Importance of randomness in biological networks: A random matrix analysis

Abstract

Random matrix theory, initially proposed to understand the complex interactions in nuclear spectra, has demonstrated its success in diverse domains of science ranging from quantum chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by providing a new dimension to complex systems research. We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate the importance of randomness in interactions for deducing crucial properties of the underlying system. This paper provides an overview of the importance of random matrix framework in complex systems research with biological systems as examples. © Indian Academy of Sciences.