artificial_networks {snowboot}

10 Simulated Networks of Order 2000 with Polylogarithmic (0.1, 2) Degree Distributions

Description

A list called "artificial_networks". The length of the list is 10, and each element is a network object of order 2000. These networks were simulated using the polylogarithmic (aka Gutenberg–Richter law) degree distribution with parameters \delta = 0.1 and \lambda = 2 as shown in the following equations:

f(k) = k^{-{\delta}}e^{-{k/{\lambda}}}/Li_{\delta}(e^{-{1/\lambda}})

Li_{\delta}(z)=\sum_{j=1}^{\infty} z^{-j}/{j^{\delta}},

where \lambda > 0 (see Newman et al. 2001, Gel et al. 2017, and Chen et al. 2018 for details).

Usage

artificial_networks

Format

A list containing 10 network objects. Each network object is a list with three elements:

degree

the degree sequence of the network, which is an integer vector of length n;

edges

the edgelist, which is a two-column matrix, where each row is an edge of the network;

n

the network order (number of nodes in the network). The order is 2000.

References

Chen Y, Gel YR, Lyubchich V, Nezafati K (2018). “Snowboot: bootstrap methods for network inference.” The R Journal, 10(2), 95–113. doi: 10.32614/RJ-2018-056.

Gel YR, Lyubchich V, Ramirez Ramirez LL (2017). “Bootstrap quantification of estimation uncertainties in network degree distributions.” Scientific Reports, 7, 5807. doi: 10.1038/s41598-017-05885-x.

Newman MEJ, Strogatz SH, Watts DJ (2001). “Random graphs with arbitrary degree distributions and their applications.” Physical Review E, 64(2), 026118. doi: 10.1103/PhysRevE.64.026118.