Social patterns revealed through random matrix theory

Despite the tremendous advancements in the field of network theory, very few studies have taken weights in the interactions into consideration that emerge naturally in all real world systems. Using random matrix analysis of a weighted social network, we demonstrate the profound impact of weights in interactions on emerging structural properties. The analysis reveals that randomness existing in particular time frame affects the decisions of individuals rendering them more freedom of choice in situations of financial security. While the structural organization of networks remain same throughout all datasets, random matrix theory provides insight into interaction pattern of individual of the society in situations of crisis. It has also been contemplated that individual accountability in terms of weighted interactions remains as a key to success unless segregation of tasks comes into play. Apprehending various physical systems under the framework of networks has been in practice since a couple of decades [1,2]. Recent years have realized the need of this framework in understanding a myriad of social phenomena in various disciplines ranging from psychology to economics [3] for instance, in understanding spread of behaviour across a population [4], assessing organizational performance [5], outbreak detection of disease propagation [6]. In this Letter, we delve in to the intricacies of society using Bollywood, the largest film industry of the world [7] as a model. Being a mixture of art, business and entertainment, Bollywood, with 100 years of cinematic heritage has emerged as a key artifact providing a host of insights into shifting ideals, fantasies, lifestyles, opinions and views of the ever-evolving Indian society [8]. Making nearly one thousand feature films and fifteen hundred short films per year, the Indian film industry is the largest in the world. Cinemas in the UK have been screening Bollywood movies since the late 1960s and the spread of Indian population overseas renders Bollywood stars to gain popularity both home and abroad [9]. Bollywood provides a legitimate ground to capture the dynamically evolving nature of the diasporic society, where definitions of lead actors and their credentials of success was captured in terms of the payoff and overlap of the actors and the prevailing gender disparity in the society was emphasized upon [10]. Although Hollywood, a much smaller counterpart has been investigated using various statistical techniques [11], analysis over an evolving time scale was not emphasized upon and impact of interaction strengths on social behaviour has also been largely ignored despite the realization of importance of weights in understanding system dynamics [12]. For example, importance of weak ties has been emphasized in maintaining integrity of social systems [13]. Further, the strength of interactions have been found to play a pivotal role in analysis of many other systems such as food-web structure, metabolic networks, scientific collaboration ties, air transportation networks, internet traffic [14], suggesting that weights in interactions should be incorporated in order to have a more comprehensive picture of the structural organization of a system, hence forming a fair ground for us to investigate the weighted Bollywood networks. This Letter, using random matrix theory (RMT), an involved mathematical tool which has demonstrated its success in unveiling crucial properties of various complex systems ranging from many body quantum systems [15] to biological ones [16], analyses the weighted social networks and reveals that weights play a decisive role in extracting crucial aspects of human behaviour. Furthermore, we