Fig. 2

Unbiased sampling of paths from neighborhood graphs. a An example of the PEN sampling tree. b URPEN returns each path at a frequency corresponding with the sampling level, whereas Radial Random Walk (RRW) results in biased sampling of the graph. Examples of RRW upsampled and downsampled paths are shown in the top right corner of the 20% sampling panel. The sampling probability in URPEN is set to \(p=(1, 1, \ldots , 1, 0.2)\) for 20% sampling, and \(p=(1, 1, \ldots , 1, 0.6)\) for 60% sampling. This test was performed 1000 times. c Sampling quality with URPEN and RRW on the bipolar cell type graph and a random graph with 12000 nodes. d Sampling speed for non-radial and radial sampling on the bipolar and random networks