# Zachary's karate club

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.

### ZKCC Trophy recipients

• 22nd Luca Gallo (July 2023)
• 21st Santo Fortunato (July 2022)
• 20th Jesús Arroyo (July 2021)
• 19th Jean-Gabriel Young (September 2020)
• 18th Emma Towlson (May 2019)
• 17th Philipp Hövel (March 2019)
• 16th Clara Granell (September 2018)
• 15th Leto Peel (June 2018)
• 14th Aric Hagberg (March 2018)
• 13th Megha Padi (March 2018)
• 12th Amir Rubin (January 2017)
• 11th Federico Battiston (September 2016)
• 10th Giona Casiraghi (July 2016)
• 9th Filippo Radicchi (May 2016)
• 8th Qing Ke (September 2015)
• 7th Manlio De Domenico (July 2015)
• 6th Tiago Peixoto (June 2015)
• 5th Mark Newman (June 2014)
• 4th Marián Boguñá (September 2013)
• 3rd YY Ahn (July 2013)
• 2nd Mason Porter (June 2013)
• 1st Cristopher Moore (May 2013)

## References

1. ^ Girvan, M.; Newman, M. E. J. (2002). "Community structure in social and biological networks". Proceedings of the National Academy of Sciences. 99 (12): 7821–7826. doi:10.1073/pnas.122653799. PMC 122977. PMID 12060727.
2. ^ Zachary, W. W. (1977). "An Information Flow Model for Conflict and Fission in Small Groups". Journal of Anthropological Research. 33 (4): 452–473. arXiv:1707.03587. doi:10.1086/jar.33.4.3629752. JSTOR 3629752. S2CID 197843028.
3. ^ Zachary's Karate Club data set 78 edges
4. ^ Zachary's Karate Club data set 77 edges
5. ^ "Zachary Karate Club CLUB". Retrieved 2016-07-12.
6. ^ "Network Scientists with Karate Trophies". Retrieved 2015-06-05.