In this homework, you will extend your work from the previous homework and generate random graphs using some properties of the real graph you created/used last time.
Choose one of the networks you created with Lost Circles, the Wikipedia code, or the Twitter notebook in the prior homeworks, which we'll call Yg, and use NetworkX to create a random graph (i.e., an Erdos-Renyi graph), we'll call ER, using the same number of nodes and approximately the same number of edges as your Yg graph.
What value of p did you use to construct your ER graph?
Provide a visualization of this ER and your Yg graph.
How many nodes are in ER?
How many edges are in ER and in Yg?
What are the densities of ER and Yg?
What are the average local clustering coefficients of ER and Yg?
What are the diameters of ER and Yg?
Construct a histogram for the degree distributions in both ER and Yg.
Describe your observations about the differences and similarities between these two graphs.
With the Yg network you chose above, create a Watts Strogatz network with the same number of nodes, which we'll call WS, to approximate your graph.
What value of d did you use to construct your WS graph?
Provide a visualization of this WS and your Yg graph.
How many nodes are in WS?
How many edges are in WS and in Yg?
What are the densities of WS and Yg?
What are the average local clustering coefficients of WS and Yg?
What are the diameters of WS and Yg?
Construct a histogram for the degree distributions in both WS and Yg.
Describe your observations about the differences and similarities between these two graphs.