 
Summary: CMPS 497E: Graphs and networks in systems biology
Homework assignment 1, due Tuesday Jan. 20
1. Find an example for a network in your research area or everyday life.
Define the nodes and edges and give/estimate their numbers. Are the edges
directed or not? If it is not too large, draw the network.
Characterize the network using the graph concepts learned in class. For
example (but don't restrict yourself to these!), is it connected (strongly con
nected) or not, what is the average, maximum and minimum node degree,
what is the (estimated) maximum distance between two nodes, are there any
circuits or completely connected subgraphs in the network? Which of these
graph measures are most informative for your chosen network?
2. Start with 10 isolated nodes.
(a) For each pair of nodes, throw with a die, and connect them if the
number on the die is 1; alternatively write a code that does the same. De
scribe the graph you obtained. Is it connected or not? What is the average
degree and the degree distribution? Are there any cycles?
(b) Now connect node pairs if the number is 1 or 2. How is the graph
different from the previous case?
(c) Extra credit question: How many edges do you expect a graph with N
nodes will have if they are accepted by throwing with a die (in other words,
