A network representation of social relationships among the 34 individuals in the karate club studied by Zachary.

Zachary's karate club is a 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. The network became a popular example of community structure in networks after its use by Michelle Girvan and Mark Newman in 2002.^[1]

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.^[2] The network captures 34 members of a karate club, documenting links between pairs of members who interacted outside the club. 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 standard 78-edge network data set for Zachary's karate club is publicly available 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]

Although this version of the network is considered standard, the connection between nodes 34 and 23 is ambiguously reported in Zachary's original paper. A 77-edge version, which omits this edge, is also publicly available.^[4]

Zachary Karate Club Club

Zachary Karate Club Club is a honorific group^[5] 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^[6] in 2013, at a conference at the Santa Fe Institute.

References

• Koprinkova-Hristova, Petia; Mladenov, Valeri; Kasabov, Nikola K. (2014-09-02). Artificial Neural Networks: Methods and Applications in Bio-/Neuroinformatics - Volume 4 of Springer Series in Bio-/Neuroinformatics - Spring, 2014. ISBN 9783319099033.

External links

• Network Scientists with Karate Trophies
• K-Means Clustering with Python Tutorial using Zachary's Karate Club dataset