Path diversity improves the identification of influential spreaders

Identifying influential spreaders in complex networks is a crucial problem which relates to wide applications. Many methods based on the global information such as $k$-shell and PageRank have been applied to rank spreaders. However, most of related previous works overwhelmingly focus on the number of paths for propagation, while whether the paths are diverse enough is usually overlooked. Generally, the spreading ability of a node might not be strong if its propagation depends on one or two paths while the other paths are dead ends. In this Letter, we introduced the concept of path diversity and find that it can largely improve the ranking accuracy. We further propose a local method combining the information of path number and path diversity to identify influential nodes in complex networks. This method is shown to outperform many well-known methods in both undirected and directed networks. Moreover, the efficiency of our method makes it possible to be applied to very large systems.Comment: 6 pages, 6 figure

An XMM-Newton study of the mixed-morphology supernova remnant W28 (G6.4-0.1)

We have performed an XMM-Newton imaging and spectroscopic study of supernova remnant (SNR) W28, a prototype mixed-morphology or thermal composite SNR, believed to be interacting with a molecular cloud. The observed hot X-ray emitting plasma is characterized by low metal abundances, showing no evidence of ejecta. The X-rays arising from the deformed northeast shell consist of a thermal component with a temperature of $\sim0.3$ keV plus a hard component of either thermal (temperature $\sim 0.6$ keV) or non-thermal (photon index $=0.9$-2.4) origin. The X-ray emission in the SNR interior is blobby and the corresponding spectra are best described as the emission from a cold ($kT\sim0.4$ keV) plasma in non-equilibrium ionization with an ionization timescale of $\sim4.3\times 10^{11}$ cm$^{-3}$ s plus a hot ($kT \sim 0.8$ keV) gas in collisional ionization equilibrium. Applying the two-temperature model to the smaller central regions, we find non-uniform interstellar absorption, temperature and density distribution, which indicates that the remnant is evolving in a non-uniform environment with denser material in the east and north. The cloudlet evaporation mechanism can essentially explain the properties of the X-ray emission in the center and thermal conduction may also play a role for length scales comparable to the remnant radius. A recombining plasma model with an electron temperature of $\sim 0.6$ keV is also feasible for describing the hot central gas with the recombination age of the gas estimated at $\sim2.9\times 10^4$ yr.Comment: 16 pages, 7 figures, 5 tables, ApJ in pres