it takes forever to run the question $5\mathrm{.}3$ and $5\mathrm{.}4$ due to the large data, please re$-$do the codes, so that it takes shorter time. In addition, please add a code to check that there are no edges between nodes of the same type. def load$\_$github$\_$data$()->$ Tuple$[$nx$.$Graph, List$[$str$],$ List$[$str$]]$:

$"""$

Returns:

G: NetworkX graph object

uid$\_$list $($list$)$: list of users

pid$\_$list $($list$)$: list of projects

$"""$

G $=$ nx$.$Graph$()$

uid$\_$list$=$set$()$

pid$\_$list$=$set$()$

with open$(\text{'}$github$\_$data.txt$\text{'},\text{'}$r$\text{'})$ as file:

for line in file:

user$\_$id$,$ project$\_$id $=$ line.split$()$

G$.$add$\_$node$($user$\_$id$,$ bipartite$=0)$

G$.$add$\_$node$($project$\_$id$,$ bipartite$=1)$

G$.$add$\_$edge$($user$\_$id$,$ project$\_$id$)$

uid$\_$list.add$($user$\_$id$)$

pid$\_$list.add$($project$\_$id$)$

# NOTE: We are also returning a list of users and projects. This will be helpful

# when getting the correct user and project indicies from the projections.

uid$\_$list $=$sorted$($uid$\_$list$)$

pid$\_$list$=$ sorted$($pid$\_$list$)$

return G$,$ uid$\_$list, pid$\_$list # Create a function to create the User$-$Project Matrix

def calculate$\_$projections$($G$,$ uid$\_$list, pid$\_$list$)->$ Tuple$[$sp$.$sparse.spmatrix, sp$.$sparse.spmatrix$]$:

$"""$

Inputs:

G: NetworkX graph object

uid$\_$list $($list$)$: list of users

pid$\_$list $($list$)$: list of projects

Returns:

user$\_$matrix $($sp$.$sparse.spmatrix$)$: one mode projection for users

project$\_$matrix $($sp$.$sparse.spmatrix$)$: one mode projection for projects

$"""$

$"""$

users$\_$projection $=$ np$.$array$([0,0])$

projects$\_$projection $=$ np$.$array$([0,0])$

$"""$

adjacency$\_$matrix $=$ bipartite.biadjacency$\_$matrix$($G$,$ row$\_$order$=$uid$\_$list, column$\_$order$=$pid$\_$list$)$

users$\_$projection $=$ adjacency$\_$matrix.dot$($adjacency$\_$matrix.T$)$

projects$\_$projection $=$ adjacency$\_$matrix.T$.$dot$($adjacency$\_$matrix$)$

return users$\_$projection, projects$\_$projection # Write a function that will return the pair of users that share the highest number of Github projects between them.

def get$\_$user$\_$pair$($M$,$ uid$\_$list$)->$ Tuple$[$str$,$ str$]$:

$"""$

Inputs:

M: projected matrix

uid$\_$list $($list$)$: list of users

Returns:

u$1($str$)-$ first user

u$2($str$)-$ second user

$"""$

max$\_$value $=-1$

n $=$ len$($uid$\_$list$)$

for i in range$($n$)$:

for j in range$($i $+1,$ n$)$:

if M$[$i$,$ j$]>$ max$\_$value:

max$\_$value $=$ M$[$i$,$ j$]$

u$1,$u$2=$ uid$\_$list$[$i$],$ uid$\_$list$[$j$]$

return u$1,$ u$2$ # Write a function that will return the pair of projects that share the highest number of users between them.

def get$\_$project$\_$pair$($M$,$ pid$\_$list$)->$ Tuple$[$str$,$ str$]$:

$"""$

Inputs:

M: projected matrix

pid$\_$list $($list$)$: list of projects

Returns:

p$1($str$)-$ first project

p$2($str$)-$ second project

$"""$

#max$\_$value $=$ np$.$max$($M$)$

#indices $=$ np$.$where$($pid$\_$list$==$max$\_$value$)$

#p$1=$ pid$\_$list$[$indices$[0]]$

#p$2=$ pid$\_$list$[$indices$[1]]$

max$\_$value $=-1$

M $=$ sp$.$sparse.csr$\_$matrix$($M$)$

n $=$ len$($pid$\_$list$)$

for i in range$($n$)$:

for j in range$($i $+1,$ n$)$:

if M$[$i$,$ j$]>$ max$\_$value:

max$\_$value $=$ M$[$i$,$ j$]$

p$1,$p$2=$ pid$\_$list$[$i$],$ pid$\_$list$[$j$]$

return p$1[0],$ p$2[0]$