An interactive companion to Lee, Kim & Jeong, “Statistical properties of sampled networks,” Phys. Rev. E 73, 016102 (2006). Build a small network, take a node, link or snowball sample, and compare the degree exponent, betweenness exponent, path length, assortativity and clustering of the sample against the original.
For node and link sampling, Eq. (5) predicts the sampled degree distribution from the original one: every link of a node survives independently with probability α. Snowball sampling breaks that assumption, which is why its hubs keep their full degree.
Circles: original network. Colored markers: this sample. Dashed line: Eq. (5), shown for node and link sampling (compare Fig. 3).
Each dot is a sampled node. The solid line is y = x (degree fully kept); the dashed line is y = αx, the Eq. (5) expectation. Snowball hubs sit on y = x, as in Fig. 4.
Repeat each method many times across α = 0.1 … 1 on the current network, and see whether the trends of Figs. 2, 5, 6, 8 and 10 and Table II appear.
The paper's summary of how each quantity moves as the sampling fraction drops (⇑ increase, ⇓ decrease, = unchanged, ⇕ depends on the network). The path-length column comes from Sec. III A. After a sweep, each cell also shows what this network did at small α (0.2–0.4).