 
Summary: PHYS 597A: Graphs and networks in systems biology
Homework assignment 2, due Tuesday Jan. 27
1. Construct a graph with 15 nodes and 20 edges. The edges can be
undirected or directed; note that you will need to use the digraph framework
if there is even one directed edge. 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.
2. (a) N nodes are connected by N 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
the ring is connected by an edge. What is the clustering coefficient of the
