Zachary's karate club

Social Network Model of Relationships in the Karate Club
Visualization of the social relationships among the 34 individuals in the karate club.

Zachary's karate club is a well-known social network of a university karate club described in the paper "An Information Flow Model for Conflict and Fission in Small Groups" by Wayne W. Zachary.

Network description

A social network of a karate club was studied by Wayne W. Zachary for a period of three years from 1970 to 1972.[1] The network captures 34 members of a karate club, documenting 78 pairwise links between members who interacted outside the club.[2] During the study a conflict arose between the administrator "John A" and instructor "Mr. Hi" (pseudonyms), which led to the split of the club into two. Half of the members formed a new club around Mr. Hi; members from the other part found a new instructor or gave up karate. Based on collected data Zachary correctly assigned all but one member of the club to the groups they actually joined after the split.

Zachary's methodology

Before the split each side tried to recruit adherents of the other party. Thus, communication flow had a special importance and the initial group would likely split at the "borders" of the network. Zachary used the maximum flow – minimum cut Ford–Fulkerson algorithm from “source” Mr. Hi to “sink” John A: the cut closest to Mr. Hi that cuts saturated edges divides the network into the two factions. Zachary correctly predicted each member's decision except member #9, who went with Mr. Hi instead of John A.

Data set

The data set for Zachary's karate club is in open access on the internet.[3] The data can be summarized as list of integer pairs. Each integer represents one karate club member and a pair indicates the two members interacted. The data set is summarized below and also in the adjoining image. Node 1 stands for the instructor, node 34 for the club administrator / president.

[2 1]
[3 1] [3 2]
[4 1] [4 2] [4 3]
[5 1]
[6 1]
[7 1] [7 5] [7 6]
[8 1] [8 2] [8 3] [8 4]
[9 1] [9 3]
[10 3]
[11 1] [11 5] [11 6]
[12 1]
[13 1] [13 4]
[14 1] [14 2] [14 3] [14 4]
[17 6] [17 7]
[18 1] [18 2]
[20 1] [20 2]
[22 1] [22 2]
[26 24] [26 25]
[28 3] [28 24] [28 25]
[29 3]
[30 24] [30 27]
[31 2] [31 9]
[32 1] [32 25] [32 26] [32 29]
[33 3] [33 9] [33 15] [33 16] [33 19] [33 21] [33 23] [33 24] [33 30] [33 31] [33 32]
[34 9] [34 10] [34 14] [34 15] [34 16] [34 19] [34 20] [34 21] [34 23] [34 24] [34 27] [34 28] [34 29] [34 30] [34 31] [34 32] [34 33]

Zachary Karate Club Club

Zachary Karate Club Club is a honorific group[4] that awards membership in the group, along with a traveling trophy, to a scientist who is the first to use Zachary's Karate Club as an example at a conference on networks. The first scientist to be awarded was Cristopher Moore[5] in 2013.

ZKCC Trophy recipients[4]

References

  1. ↑ Wayne W. Zachary. "An Information Flow Model for Conflict and Fission in Small Groups". University of New Mexico. JSTOR 3629752.
  2. ↑ Barabási, Albert-László (2015). Network Science (PDF). Cambridge University Press.
  3. ↑ Zachary's Karate Club data set
  4. 1 2 "Zachary Karate Club CLUB". Retrieved 2016-07-12.
  5. ↑ "Network Scientists with Karate Trophies". Retrieved 2015-06-05.
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