 
Summary: PHYS 597A: Graphs and networks in systems biology
Homework assignment 2, due Thursday Sept. 10
1. Construct a graph or digraph with 15 nodes and 20 edges. Extra credit
will be given for using the digraph framework. Determine
(a) the degree distribution of the graph, or the in and outdegree distri
butions if the graph is directed.
(b) the distribution of the clustering coefficients. The clustering coeffi
cient of isolated nodes or of leaf nodes (nodes of degree one) is not defined.
If you are using the digraph framework, how did you define the clustering
coefficient(s)?
2. (a) N nodes are connected by N undirected edges such that they form
a cycle (also called a ring lattice). How does the maximum distance between
nodes (the diameter) depend on N?
Tip: If dealing with N seems too abstract, do it for a few values (e.g.
N=4,6,8,10) and see if a pattern emerges. You do not need to determine the
exact relationship between the diameter and the number of nodes, only the
functional form of the dependence (i.e. is it logarithmic, linear, exponential
etc.). This relationship is called scaling, and is used in sentences as "the
maximum distance scales logarithmically with the number of nodes".
(b) On the ring lattice from above every pair of nodes at distance two on
