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 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. 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 if they have a relationship. Initially the network was found to have a small-world property. Afterwards, it was discovered that it exhibits a scale-free behavior. 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, and Barabási and Albert in and. 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:
The network characteristics and scaling exponents given by Barabási and Albert, indicates the scale-free behavior:
Therefore, the underlying network has the scale-free degree distributionp ~ k−γactor, with an exponent γactor = 2.3 ± 0.1,.
According to, 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 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 a specific time period and only picking the top three co-stars in each movie.
