 
Summary: PHYS 597A: Graphs and networks in systems biology
Homework assignment 1, due Thursday Sept. 3
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 (if the edges
are undirected) strongly or weakly connected (if the edges are directed), 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 infor
mative 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
