 
Summary: PHYS 597A: 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 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. Describe 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) 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, they are accepted
