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***** To join INSNA, visit http://www.insna.org ***** In a previous appeal to the Pajek list, I tried to verbally describe the following problem. Not, in retrospect, a good idea. What follows is the printout of a Pajek session in which (1) I import a 2-mode network created from an edge list with 1824 actors (creators) and 3 events (agencies) and use Net>Components>Bi-Components to isolate the articulation points. The question I am trying to answer is how many creators work on projects for more than one agency.  The result is 184 creators plus 3 agencies. Then (2) I import a 2-mode network created from an edge list with 1824 creators and 663 ads and an extended partition containing four clusters, 3 agency attributes and a constant for the creators. When I use Operations>Shrink Network>Partition to shrink the network, leaving only the creators cluster unshrunk, the result is a network with 1827 vertices=1824 creators+3 vertices representing the clusters of ads corresponding to the three ad attributes. Looks at first glance like the network described in (1). But when I try Net>Components>Bi-Components on this network, the result is radically different from (1), with 655 vertices identified as articulation points, only two of them agency clusters. Why this difference? All this is spelled out in more detail in the Pajek session report appended below.

I will be deeply grateful to anyone who can explain to me the algorithmic, mathematical or idiot-mistake reasons why the results of the two procedures differ.

John

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Reading Network   ---    Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\Creator Agency FM96.net

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 Working...

           7071 lines read.

 Time spent:  12:00:00 AM


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1. Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\Creator Agency FM96.net [2-Mode] (1827)<-exported directly from database as edgelist of creators (1824) and agencies (3).

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Number of vertices (n): 1827

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                                       Arcs          Edges

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Number of lines with value=1              0            831

Number of lines with value#1              0           4411

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Total number of lines                     0           5242

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Number of loops                           0              0

Number of multiple lines                  0           3210

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Density1 [loops allowed] = 0.00314087

Density2 [no loops allowed] = 0.00314259

Average Degree = 5.73836891


2-Mode Network: Rows=1824, Cols=3

                Density [2-Mode] = 0.95796784



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Removing multiple lines

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 Working...

 100.00% finished.

 Time spent:  12:00:00 AM


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Biconnected Components

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 Time spent:  12:00:00 AM

 Partition of lines according to biconnected components stored as a Multiple Relation Network.


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2. Articulation points in N2 (1827)

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Dimension: 1827

The lowest value:  0

The highest value: 1


Frequency distribution of cluster values:


   Cluster      Freq     Freq%   CumFreq  CumFreq% Representative

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         0      1640   89.7646      1640   89.7646 Ada1317

         1       187   10.2354      1827  100.0000 Oka258

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       Sum      1827  100.0000 


Note: The 187 articulation points include 184 creators and 3 agencies (Dentsu, Hakuhodo, Other)



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Reading Network   ---    Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\CreatorsAdsRoles96[Single Line].net

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 Working...

           6879 lines read.

 Time spent:  12:00:00 AM


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Reading Partition   ---    Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\Agency Partition 96.clu

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 Time spent:  12:00:00 AM


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3. Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\Agency Partition 96.clu (663)

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Dimension: 663

The lowest value:  1

The highest value: 4


Frequency distribution of cluster values:


   Cluster      Freq     Freq%   CumFreq  CumFreq% Representative

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         1       245   36.9532       245   36.9532         1

         2       128   19.3062       373   56.2594        12

         4       290   43.7406       663  100.0000         3

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       Sum       663  100.0000


Note: Partition contains three agency clusters (Agency No. 3 is ADK, which does not appear in the data until 2001).



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4. Y:\Documents\Magic Briefcase\Winner's Circles\NetworksRevisedNov2011\CAR96\CreatorsAdsRoles96[Single Line].net [2-Mode] (2487)

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Number of vertices (n): 2487

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                                       Arcs          Edges

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Total number of lines                     0           4390

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Number of loops                           0              0

Number of multiple lines                  0              0

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Density1 [loops allowed] = 0.00141952

Density2 [no loops allowed] = 0.00142010

Average Degree = 3.53035786


2-Mode Network: Rows=1824, Cols=663

                Density [2-Mode] = 0.00363016


Note: Simplified 2-mode network contains 1824 creators (rows) and 663 ads (columns).



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Shrinking

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 Working...

 100.00% shrinking lines finished.    Time spent: 12:00:00 AM

 100.00% shrinking vertices finished. Time spent: 12:00:00 AM

 Time spent:  12:00:00 AM


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6. Shrinking C5 [0] (1827)

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Dimension: 1827

The lowest value:  0

The highest value: 4


Frequency distribution of cluster values:


   Cluster      Freq     Freq%   CumFreq  CumFreq% Representative

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         0      1824   99.8358      1824   99.8358 Oka258

         1         1    0.0547      1825   99.8905 #AD1_96

         2         1    0.0547      1826   99.9453 #AD21_96

         4         1    0.0547      1827  100.0000 #AD3_96

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       Sum      1827  100.0000


Note: Following shrinking, the resulting network contains 1827 vertices=1824 creators + 3 representing ad clusters broken down by agency.


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Biconnected Components

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 Time spent:  12:00:00 AM

 Partition of lines according to biconnected components stored as a Multiple Relation Network.


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8. Articulation points in N5 (1827)

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Dimension: 1827

The lowest value:  0

The highest value: 1


Frequency distribution of cluster values:


   Cluster      Freq     Freq%   CumFreq  CumFreq% Representative

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         0      1172   64.1489      1172   64.1489 Mat2737

         1       655   35.8511      1827  100.0000 #AD1_96

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       Sum      1827  100.0000


Note: When, however, Net>Components>Bi-Components is applied to this network, the number of articulation points increases from 187 (184 creators+3 agencies) to 655 (653 creators+2 agency clusters. One agency cluster is not an articulation point. The question that is driving me crazy is why this difference.






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8. Articulation points in N5 (1827)

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Dimension: 1827

The lowest value:  0

The highest value: 3



--
John McCreery
The Word Works, Ltd., Yokohama, JAPAN
Tel. +81-45-314-9324
[log in to unmask]
http://www.wordworks.jp/
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