------------
( ... 0.0021] 0 0.0000 0 0.0000
( 0.0021 ... 0.3869] 599706 99.4481 599706 99.4481
( 0.3869 ... 0.7717] 2464 0.4086 602170 99.8567
( 0.7717 ... 1.1564] 454 0.0753 602624 99.9320
( 1.1564 ... 1.5412] 175 0.0290 602799 99.9610
( 1.5412 ... 1.9260] 93 0.0154 602892 99.9765
( 1.9260 ... 2.3108] 53 0.0088 602945 99.9852
( 2.3108 ... 2.6956] 27 0.0045 602972 99.9897
( 2.6956 ... 3.0804] 15 0.0025 602987 99.9922
( 3.0804 ... 3.4651] 6 0.0010 602993 99.9932
( 3.4651 ... 3.8499] 3 0.0005 602996 99.9937
( 3.8499 ... 4.2347] 6 0.0010 603002 99.9947
( 4.2347 ... 4.6195] 11 0.0018 603013 99.9965
( 4.6195 ... 5.0043] 2 0.0003 603015 99.9968
( 5.0043 ... 5.3891] 3 0.0005 603018 99.9973
( 5.3891 ... 5.7738] 0 0.0000 603018 99.9973
( 5.7738 ... 6.1586] 1 0.0002 603019 99.9975
( 6.1586 ... 6.5434] 5 0.0008 603024 99.9983
( 6.5434 ... 6.9282] 2 0.0003 603026 99.9987
( 6.9282 ... 7.3130] 1 0.0002 603027 99.9988
( 7.3130 ... 7.6978] 0 0.0000 603027 99.9988
( 7.6978 ... 8.0825] 2 0.0003 603029 99.9992
( 8.0825 ... 8.4673] 0 0.0000 603029 99.9992
( 8.4673 ... 8.8521] 1 0.0002 603030 99.9993
( 8.8521 ... 9.2369] 0 0.0000 603030 99.9993
( 9.2369 ... 9.6217] 1 0.0002 603031 99.9995
( 9.6217 ... 10.0065] 0 0.0000 603031 99.9995
( 10.0065 ... 10.3912] 2 0.0003 603033 99.9998
( 10.3912 ... 10.7760] 0 0.0000 603033 99.9998
( 10.7760 ... 11.1608] 1 0.0002 603034 100.0000
---------------------------------------------------------------------------------------------------
Total 603034 100.0000
Line cut at 2 = 84 nodes
The pictures is the same to the previous link cut result, saved as KK_normLsum_LineCut(84nodes).net
Islands [2,100] = 426 islands:
1 100 0.4343 22019 95.6225 ACQUAINTANCE
2 7 0.0304 22026 95.6529 ACETYL_CHOLINE_ESTERASE
3 5 0.0217 22031 95.6746 DIPTERA
4 5 0.0217 22036 95.6964 JOINT_ATTENTION
5 5 0.0217 22041 95.7181 EXCHANGE_NETWORK
6 5 0.0217 22046 95.7398 CONTEXTUALIZED_RESEARCH
7 5 0.0217 22051 95.7615 ENERGY_INFRASTRUCTURE
8 5 0.0217 22056 95.7832 ATPG
9 5 0.0217 22061 95.8049 BRIDGE_DECK
10 5 0.0217 22066 95.8266 COLLECTIVENESS
11 5 0.0217 22071 95.8484 NEUPAL_NETWOPK
The result is the same as with MIN weights. Saved KK_normLsum_MainIsland.net.
All the substructures obtained by the link cut and islands are very similar to each other. The topics which appear are: social networking sites (+users, internet, web, social media), social capital, social support, communities, social network analysis itself, complex networks, small world. Actor-network theory appears separately.