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h7 - Albert model which one has a larger degree range 2...

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PHYS 597A, CMPSC 497E: Graphs and networks in sys- tems biology Homework assignment 7, due Tuesday Oct. 27 1. Based on what we have learned in class so far, answer the following questions in your own words. You can support your answer with formulas but formulas alone will not count as an answer. (a) Why doesn’t the average clustering coefficient of a regular lattice depend on the size of the lattice? (b) Why doesn’t the average clustering coefficient of a small world net- work (generated with the Watts-Strogatz model) depend on the size of the network? (c) Comparing two large networks of equal number of nodes and edges, one generated by the Watts-Strogatz model and one generated by the Barab´asi- Albert model, which one has a larger average distance? (d) Comparing two large networks of equal number of nodes and edges, one generated by the Watts-Strogatz model and one generated by the Barab´asi-
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Unformatted text preview: Albert model, which one has a larger degree range? 2. Construct a graph with eight nodes and twelve edges (you can do it randomly or select an example that seems interesting). (a) Propose a node measure (or combination of measures) that can serve as a proxy for the severity of the e±ect of the nodes’s removal on the connec-tivity of the network. Order the nodes by this measure from highest expected e±ect to lowest. (Hypothetical example: the lower the clustering coeFcient of the node, the higher the e±ect of its removal.) (b) ²or each node, determine what is the e±ect of its removal on the size of the remaining largest connected component, the diameter of the largest connected component, and a third measure of your choosing. Order the nodes based on these three measures from highest e±ect to lowest. Do the results match your expectations from part (a)? 1...
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