New metrics for influential spreaders identification in complex networks based on D-spectra of nodes

Identifying important nodes is of key significance in network sciences as it is closely related to information and disease spreading, structural robustness, etc. Till today, no theoretically proved optimal metric for measuring the importance of nodes is known, while a lot of metrics, mostly heuristic, have been studied. In this paper, we propose several heuristic metrics that are constructed from D-spectra of vertices for discussion. The latter is a graph invariant which is induced by D-chain decompositions of graphs, a recently introduced framework for studying network structures by the first author, Bura and Reidys (SIAM J. Appl. Dyn. Syst. 18, 2019, pp. 2181–2201). Statistical analyses based on numerous data from running the SIR model on real-world and random networks show that some of our proposed metrics outperform a number of well-known metrics such as the H-index, the core values, the betweenness centrality and the closeness centrality.