The Planted Degree Model
Sparse Random Networks
The binomial model can be tweaked to generate sparse networks $\mathcal G_{n,\frac cn}$:
- By changing the linking probability we bias the seelction process.
-
In $\mathcal G_{n,p}$ the probability of picking a network with $m$ lines is:
\[{N\choose m}p^m(1-p)^{N-m}\]where $N={n\choose2}$.
When $p$ is small, this expression gives a higher change to graph with few links.
Random Networks with Arbitrary Degrees
Take the following method:
- Assign each node the desired number of degree stubs.
- For each node’s stub, assign an arc to another node’s stub using a random number.