BLG549E-Homework 1 Solved

Jupyter Notebook Installation
You need to have Python and Pip installed in your computer to install Jupyter Notebook.

Windows
On command prompt (cmd.exe with admin mode):

C:\**path** python −m pip install jupyter

After changing your current folder to the folder which you want to work on (see ’cd’ command):

C:\**your_working_folder** jupyter notebook

Then it will be launched on your default browser

Ubuntu/Linux/Unix/Mac
On Terminal: $ pip install notebook

Then launch with:

$ jupyter notebook

For more information: https://jupyter.org/install

Introduction
You will carry out all the tasks below using Ipython Notebook. Simply add all your work to the provided template file HW1_template.ipynb using jupyter notebook. In this homework, you will code up several experiments in Oldham et al. paper[3] (You can click anywhere on this sentence instead of a small, hard-to-click word "here" to find the paper).To this aim, first simulate 40 networks: 20 unconstrained weighted using Erdos-Renyi generative model [1] and 20 constrained unweighted using MaslovSneppen algorithm [2]. For more details, check the attached supplementary material. For this task, you can use ready-made pieces of code. But all needs to be commented out. The number of nodes in each network category (e.g., ER) should equal to 200.

Part A Simulate random weighted and unweighted networks
1.     Briefly explain how Erdos-Renyi generative model works.

2.     What are the key properties of Erdos-Renyi graphs?

3.     Briefly explain how Maslov-Sneppen algorithm works.

4.     What are the key properties of Maslov-Sneppen graphs?

5.     Visualize two random graphs you simulated (ER and MS).

 

Figure 1: Example visualization of two graphs.

Part B: Analyzing Erdos-Renyi and Maslov-Sneppen graphs using centrality measures (
1.     Code up the necessary steps to reproduce plots A and B in Figure 2 using the Centrality Measure Correlation(CMC)s of the 40 networks you simulated: 20 weighted Erdos-Renyi and 20 unweighted Maslov-Sneppen networks.

2.     What conclusions can you derive from the plots?

 

Figure 2: Distributions of Centrality Measure Correlations (CMCs) for example unweighted and weighted networks. Distributions of CMCs for every pair of centrality measures for five example unweighted (panel A); and weighted networks (panel B). Networks have been ordered from highest (left) to lowest (right) median CMC. Both the figure and the caption is from [3]

3.      Code up the necessary steps to reproduce Figure 3 (A to D) using the between-network CMCs of the 40 networks you simulated: 20 weighted ErdosRenyi and 20 unweighted Maslov-Sneppen networks.

4.     What conclusions can you derive from the plots?

 

Figure 3: Mean and standard deviation of between-network CMCs. Panels A and B show the between-network CMC mean and standard deviation for unweighted measures, respectively. Panels C and D show the between-network CMCs mean and standard deviation for weighted measures, respectively. Both the figure and the caption is from [3]

5.     Plot the CMC distributions using bar plots as in the Figure 4 for your 20 unweighted and 20 weighted networks. What do you notice?

 

Figure 4: Example bar plot of CMC distributions.

Part C: Association between mean within-network Centrality Measure Correlation(CMC) and network properties
1.     Choose two different network properties (e.g., modularity and density) and regenerate similar plots to Figure 5 by plotting the mean within-network CMC against the selected network property. Erdos-Renyi networks should have the same color (e.g., transparent blue) and Maslov-Sneppen networks can be assigned a different color (e.g., transparent red). You can use existing codes to compute the network properties.

2.     Interpret your plots. What conclusions can you derive?

 

Figure 5: Association between mean within-network CMC and network properties in unweighted networks. The association between the mean within-network CMC (the average of all CMCs within a single network) and each of the global topological properties. Networks are coloured by their natural category (blue = social, grey = technological, brown = biological, orange = informational, purple = transportation; green = economic). Both the figure and the caption is from [3]