Analyze the following synthetic network:

Create an Erdos Renyi graph with $100$ nodes and $0\mathrm{.}05$ as the probability of node creation. Draw this network using Python and attach a screenshot. $(2$ points$)$

Calculate the following for this network:

Number of edges. $(1$ point$)$

Density of this network. $(1$ point$)$

Find the clustering coefficient for each node within the network. What does the clustering coefficient of $1$ for a node signify? What does the clustering coefficient of $0$ for a node signify? $(1$ point$)$

What is the average clustering coefficient for this network? $(1$ point$)$

What is the transitivity of this network? $(1$ point$)$

Find the eccentricity for each node within the network. $(1$ point$)$

What is the diameter of this network? What is the radius? $(1$ point$)$

Calculate the degree centrality, closeness centrality, and betweenness centrality for each node within this network. $(1$ point$)$