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The focus of this work is on estimation of the in-degree distribution indirected networks from sampling network nodes or edges. A number of samplingschemes are considered, including random sampling with and without replacement,and several approaches based on random walks with possible jumps. When samplingnodes, it is assumed that only the out-edges of that node are visible, that is,the in-degree of that node is not observed. The suggested estimation of thein-degree distribution is based on two approaches. The inversion approachexploits the relation between the original and sample in-degree distributions,and can estimate the bulk of the in-degree distribution, but not the tail ofthe distribution. The tail of the in-degree distribution is estimated throughan asymptotic approach, which itself has two versions: one assuming a power-lawtail and the other for a tail of general form. The two estimation approachesare examined on synthetic and real networks, with good performance results,especially striking for the asymptotic approach.

Sampling-based Estimation of In-degree Distribution with Applications to Directed Complex Networks