A hybrid approach for pair-wise layer similarity in a multiplex network

The development in network science shows various applications of network science concepts in different fields of research. Recently, the analysis using multilayer network has drawn attention of researchers for its multifaceted modeling framework. This paper discusses layer similarity in a multiplex network that is a special type of multilayer network. We investigate one of the recent approaches in layer similarity that uses cosine similarity as a neighborhood-based approach of defining node and layer similarity. We show the problem with the existing approach of similarity and introduce neighborhood-structural and neighborhood-spectral composition to explain node and layer similarity. In these compositions, we add structural and spectral discrepancies as penalty factor to neighborhood similarity. We use k-shell decomposition and eigenvector ranking to define structural and spectral importance, respectively. The final layer similarity combines both neighborhood-structural and neighborhood-spectral compositions to evaluate layer similarity. Like the existing approach, the proposed approach focuses on pair-wise layer similarity. The results show that there exist some differences in ranking pair-wise layer similarity between the proposed and exiting approach. A high degree of correlation is found between the proposed and existing approach. The proposed penalty factor captures the mismatch in ranking. The average accuracy of link prediction is found to be better in case of proposed approach than the existing approach.