Origin and implications of zero degeneracy in networks spectra.
The spectra of many real world networks exhibit properties which are different from those of random networks generated using various models. One such property is the existence of a very high degeneracy at the zero eigenvalue. In this work, we provide all the possible reasons behind the occurrence of the zero degeneracy in the network spectra, namely, the complete and partial duplications, as well as their implications. The power-law degree sequence and the preferential attachment are the properties which enhances the occurrence of such duplications and hence leading to the zero degeneracy. A comparison of the zero degeneracy in protein-protein interaction networks of six different species and in their corresponding model networks indicates importance of the degree sequences and the power-law exponent for the occurrence of zero degeneracy.
Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Indore 452017, India.
Alok
A
Yadav
Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Indore 452017, India.
Sarika
S
Jalan
D000465:Algorithms; D000818:Animals; D005075:Biological Evolution; D017173:Caenorhabditis elegans; D003198:Computer Simulation; D004331:Drosophila melanogaster; D004926:Escherichia coli; D016480:Helicobacter pylori; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D025941:Protein Interaction Mapping; D012441:Saccharomyces cerevisiae; D013598:Systems Theory