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CSYS5020: Interdependent Civil Systems – Assignment 1
Assignment set by: Dr. Mahendra Piraveenan, UoS coordinator
Due Date: 14th April Friday 2016 at 8.00 PM Submission: Electronic
This assignment should be attempted individually. This assignment constitutes 30% of your final assessment in this subject. Name of the file submitted should be studentnumber--ICS--
1.pdf or studentnumber--ICS--1.zip or studentnumber--ICS--1.rar
The University takes plagiarism or allegations of plagiarism seriously. All students are encouraged to familiarise themselves with the University plagiarism policy before attempting this assignment. Computer scripts and other automated methods may be used to detect similarity of assignment submissions.
Before you begin the assignment, download the following networks files, which are available in Blackboard.
In this question, you will use some basic functionalities of Cytoscape.
i. Open the four provided network files in Cytoscape. Please visualise them using the following layouts. Net1 and Net2 - Prefuse force directed layouts. Net3 - Degree sorted circle layouts. Net4 – Organic Layout. Attach screenshots of these layouts to your answer. (8 marks)
ii. Find out the value of following parameters for Net1 and Net4: Clustering coefficient, average path length, average degree, network density, network heterogeneity. Write down the values in your answer. (5 marks)
iii. Using cytoscape, comment on whether Net4 is a scale-free network. To do this, fit a power law to its degree distribution using Cytoscape (only). Write down the scale-free exponent and quantify the level of scale-freeness, justifying your answer. (3 marks)
iv. Create a visualisation of Net 4 where nodes with higher betweenness centrality have higher node size. Node shape should be circular, with the radius of circles positively correlated with the betweenness of nodes. Make sure that the scale of the visualisation is such that all nodes are of reasonable size. Attach a screenshot. (4 marks)
v. Now, create a different visualisation of Net4 where node colours are correlated to the closeness centrality of nodes. Nodes with higher closeness should have bright colours whereas nodes with lower closeness should have dark colours. The shape pf the nodes should be circular. Again, ensure that all nodes are visible, and attach a screenshot. (4 marks)
vi. Create a copy of Net4, and in this copy, remove all duplicated edges and self-loops. Create visualisations of the original Net4, and the copy, where now node degree is positively correlated with node size. Attach both views as screenshots. Compare and comment on these two views. (6 marks)
This question is about assortativity.
i. Write down the ‘degree distributions’ of Net 1 and Net2. Use the kronecker delta function to write down your answer. (4 marks)
ii. Write down the ‘remaining degree distributions’ of Net 1 and Net2. Again use kronecker delta function and show all workings. What is the average, µ of each remaining degree distribution? (6 marks)
iii. What is the standard deviation, s, of each remaining degree distribution? (4 marks)
iv. Compute the assortativity of Net 1 and Net 2 using an edged-based summation.
Compare and comment on your answers. (12 marks)
v. Construct an edge assortativity distribution for Net 1 and Net2, either by hand or using Excel. Show all workings. What is the average edge assortativity of Net 1? What is the average edge assortativity of Net2? (Note well that in answering this question, you will need to use µ and s. If you use the numbers that were computed in parts ii and iii, remaining degrees should be used as ji and ki, because these quantities were computed using remaining degrees. Alternatively, you can re-calculate µ and s using expected degrees, and then use degrees for ji and ki). (8 marks)
vi. Construct a node assortativity distribution for Net1 and Net2. Attach you plots and show all workings. (6 marks)
This question is about using Pajek.
i. Use Cytoscape to export and save Net1, Net2, Net3, and Net4 in a format which Pajek can read. (5 marks)
ii. Load all four networks into Pajek. Attach screenshots. (1 marks)
iii. Create a three dimensional view of Net 4. Rotate the view until the node with the highest degree is at the front and in the middle. Take a screenshot of this view and attach it to your answer. (6 marks)
iv. Generate the following distributions for Net 4 using the functionalities available in
Pajek. Save them as Pajek vectors and attach them to your answer. (6 marks)
a. Degree distribution
b. Betweenness centrality distribution
c. Closeness centrality distribution
v. Pajek has implemented functionalities to extract and manipulate various sub networks from a given network. Using this, exact the sub network of all the nodes which have degrees higher than k in the original Net4. (This sub network is called the k – core of the original network). The sub network should only contain those nodes that had degrees higher than k and links that are between such nodes. Undertake this exercise for k = 1,2,3,5 and 10. (8 marks)
vi. Convert this k – core networks to a format that could be understood by Cytoscape. Export them to Cytoscape and save these networks in a Cytoscape session called kcore session. Either take screenshots of all the k-core networks and attach them or Attach this Cytoscape session to your answer. (4 marks)
The marks are given out of 100, and your total mark for this assignment will be multiplied by 0.3 to compute your final assignment mark for this assignment out of 30.
END OF ASSIGNMENT QUESTIONS