Calculate and plot six different centrality metrics for two different data

sets. The first data set is $$US$\_$airports.txt$.$ It is an undirected, weighted network of flights among the $500$ busiest commercial airports in the United States. The weights represent the number of seats available on the flights between a pair of airports. $($example: $1471)$ The second dataset is $$Yeast$.$txt$$ which represents a directed, unweighted $($weights all equal to $1)$ transcription network of operons and their pairwise interactions via transcription factor$-$based regulation, within the yeast Saccharomyces cerevisiae. Import this network as an undirected network. $($example: $11941).1)$ Complete the load$\_$graphs function to load both the airport and yeast networks from their data files as undirected graphs. $2)$ Complete the top$\_10\_$nodes

function to compute the top $10$ nodes according to each of the centrality metrics. $3)$Complete the calculate$\_$similarity$\_$matrix function to compare the top $10$ nodes

you obtained from each metric in part $1\mathrm{.}1$ using the Jaccard Similarity Index. You will need to implement your own Jaccard Similarity Index based on set$-$wise comparisons to compare the sets of top $10$ nodes coming from different centrality metrics $-$ do not rely on existing packages because the similarity we are expecting is defined on sets, while some package implementations perform an element$-$wise operation. Complete the plot$\_$similarity$\_$heatmap function to plot the similarity index using a

heatmap of the data that has the following format, but populating it with your own index values. Note: You must display the actual index values. which centrality

metric would you consider to be the most relevant for these networks? Justify your

answer. def load$\_$graphs$()$:

$"""$

$$

$$ Returns:

$$ G$\_$airport: NetworkX Graph Object

$$ G$\_$yeast: NetworkX Graph Object

$$

$"""$

$$

$$ return G$\_$airport, G$\_$yeast. def top$\_10\_$nodes$($G$)$:

$"""$

$$ Inputs:

$$ G: NetworkX Graph Object

$$

$$ Returns:

$$ top$\_10\_$nodes$\_$dict: dict$[$list$[$int$]]$

$$

$"""$

$$ top$\_10\_$nodes$\_$dict $=\{$

$$ 'eigen': eigen,

$$ 'katz': katz,

$$ 'page$\_$rank': page$\_$rank,

$$ 'closeness': closeness,

$$ 'harmonic': harmonic,

$$ 'betweeness': betweeness

$\}$

$$ return top$\_10\_$nodes$\_$dict. def calculate$\_$similarity$\_$matrix$($top$\_$nodes$\_$dict$)$:

$"""$

$$ Inputs:

$$ top$\_$nodes$\_$dict: dict$[$list$[$int$]]$

$$

$$ Returns:

$$ similarity$\_$matrix: np$.$array

$$

$"""$

$$ return similarity$\_$matrix

def plot$\_$similarity$\_$heatmap$($similarity$\_$matrix, data$\_$name, save$=$False$)$:

$"""$

$$ Inputs:

$$ similarity$\_$matrix: np$.$array

$$ data$\_$name: str

$$

$"""$

$$ plt$.$figure$($figsize$=(7,7))$

$$ plt$.$show$()$

$$

$$ if save:

$$ plt$.$savefig$($f$\text{'}\{$data$\_$name$\}\_$similarity$\_$matrix.png$\text{'})$

$$ plt$.$close$().$