Randomness and structure in collaboration networks: A random matrix analysis

Abstract

We investigate the Geom collaboration network under the random matrix theory framework. While the spectral density exhibiting triangular shape with high degeneracy at zero emphasizes on the complexity of interactions in underlying system, the spectral fluctuations provide a measure of the complexity. The short-range correlations follow the random matrix prediction, suggesting the existence of a minimal amount of randomness in the interactions between authors, whereas the long-range correlations deviating from the random matrix prediction implicate more directionality in collaboration behavior leading to less randomness. A higher degeneracy at -1 eigenvalue in the Geom collaboration network as compared with its configuration model indicates a large number of close to complete subgraphs in the network, suggesting collaboration groups among scientists. These structures can be considered to convey the same school of thoughts, whereas the randomness in spectra might be arising due to the intermingling of different collaboration modules. These results lead us to propagate that a blend of directional advancement and the mixing of schools of thoughts is essential for the steady development of a particular field of research. © 2014 IEEE.