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 the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally. In the part ...

in networks after its use by

Michelle Girvan Michelle Girvan (born 1977) is an American physicist and network scientist whose research combines methods from dynamical systems, graph theory, and statistical mechanics and applies them to problems including epidemiology, gene regulation, and ...

and

Mark Newman Mark Newman is an English-American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contri ...

in 2002.

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. 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 A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the ...

for Zachary's karate club is publicly available on the internet.Zachary's Karate Club data set 78 edges
/ref> 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. 1 1 2 1 2 3 1 1 1 5 6 1 2 3 4 1 3 0 3

1 1 1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1 ...

1 5 1 6 2 1 3 1 3 4 4 1 4 2 4 3

4 4 4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures. In mathematics Four is the smallest c ...

7 6 7 7 8 1 8 2 0 1 0 2 2 1

2 2 Two Two (투투) was a Korea Korea ( ko, 한국, or , ) is a peninsular region in East Asia. Since 1945, it has been divided at or near the 38th parallel, with North Korea (Democratic People's Republic of Korea) comprising its northern ...

6 24 6 25 8 3 8 24 8 25 9 3 0 24 0 27 1 2 1 9 2 1 2 25 2 26 2 29 3 3 3 9 3 15 3 16 3 19 3 21 3 23 3 24 3 30 3 31 3 32 4 9 4 10 4 14 4 15 4 16 4 19 4 20 4 21 4 23 4 24 4 27 4 28 4 29 4 30 4 31 4 32 4 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.Zachary's Karate Club data set 77 edges
/ref>

Zachary Karate Club Club

Zachary Karate Club Club is a honorific group 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 Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey)Curriculum vitae

in 2013, at a conference at the
Santa Fe Institute The Santa Fe Institute (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe, New Mexico, United States and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, includ ...
.

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 Aric Hagberg is an American applied mathematician and academic, working in nonlinear dynamics, pattern formation and complex systems. He is the deputy division leader of the computer, computational, and statistical sciences division at Los Alamos ...
(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 Mark Newman is an English-American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contri ...
(June 2014) *4th Marián Boguñá (September 2013) *3rd YY Ahn (July 2013) *2nd
Mason Porter Mason A. Porter is an American mathematician and physicist currently at the University of California, Los Angeles. He is an Elected Fellow of the American Physical Society. He was elected to the 2018 class of fellows of the American Mathematical ...
(June 2013) *1st
Cristopher Moore Cristopher David Moore, known as Cris Moore, (born March 12, 1968 in New Brunswick, New Jersey)Curriculum vitae
(May 2013)

References
* {{cite book , url=https://books.google.com/books?id=MMRpBAAAQBAJ&q=%22Zachary%27s+karate+club%22&pg=PA121 , title=Artificial Neural Networks: Methods and Applications in Bio-/Neuroinformatics - Volume 4 of Springer Series in Bio-/Neuroinformatics - Spring, 2014 , isbn=9783319099033 , last1=Koprinkova-Hristova , first1=Petia , last2=Mladenov , first2=Valeri , last3=Kasabov , first3=Nikola K. , date=2014-09-02

External links

Network Scientists with Karate Trophies

K-Means Clustering with Python Tutorial using Zachary's Karate Club dataset
Social network analysis Test items