 
Summary: PHYS 597A, CMPS 497E: Graphs and networks in sys
tems biology
Homework assignment 6, due Tuesday Feb. 23
1.Read chapter III, sections AF (pages 5458) and chapter V, sections A
C (pages 6366) of "Statistical mechanics of complex networks". Write down
three questions or ideas that you had while reading about random graphs.
Follow up on your questions and let me know what you find.
2. Answer the following questions:
a) At what connection probability you expect the existence of 1. a tree
with six nodes, 2. a cycle with six nodes, and 3. a completely connected
subgraph with six nodes in a random graph?
b) A random graph has a connected component that unites a large fraction
of its nodes. What is our expectation for the graph's average degree?
c) A random graph has the following degree distribution:
P(k) = Ck
11
1
3
k
2
