Crude, Simple, Effective

Crude, Simple, Effective

Using Pajek to Analyze 2-Mode Networks

John McCreeryThe Word Works, Ltd

INSNA 2013, Xi’an, China

Using Pajek to Analyze 2-Mode Networks

John McCreeryThe Word Works, Ltd

INSNA 2013, Xi’an, China

Assumptions

• 2-mode affiliation networks: actors + events

• Events have attributes

• You are interested in how those attributes shape relations between actors

Example

• Actors are advertising creatives

• Events are project teams that produce award-winning ads

• The logic is generalizable to all 2-mode networks where nodes in one mode can be subdivided by attributes

BackgroundBackground

The Research PlanDATA: Credits from winning ads in the TokyoCopywriters Club Annual

SNA: Explore networks linking members of winning teams

DESK RESEARCH: Books and articles written by or about central figures in the networks

INTERVIEWS: Conversations with central figures using output from SNA and desk research as stimulus material

The Data

3634

22907

7018

Note1: Ad production requires multiple rolesNote 2: Creators may play more than one roleNote 3: Multiple creators may play the same role

Why SNA?

• Explore network structures to see how they changed over time

• Identify industry stars, and

• Track their careers

Why Pajek?

• Freeware

• Exploratory Social Network Analysis with Pajek

• Looked right for what I was trying to do

First Encounter

Stumbling Blocks

• “Techniques for analyzing one-mode networks cannot always be applied to two-mode networks without modification or change of meaning. Special techniques for two-mode networks are very complicated....

• “The solution commonly used...is to change the two-mode network into a one-mode network, which can be analyzed with standard techniques.”

• Inevitably, however, this approach destroys useful information.

For Example• We begin with the combined network that contains data for all

six networks (1981-2006)

• After simplifying the network to remove multiple lines, we click on the info icon (Rows=Creators, Columns=Ads)

==============================================================================1. Z:\Documents\Magic Briefcase\Winner's Circles\NetworksRevised January 2012\CAR81-06\Creator Ads Roles 81-06[Single Line].net [2-Mode] (10652)==============================================================================Number of vertices (n): 10652---------------------------------------------------------- Arcs Edges----------------------------------------------------------Total number of lines 0 22907----------------------------------------------------------Number of loops 0 0Number of multiple lines 0 0----------------------------------------------------------

2-Mode Network: Rows=7018, Cols=3634Density [2-Mode] = 0.00089819Average Degree = 4.30097634

A Giant Component

• Using Network>Create Partition>Components>Weak, we determine that the network contains 94 components, including one giant component that accounts for 95.9% of all nodes.

• This network seems to be highly connected. But the single giant component conceals underlying structures.

• We need to look more deeply.

Crude, Simple, Effective Solutions

• Extended partitions

• Shrinking networks and examining degree distributions

• Using k-neighbor and extended partitions to track and compare careers

Extended PartitionsExtended Partitions

Question

• We know that the Japanese advertising industry is an oligopoly dominated by two giant agencies, Dentsu and Hakuhodo, with ADK No. 3

• How many creators work on projects for more than one agency?

The Agency Partition• My Filemaker Pro database makes it simple to partition the Ads using the

attribute Agency

• When I import that partition and check info, I see that I have a partition with four clusters (1=Dentsu, 2=Hakuhodo, 3=ADK, 4= Other) that covers a total of 3634 nodes.

• When I try to use Operations>Network+Partition>Extract Subnetwork, Pajek generates an error message “Network and Partition of equal size needed.”

==============================================================================1. Z:\Documents\Magic Briefcase\Winner's Circles\NetworksRevised January 2012\CAR81-06\Agencies 81-06.clu (3634)==============================================================================Dimension: 3634The lowest value: 1The highest value: 4

Frequency distribution of cluster values:

Cluster Freq Freq% CumFreq CumFreq% Representative ---------------------------------------------------------------- 1 1187 32.6637 1187 32.6637 1 2 628 17.2812 1815 49.9450 40 3 47 1.2933 1862 51.2383 295 4 1772 48.7617 3634 100.0000 3 ---------------------------------------------------------------- Sum 3634 100.0000

Extending the Partition

• To create a partition of equal size, I begin with Partition>Create Constant Partition, setting the dimension to 7018 (the number of creators) and the constant to 0.

• Then with the constant partition in the first partition field and the agency partition in the second partition field, I use Partitions>Fuse Partition

• I save the extended partition for later use.

==============================================================================3. Fusion of C2 and C1 (10652)==============================================================================Dimension: 10652The lowest value: 0The highest value: 4

Frequency distribution of cluster values:

Cluster Freq Freq% CumFreq CumFreq% Representative ---------------------------------------------------------------- 0 7018 65.8843 7018 65.8843 Nak1 1 1187 11.1434 8205 77.0278 AD1_01 2 628 5.8956 8833 82.9234 AD7_86 3 47 0.4412 8880 83.3646 AD50_01 4 1772 16.6354 10652 100.0000 AD1_81 ---------------------------------------------------------------- Sum 10652 100.0000

Shrinking networks and examining degree

distributions

Shrinking networks and examining degree

distributions

Shrink and Examine Degree• With the simplified network and extended partition as input, I use

Operations>Network+Partition>Shrink Network, leaving the 0 cluster, the creatives, unshrunk

• We know that we are starting with a 2-mode network, in which creators can only be linked directly to ads. Thus, in the shrunk network, creators will have at most four immediate neighbors

• Using Network>Create Partition>Degree>All, we find that of 7018 creators, 5976 have worked for only one agency, 822 for two agencies, 195 for three agencies, and only 25 for four agencies. As an added bonus we can see the total number of creatives who have worked for each of the agencies (our database makes it simple to track down the agency that created the ad whose label is used for the agency cluster)

==============================================================================5. All Degree Partition of N2 (7022)==============================================================================Dimension: 7022The lowest value: 1The highest value: 3362

Frequency distribution of cluster values:

Cluster Freq Freq% CumFreq CumFreq% Representative ---------------------------------------------------------------- 1 5976 85.1040 5976 85.1040 Saw5 2 822 11.7061 6798 96.8100 Nak1 3 195 2.7770 6993 99.5870 Nak190 4 25 0.3560 7018 99.9430 Yag350 230 1 0.0142 7019 99.9573 #AD50_01 1779 1 0.0142 7020 99.9715 #AD7_86 2934 1 0.0142 7021 99.9858 #AD1_01 3362 1 0.0142 7022 100.0000 #AD1_81 ---------------------------------------------------------------- Sum 7022 100.0000

Using k-neighbor and extended partitions to track

and compare careers

Using k-neighbor and extended partitions to track

and compare careers

Largest No. of AdsTable 1. Highest Degree Creators in 2-Mode Network

=Number of Ads in AnnualsRank Vertex Cluster Id1 17 244 Nak1902 3 172 Sas33 56 139 Soe9034 54 126 Aki2645 35 90 Oka2586 311 89 Iwa1017 47 84 Mak658 45 84 Kas909 564 71 Oka116510 48 67 Oos11311 21 67 Ito622612 51 63 Jum19313 770 60 Hos26514 280 59 Miy95215 1 58 Nak116 100 54 Saw817 316 52 Sak11818 773 51 Yos639119 380 50 Nis141520 290 49 Fuj112

Largest No. of Co-WorkersTable 2. Highest Degree Creators in 1-Mode Network

=Ties to Other CreatorsRank Vertex Cluster Id1 3 421 Sas32 17 345 Nak1903 35 332 Oka2584 311 289 Iwa1015 48 254 Oos1136 216 210 Tad277 202 206 Sig2838 54 199 Aki2649 100 198 Saw810 56 173 Soe90311 1706 171 Ter53612 51 169 Jum19313 1573 162 Kim48814 1827 159 Sat59715 78 157 Ish37016 305 157 Ato5117 2446 152 Som103218 339 151 Mr.667219 290 147 Fuj11220 475 146 Kam122

With Pajek

•Read Network

•Read Extended Media Partition

•Network>Create Partition>k-Neighbors

•#Extended Partition first, k-Neighbors partition second

•Partitions>Extract SubPartition (Second from First)

Ads by Media1=TV, 2=Radio,3=Newspaper,4=Magazine,5=Poster, 6=Other

K1, Ads by Media, Nakahata Takashi=====================================================================Dimension: 244

Frequency distribution of cluster values:

Cluster Freq Freq% CumFreq CumFreq% Representative ----------------------------------------------------------------

1 40 16.3934 40 16.3934 7 2 2 0.8197 42 17.2131 189 3 92 37.7049 134 54.9180 1 4 36 14.7541 170 69.6721 28 5 68 27.8689 238 97.5410 2 6 6 2.4590 244 100.0000 39 ---------------------------------------------------------------- Sum 244 100.0000

K1, Ads by Media, Sasaki Hiroshi=====================================================================Dimension: 172

Frequency distribution of cluster values:

Cluster Freq Freq% CumFreq CumFreq% Representative ---------------------------------------------------------------- 1 67 38.9535 67 38.9535 2 2 6 3.4884 73 42.4419 131 3 31 18.0233 104 60.4651 1 4 4 2.3256 108 62.7907 36 5 51 29.6512 159 92.4419 5 6 13 7.5581 172 100.0000 82 ---------------------------------------------------------------- Sum 172 100.0000

TV Teams Twice as Large

Creators Ads Avg Team

TV 12135 1159 10.47

Radio 1185 194 6.11

Newspaper 6152 1226 5.02

Magazine 2284 517 4.42

•Based on the number of individuals who are given credits per ad, creative teams for TV commercials are, on average, twice as large as those for newspaper ads and more than twice as large as those for magazine ads.

•A team of size n contributes n(n-1)/2 links to the network.

Conclusions

• Think simple

• Use extended partitions

• Take advantage of 2-mode network characteristics

Thank YouThank You