# Does marginalization increase the number of edges in Graph SLAM?

I thought marginalization does not change the number of the edges but this material (page 11) describes that as a result of marginalization we will have more edges in graph. Why does it increase the edges?

For those who does not want to open the page, it is written as follows.

Marginalization: Cons Con: More edges in graph

1. Feature with N observations leads to O(N2) edges
2. Slower/harder to solve, (Information Matrix less sparse)

When moving from pose $x_t$ to $x_{t+1}$, the SLAM algorithm would naturally want to marginalize the $x_t$ node away: but that means the direct landmark-pose observations that were encoded in the edges connecting $x_t$ and $L_i$ would now have to be rewired to be incident on $x_{t+1}$, which is equivalent to obtaining new observations of $L_i$. Notice how the information matrix becomes denser.