social network analysis Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) ...

, the co-stardom network represents the

collaboration graph In mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge wheneve ...

of film actors i.e. movie stars. The co-stardom network can be represented by an undirected graph.

Nodes In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two or more curves, lines, ...

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 A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is ...

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. Initially, the network was found to have a small-world property. Afterwards, it was discovered that more precisely it exhibits a scale-free (power-law) behavior. The co-stardom network can also be represented by a

bipartite graph In the mathematics, mathematical field of graph theory, a bipartite graph (or bigraph) is a Graph (discrete mathematics), graph whose vertex (graph theory), vertices can be divided into two disjoint sets, disjoint and Independent set (graph theo ...

where nodes are of two types: actors and movies. Links connect different types of nodes (i.e. actors to movies) if they have a relationship (actors in a movie). The parlor game of

Six Degrees of Kevin Bacon Six Degrees of Kevin Bacon or Bacon's Law is a parlor game where players challenge each other to choose an actor whom they connect to another actor via a film in which both actors appeared: this is repeated to try to find the shortest path that ...

involves finding paths in this network from specified actors to

Kevin Bacon Kevin Norwood Bacon (born July 8, 1958) is an American actor. Known for various roles, including leading man characters, Bacon has received numerous accolades such as a Golden Globe Award and a Screen Actors Guild Award. Bacon made his featu ...

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. * According to Watts and Strogatz, 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 :Average

clustering coefficient In graph theory, a clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster together. Evidence suggests that in most real-world networks, and in particular social networks, nodes tend to create tightly knit groups ...

: 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, indicates the scale-free behavior: :Size: 212 250 :Average degree(connectivity): 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. * According to Newman, Strogatz and Watts, the movie actor network can be described by a bipartite graph. Contrary to the studies described previously, they study a

with nodes of two types: movies and actors, with links, with edges linking an actor to a movie they appear in. Co-stars are both linked to the same movie they appear in. Therefore, the collaboration graph of film actors can be constructed using a

transformation matrix In linear algebra, linear transformations can be represented by matrices. If T is a linear transformation mapping \mathbb^n to \mathbb^m and \mathbf x is a column vector with n entries, then there exists an m \times n matrix A, called the transfo ...

of the bipartite graph interaction matrix.

Data collection

The Internet Movie Databas
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

{{DEFAULTSORT:Co-Stardom Network Application-specific graphs Interpersonal relationships