Finish the calc$\_$grph$\_$statistics function to compute the network diameter, characteristic path length $($CPL$),$ average clustering coefficient, transitivity, assortativity, and degree sequence $($a list of all degrees for each node$).$ Provide a dictionary of the results with the name of each statistic as the key.

Finish the sweep$\_$louvaine$\_$res function to detect community structures within the graph. Utilize the Louvain algorithm to determine the optimal partition. Utilize $10$ different resolution parameters from min$\_$resolution to max$\_$resolution $($inclusive$),$ and compare the result of each partition to the ground truth $($you can find the ground truth in the value field associated with each node in the graph$)$ using the normalized mutual information function. Return the list of resolutions and NMIs from the resulting community assignments. Additionally, complete the plt$\_$nmi$\_$res function to exhibit the NMI for each resolution as a line plot.

import networkx as nx

from networkx.algorithms.community import louvain$\_$communities

import numpy as np

import matplotlib.pyplot as plt

from typing import Tuple, List, Dict, Union

def ld$\_$ftball$\_$graph$()->$ nx$.$Graph:

G $=$ nx$.$read$\_$gml$("$ftball$.$gml$")$

return G

def calc$\_$grph$\_$statistics$($G: nx$.$Graph$)->$ Dict$[$str$,$ Union$[$float$,$ List$[$int$]]]$:

$"""$

Inputs:

G: NetworkX graph object

Returns:

Dictionary of graph statistics

$"""$

return graph$\_$statistics

def sweep$\_$louvaine$\_$res$($G: nx$.$Graph, min$\_$resolution: int$=1,$ max$\_$resolution: int$=10)->$ Tuple$[$List$[$int$],$ List$[$float$]]$:

$"""$

Inputs:

G: NetworkX graph object

min$\_$resolution : integer

max$\_$resolution : integer

Returns:

Tuple of list of resolutions and list of NMIs

$"""$

return resolutions, nmis

def plt$\_$nmi$\_$res$($resolutions: List$[$int$],$ nmis: List$[$float$],$ save: bool$=$False$)->$ None:

$"""$

Inputs:

resolutions : list

nmis : list

save: boolean

Returns:

None

$"""$