The dendrogram is formulated as a directed graph. Each leaf node $($node with no outgoing edges$)$ in the dendrogram represents a node in the empirical network. Each non$-$leaf node stores the information about its left$/$right child $($L$/$R$)$ and the probability of leaf nodes in the left tree connecting to the leaf nodes in the right tree $($p$),$ as node attributes

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

$"""$

Inputs:

dendrogram: NetworkX graph object

Returns:

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

$"""$

return edge$\_$probs

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

$"""$

Inputs:

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

Returns:

H: NetworkX graph object

$"""$

return H

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

$"""$

Inputs:

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

n$\_$graphs: int

Returns:

a list of NetworkX graph object

$"""$

return graphs