Complete the calculate$\_$inter$\_$community$\_$density function to calculate the

intercommunity connection density matrix $($see matrix P in L$12$: Generating Networks

with Community Structure for the definition$).$

Additionally, complete the plot$\_$p$\_$matrix function to plot the inter$-$community detection

density matrix as a heatmap. Make sure to annotate the values within each cell and

provide a legend.

def calculate$\_$inter$\_$community$\_$density$($G: nx$.$Graph, partition: list$)->$ Tuple$[$np$.$ndarray, List$[$int$]]$:

$"""$

Inputs:

G: NetworkX graph object

partition : list

Returns:

Tuple of np array and List$[$int$],$ intercommunity connection density matrix

$"""$

return p$,$ sizes

def plot$\_$p$\_$matrix$($p: np$.$ndarray, save: bool$=$False$)$:

$"""$

Inputs:

p: np array, intercommunity connection density matrix

save: boolean

Returns:

None

$"""$

if save:

plt$.$savefig$(\text{'}1\_3.$png$\text{'})$

plt$.$show$()$