Network topology inference with estimated node importance

In real life, the actual topology of a network is often difficult to observe or even unobservable, which seriously limits our analysis and understanding of such networks. How to accurately infer the network structure from easily observed data is extremely urgent. In this letter, we try to improve the inference accuracy by introducing the heterogeneity of nodes during the network reconstruction, and propose a novel method to estimate the importance of nodes directly from the spreading results. The results on both synthetic and empirical data sets show that our algorithms can effectively improve the inference accuracy, especially when the observed data is insufficient