Degree Correlations in Erds$-$Rnyi Networks

Consider the Erds$-$Rnyi G$($N$,$L$)$ model of random networks, introduced in CHAPTER $2($BOX $3\mathrm{.}1$ and SECTION $3\mathrm{.}2),$ where N labeled nodes are connected with L randomly placed links. In this model, the probability that there is a link connecting nodes i and j depends on the existence of a link between nodes l and s$.$

Write the probability that there is a link between i and j$,$ eij and the probability that there is a link between i and j conditional on the existence of a link between l and s$.$

What is the ratio of such two probabilities for small networks? And for large networks?

What do you obtain for the quantities discussed in $($a$)$ and $($b$)$ if you use the Erds$-$Rnyi G$($N$,$p$)$ model?

Based on the results found for $($a$)-($c$)$ discuss the implications of using the G$($N$,$L$)$ model instead of the G$($N$,$p$)$ model for generating random networks with small number of nodes