Graphlets importance ranking in complex networks based on the spectral energy contribution

ABSTRACT Recursive decomposition of networks is a widely used approach in network analysis for factorization of network structure into small subgraph patterns with few nodes. These patterns are called graphlets (motifs), and their analysis is considered as a common approach in bioinformatics. This paper focuses on evaluating the importance of graphlets in networks and proposes a new analytical model for ranking the graphlets importance based on their contribution to the graph energy spectrum. Besides, a general formula is provided to calculate the graphlet energy contribution to the total energy of a graph; then the energy value of the graph is estimated based on its graphlets. The results of the empirical analysis of synthetic and real networks are consistent with the theoretical results and suggest that the proposed analytical model can accurately estimate the structural features of a given graph based on its graphlets.