Influence of Reciprocal links in Social Networks

In this Letter, we empirically study the influence of reciprocal links, in order to understand its role in affecting the structure and function of directed social networks. Experimental results on two representative datesets, Sina Weibo and Douban, demonstrate that the reciprocal links indeed play a more important role than non-reciprocal ones in both spreading information and maintaining the network robustness. In particular, the information spreading process can be significantly enhanced by considering the reciprocal effect. In addition, reciprocal links are largely responsible for the connectivity and efficiency of directed networks. This work may shed some light on the in-depth understanding and application of the reciprocal effect in directed online social networks

The energy distribution of relativistic electrons in the kilo-parsec scale jet of M87 with Chandra

The X-ray emission from the jets in Active Galactic Nuclei (AGN) carries important information on the distributions of relativistic electrons and magnetic fields on large scales. We reanalyze archival Chandra observations on the jet of M87 from 2000 to 2016 with a total exposure of 1460 kiloseconds to explore the X-ray emission characteristics along the jet. We investigate the variability behaviours of the nucleus and the inner jet component HST-1, and confirm indications for day-scale X-ray variability in the nucleus contemporaneous to the 2010 high TeV gamma-ray state. HST-1 shows a general decline in X-ray flux over the last few years consistent with its synchrotron interpretation. We extract the X-ray spectra for the nucleus and all knots in the jet, showing that they are compatible with a single power-law within the X-ray band. There are indications of the resultant X-ray photon index to exhibit a trend, with slight but significant index variations ranging from $\simeq 2.2$ (e.g. in knot D) to $\simeq 2.4-2.6$ (in the outer knots F, A, and B). When viewed in a multi-wavelength context, a more complex situation is arising. Fitting the radio to X-ray spectral energy distributions (SEDs) assuming a synchrotron origin, we show that a broken power-law electron spectrum with break energy $E_b$ around $1~(300\mu G/B)^{1/2}$ TeV allows a satisfactorily description of the multi-band SEDs for most of the knots. However, in the case of knots B, C and D we find indications that an additional high energy component is needed to adequately reproduce the broadband SEDs. We discuss the implications and suggest that a stratified jet model may account for the differences.Comment: accepted for publication in A&