degree distribution

Assignment 1


2024, ינוי7 -7.6.24 השגה


Please combine any code together with text responses in a single upload file to Lemida by the deadline.


1. Read in the file uploaded with the assignment airport-network.gml. You can read the file into network using the network command nx.read_gml(‘airportnetwork.gml’), where the argument in the middle is the filename.


a. Make a log-log plot of the degree distribution of this network. Also


compute its global clustering coefficient using the command




b. Make an Erdos-Renyi Graph with the same average degree as this network


and plot its degree distribution. You may use the network command


nx.erdos_renyi_graph(), with the appropriate values of N and p (you will


have to calculate the correct p). Compare this to the actual degree




c. Using nx.configuration_model(G), create a network with the same degree


distribution as the original network and compare its clustering coefficient




2. Consider an Erdos-Renyi network with N=6,000 nodes, connected with


probability p=0.0001.


a. What is the expected number of links L?


b. In what regime is the network (critical, subcritical, supercritical, fully




c. Assuming the same value of p, what value of N would lead to a network


with an average degree of k=10.


3. Degree and components


a. Consider an undirected network of size N in which each node has exactly


degree k = 1 (not average degree k=1!). What has to be true of N for this


network to exist? What is the degree distribution of this network? How


many components does this network have?


b. Consider now a network in which each node has degree k = 2 and


clustering coefficient C = 1. What has to be true of N for this network to


exist? Describe what this network looks like.

Assignment 1