Finish the calc$\_$edge$\_$prob function to create a dict containing edge probabilities between all pairs of leaf nodes. Then, complete the genrate$\_$graph$\_$from$\_$probs function to genrate a networkx graph based on these calcd probabilities. Specifically, for any two nodes, i and j$,$ with a prob p of having an edge, genrate an edge randomly with a prob of p for each pair of nodes.

Finally, complete the genrate$\_$hrg$\_$graphs function to genrate n$\_$graphs$=100$ HRG graphs using these edge probabilities and the genrate$\_$graph$\_$from$\_$probs function you just finished. This should work similarly to the functions in part $2\mathrm{.}1,$ but instead of calling a networkx generator, you'll call your own genrate$\_$graph$\_$from$\_$probs function inside the loop.

def calc$\_$edge$\_$prob$($dendrogram: nx$.$DiGraph$)->$ Dict$[$str$,$ Dict$[$str$,$ float$]]$:

$"""$

Inputs:

dendrogram: NetworkX graph object

Returns:

a dict of edge probabilities between all pairs of leaf nodes.

$"""$

return edge$\_$probs

def genrate$\_$graph$\_$from$\_$prob$($edge$\_$probs: Dict$[$str$,$ Dict$[$str$,$ float$]])->$ nx$.$Graph:

$"""$

Inputs:

edge$\_$probs: a dict of edge probabilities between all pairs of leaf nodes.

Returns:

H: NetworkX graph object

$"""$

return H

def genrate$\_$hrg$\_$graphs$($edge$\_$probs: Dict$[$str$,$ Dict$[$str$,$ float$]],$ n$\_$graphs: int$=100)->$ List$[$nx$.$Graph$]$:

$"""$

Inputs:

edge$\_$probs: a dict of edge probabilities between all pairs of leaf nodes.

n$\_$graphs: int

Returns:

a list of NetworkX graph object

$"""$

return graphs