Social patterns revealed through random matrix theory

Complex Systems Lab, Indian Institute of Technology Indore - IET-DAVV Campus, Khandwa Road, Indore-452017, India

^(a) sarika@iiti.ac.in (corresponding author)

Received: 16 May 2014
Accepted: 22 October 2014

Abstract

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 remains the same throughout all datasets, random matrix theory provides insight into the interaction pattern of individuals 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.