Summary: PHYS 597A, CMPS497E: Graphs and networks in sys-
Homework assignment 8, due Tuesday March 24
1. Construct a graph with eight nodes and twelve edges (you can do it
randomly or select an example that seems interesting).
(a) Rank order the nodes by your expectation for the severity of the effect
of their removal on the connectivity of the network. What were your criteria
in doing so?
(b) For each node, determine what is the effect of its removal on the size
of the connected component, the diameter of the connected component, and
a third measure of your choosing. Rank order the nodes based on these three
measures. Do the results match your expectations?
2. Consider a disease spreading process in a fully mixed population where
individuals can be in one of three states: susceptible, infected/infectious, and
recovered/immune. At the onset of the infection there is a single infectious
individual and 10% of the population is immune.
(a) Write down the equations describing the rate of change of the fraction
of susceptible, infected and recovered individuals.
(b) What are the main parameters influencing the disease spreading pro-