The heterogeneous structure implies that a few nodes may be crucial in maintaining network structural and functional properties. Identifying these crucial nodes correctly and quickly is a primary issue as contemporarily may face the mushrooming of large-scale datasets. Besides, the ‘weight issue’ is always ignored in this field which edge weight may play a positive/negative role in contributing to the node importance in different weighted networks. This paper provides a novel algorithm, Weighted Expectation Algorithm (WEA), which aims to ensure accuracy and speed of computation by taking advantage of dynamic programming to better handle the task of large-scale networks. Additionally, the weight issue that edge weights may contribute differently is addressed by a simply quantitative definition. Two standard experiments show WEA can maintain the network structure in connectivity well (by the lowest average robustness 0.192) and identify the node importance better in the spreading function test of spreading dynamics (by the highest average Kendall’s tau-b 0.678). In addition, the time complexities of different algo-rithms are evaluated, and their time-consuming are tested, proving that WEA consumes a rela-tively short time.

The transition region is a very thin but most peculiar layer in the solar atmosphere, located between the solar chromosphere and the corona. It is a key region for understanding the coronal heating, the solar eruptions triggering, and the origin of solar winds. Here, the gradients of all physical parameters are very high, including plasma density, ionization degree, temperature, and magnetic fields, etc. Therefore, the transition region should be highly dynamic, such as fast energy releasing and transporting, plasma heating, and even particle accelerating. They include two physical aspects: thermal and non-thermal processes. The thermal processes can be observed from the ultraviolet (UV) and extreme ultraviolet (EUV) emission by multi-wavelength images. The non-thermal processes, however, should be related to radio emissions especially at millimeter wavelengths, and the frequency range should span from several GHz to beyond 300 GHz, and the emission mechanism should be highly related to the magnetic fields and variations. The ultra-wide broadband spectral observations at millimeter wavelengths with high spectral resolutions may provide rich dynamic information about the transition region, such as non-thermal energy release and transmission, the flows of plasma and energetic particles, the magnetic fields and their variations, the generation and transportation of various waves, and the formation and evolution of the source regions of solar eruptions. Here, we discussed the spectral characteristics of millimeter-wave emission from the transition region and proposed a new conception of ultra-wide broadband millimeter-wave spectrometers to observe them.