Analysing degeneracies in networks spectra

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 of the origins of 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 an opportunity to search for structures contributing to degeneracy which might have an important role in a network.

5 pages, 3 figures and Supplementary Material

References in corpus (5)

• Clique percolation in random networks
• Understanding cancer complexome using networks, spectral graph theory and multilayer framework
• Uncovering Randomness and Success in Society
• Origin and implications of zero degeneracy in networks spectra
• Extreme-value statistics of networks with inhibitory and excitatory couplings

Cited by in corpus (8)

• Spectral Theory of Sparse Non-Hermitian Random Matrices
• Spectral properties of complex networks
• Synchronization dynamics in non-normal networks: the trade-off for optimality
• Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
• Null-eigenvalue localization of quantum walks on real-world complex networks
• How to Suppress Dark States in Quantum Networks and Bio-Engineered Structures
• Random Matrix Analysis of Multiplex Networks
• Comment on "Synchronization dynamics in non-normal networks: the trade-off for optimality"