Uncovering Randomness and Success in Society

An understanding of how individuals shape and impact the evolution of society is vastly limited due to the unavailability of large-scale reliable datasets that can simultaneously capture information regarding individual movements and social interactions. We believe that the popular Indian film industry, “Bollywood”, can provide a social network apt for such a study. Bollywood provides massive amounts of real, unbiased data that spans more than 100 years, and hence this network has been used as a model for the present paper. The nodes which maintain a moderate degree or widely cooperate with the other nodes of the network tend to be more fit (measured as the success of the node in the industry) in comparison to the other nodes. The analysis carried forth in the current work, using a conjoined framework of complex network theory and random matrix theory, aims to quantify the elements that determine the fitness of an individual node and the factors that contribute to the robustness of a network. The authors of this paper believe that the method of study used in the current paper can be extended to study various other industries and organizations.

not a struggle for existence. This reflects a gradual change in the outlook of the society towards women. In order to assess success of all actors in Bollywood industry, the Filmfare Awards were introduced for rewarding both artistic and technical excellence of professionals in the Hindi language film industry of India. The National Film Awards were also introduced in 1954 but gained less popularity as compared to Filmfare as they are decided by a panel appointed by Indian Government and do not authentically reflect the choice of the global audience. The Filmfare Awards, in contrast, are voted for by both the public and a committee of experts thus gaining more acceptance over the years.

A brief review of Hollywood networks
The collaboration graph of film actors were shown to be small-world networks [2] and their properties were studied using random graph theory [3]. Relational dependency network analysis has been performed on Hollywood datasets obtained from IMDB which identify and exploit cyclic relational dependencies to achieve significant performance gains [4]. Hollywood datasets were deployed for implementation of the Layered Label Propagation algorithm, meant to reorder very large graphs [5] and the PageRank algorithm to uncover the relative importance of a node in a graph [6]. Professional links between movie actors was used as a means to fit the predictions of a continuum theory to probe for the existence of two regimes, the scale-free and the exponential regime [7]. Degree of a node can be defined as the number of nodes that are linked to the said node. Degree distribution is the plot of the degree versus the number of nodes with the particular degree.

Degree Distribution
Fig.S1 plots degree distribution of Bollywood networks.

Spectral Analyses
Paul Erdös and Alfred Rényi pioneered the study of random graph models [10], which persisted as a preferred method for studying networks for decades. Following this, the Barabási-Albert model of networks suggested that many complex networks follow a power law degree distribution, hence forming what is termed as scale free network, which emerged as a revolutionizing change in network analysis and completely changed the perspectives of the analysts [11]. Some of the popular networks studied henceforth namely the Internet, the World-Wide-Web, cellular networks, phone call networks, science collaboration networks etc. appeared to follow the power law distribution [8]. For the undirected networks constructed here all the eigenvalues are real. We observe a high degeneracy at λ = −1, with almost 40% of states having this value.

Nearest neighbor spacing distribution (NNSD)
Fig. S5 depicts NNSD of Bollywood networks. Discussion on NNSD is provided in the main article.

∆ 3 Statistics
It can be seen from Fig. S6 that the statistics agrees very well with the RMT prediction for some length for certain sets, and for some sets they do not follow RMT prediction of GOE statistics at all. The range for which ∆ 3 (L) statistics follows RMT prediction can be interpreted as providing measure of randomness in underlying network [16]. The length of the spectra which follow RMT prediction of GOE statistics is written in table 1 of main article. In some of the

Net payoff
Net payoff is a measure originally borrowed from management which is modified and used as a predictive means for assessing success. PageRank algorithm has also been used to assign ranks to nodes using a Markov chain based on the structure of the graph. This algorithm was used on Hollywood datasets to uncover the relative importance of a particular actor in the graph [6]. The  (Table S8). She has been one of the most popular female actors in Bollywood since 2007, net payoff seems to be predictive of her success.