Analysing degeneracies in networks spectra

¹ Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore - Khandwa Road, Simrol, Indore 453552, India
² Université Paris-Sud - 91405 Orsay Cedex, France
³ Center for Biosciences and Biomedical Engineering, Indian Institute of Technology Indore - Khandwa Road, Simrol, Indore 453552, India

Received: 15 February 2017
Accepted: 20 March 2017

Abstract

Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the network's adjacency matrix provides an understanding to the origins of the occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives the opportunity to search for structures contributing to degeneracy which might have an important role in a network.