For my thesis I created a simple random graph model and studied some of its properties, and I was wondering if this model has a name so I can look into it further.
The model essentially takes the Erdos-Renyi graph model and iterates it, and adds a probability $q$ at each iteration to remove a given existing edge. So more concreteley
We start with a graph $G = (V,E)$ with $E = \emptyset$. For each iteration, we consider all pairs $x,y\in V$. If $(x,y)\not\in E$ add $(x,y)$ to $E$ with probability $p$. If $(x,y)\in E$, we remove $(x,y)$ from $E$ with probability $q$. We continue this process for $t$ iterations, and then return the graph that we have at the end. We write the resulting graph as $G(n,p,q,t)$.
Thanks in advance!
This is just the Erdos-Renyi graph with different parameters: each edge will be independently in at the end with some probability $r=r(p,q,t)$ which you can in principle work out. (Indeed it has a limit as $t\to\infty$ for any nontrivial choice of $p,q$, because the state of each edge after $t$ iterations is just a two-state Markov chain.)