artificial_networks: 200 Simulated Networks of order 2000 with Polylogarithmic (0.1, 2)
Degree Distributions
Description
A list called "networks" containing 200 network objects of order 2000. These
networks were simulated using the polylogarithmic (aka Gutenberg-Richter law)
degree distribution (Newman et al., 2001; Newman, 2002) with parameters
$\delta = 0.1$ and $\lambda = 2$ as see in the following equations:
$$f(k) = k^{-{\delta}}e^{-{k/{\lambda}}}/Li_{\delta}(e^{-{1/\lambda}})$$
$$Li=\sum_{j=1}^{\infty} z^{-j}/{j^{\delta}}$$
where $\lambda > 0$. Please see refence below for details (Thompson et al, 2016).
Format
a list containing 200 network objects. Each network object is a list
with three elements:
- edges
- The edgelist of the network. A two column
matrix where each row is an edge. - degree
- The degree sequence of the network, which is
an
integer vector of length n. - n
- The network order. The order for every network is 2000.
References
Thompson, M. E., Ramirez Ramirez, L. L., Lyubchich, V. and
Gel, Y. R. (2015), Using the bootstrap for statistical inference
on random graphs. Can J Statistics. doi: 10.1002/cjs.11271