Co-stardom network explained

In social network analysis, the co-stardom network represents the collaboration graph of film actors i.e. movie stars. The co-stardom network can be represented by an undirected graph of nodes and links. Nodes correspond to the movie star actors and two nodes are linked if they co-starred (performed) in the same movie. The links are un-directed, and can be weighted or not depending on the goals of study. If the number of times two actors appeared in a movie is needed, links are assigned weights.^[1] The co-stardom network can also be represented by a bipartite graph where nodes are of two types: actors and movies. And edges connect different types of nodes (i.e. actors to movies) if they have a relationship (actors in a movie).^[2] Initially the network was found to have a small-world property.^[3] Afterwards, it was discovered that it exhibits a scale-free (power-law) behavior.^[4]

The parlor game of Six Degrees of Kevin Bacon involves finding paths in this network from specified actors to Kevin Bacon.

Network representation

In order to represent any network, it is necessary to characterize the properties of the corresponding graph of nodes and links. Studies on the collaboration network of movie actors have been described in literature such as the work done by (Watts and Strogatz, 1998), and Barabási and Albert in (1999) and (2000). The general characteristics are described below.^{[5] [6] [7] [8] [9]}

• According to Watts and Strogatz (1998), the movie/actor network indicated the following characteristics showing a small-world property of the underlying network:

Size: 225 226

Average degree: 61

Average path length: 3.65

Clustering coefficient

0.79

Compared to a random graph of the same size and average degree, the average path length is close in value. However, the clustering coefficient is much higher for the movie actor network.

• The network characteristics and scaling exponents given by Barabási and Albert (1999), indicates the scale-free behavior:

Size: 212 250

Average degree: 28.78

Clustering coefficient: 0.79

The network fits a scale-free degree distribution p(k) ~ k^-γ_actor, with an exponent γ_actor = 2.3 ± 0.1 (Barabási and Albert, 1999), (Albert and Barabási, 2000).

• According to (Newman, Strogatz, and Watts, 2001), the movie actor network can be described by a bipartite graph. Nodes in this graph are of two types: movies and actors. And the edges only connect nodes of different types. So edges link the co-stars to the movie they appear in. Therefore, the collaboration graph of film actors can be constructed using a transformation matrix of the bipartite graph interaction matrix.

Data collection

The Internet Movie Database IMDB represents one of the largest internet sources for movies/actors data. And it is where most of the datasets are collected to study the collaboration network of co-star actors. IMDB facilitates the ability to collect data for very specific and variable types of network. For example, a network can be constructed using data from all the horror movies made within the 2020–2021 timeframe and only picking the top three co-stars in each movie.

References

1. Albert . Réka . Barabási . Albert-László . Statistical mechanics of complex networks . Reviews of Modern Physics . 74 . 1 . 2002-01-30 . 0034-6861 . 10.1103/revmodphys.74.47 . 47–97. cond-mat/0106096 . 2002RvMP...74...47A . https://web.archive.org/web/20110707212510/http://www.barabasilab.com/pubs/CCNR-ALB_Publications/200201-30_RevModernPhys-StatisticalMech/200201-30_RevModernPhys-StatisticalMech.pdf . 2011-07-07 . dead .
2. Newman . M. E. J. . Strogatz . S. H. . Watts . D. J. . Random graphs with arbitrary degree distributions and their applications . Physical Review E . 64 . 2 . 2001-07-24 . 1063-651X . 10.1103/physreve.64.026118 . 026118. 11497662 . cond-mat/0007235 . 2001PhRvE..64b6118N . free.
3. Watts . Duncan J. . Strogatz . Steven H. . Collective dynamics of 'small-world' networks . Nature . Springer Nature . 393 . 6684 . 1998 . 0028-0836 . 10.1038/30918 . 440–442. 9623998 . 1998Natur.393..440W . free.
4. Barabási . Albert-László . Albert . Réka . Emergence of Scaling in Random Networks . Science . 286 . 5439 . 1999-10-15 . 0036-8075 . 10.1126/science.286.5439.509 . 509–512. 10521342 . cond-mat/9910332 . 1999Sci...286..509B .
5. Albert . Réka . Jeong . Hawoong . Barabási . Albert-László . Diameter of the World-Wide Web . Nature . Springer Nature . 401 . 6749 . 1999 . 0028-0836 . 10.1038/43601 . 130–131. cond-mat/9907038 .
6. Albert . Réka . Jeong . Hawoong . Barabási . Albert-László . Error and attack tolerance of complex networks . Nature . 406 . 6794 . 2000 . 0028-0836 . 10.1038/35019019 . 378–382. 10935628 . cond-mat/0008064 . 2000Natur.406..378A .
7. Albert . Réka . Jeong . Hawoong . Barabasi . Albert-László . Erratum: correction: Error and attack tolerance of complex networks . Nature . Springer Nature . 409 . 6819 . 2001 . 0028-0836 . 10.1038/35054111 . 542. free .
8. Newman . M. E. J. . Models of the Small World. Journal of Statistical Physics . Springer Science and Business Media LLC . 101 . 3/4 . 2000 . 0022-4715 . 10.1023/a:1026485807148 . 819–841.
9. Albert . Réka . Barabási . Albert-László . Topology of Evolving Networks: Local Events and Universality . Physical Review Letters . 85 . 24 . 2000-12-11 . 0031-9007 . 10.1103/physrevlett.85.5234 . 5234–5237. 11102229 . cond-mat/0005085 . 2000PhRvL..85.5234A .