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

- Briefly explain how Erdos-Renyi generative model works.
- What are the key properties of Erdos-Renyi graphs?
- Briefly explain how Maslov-Sneppen algorithm works.
- What are the key properties of Maslov-Sneppen graphs?
- 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

- 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****]**

- 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.
- 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****]**

- 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

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****]**

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