Networks Assignment "Introduction to Bioinformatics"
C E N T R E F O R I N T E G R A T I V E
B I O I N F O RM A T I C S V U
Exercise 1
As you learned in the lecture directed graphs can be represented via adjacencymatrices. Most graph algorithms using adjacency-matrices require running time
O(n2). Show that determining whether a graph contains a sink is doable in time O(n)
even if a representation via adjacency-matrix is used. A sink is a vertex with indegree(|V|-1) and out-degree 0.
Exercise 2
A student claims to stem from Charles the Great. Which way is easier to check the
claim: to show that Charles the Great is an ancestor of the student or to show that
the student is a descendant of Charles the Great? Explain!
Exercise 3
Below you find two drawings of an identical set of points. Cluster these set of points
by hand and using the following distance matrix as well as:
(a) single linkage (nearest neighbor)
(b) complete linkage (furthest neighbor)
Highlight the order in which you cluster the particular points and draw a
dendrogramm.
A
B
C
D
E
F
G
H
I
J
K
A
B
C
D
E
F
G
H
I
J
31
43
105
118
118
99
118
116
113
140
30
74
86
89
74
99
106
111
143
73
85
82
57
75
76
81
113
13
21
41
71
100
123
156
16
46
73
105
129
162
34
59
91
117
149
32
59
83
116
35
64
93
29
58
33
K
Exercise 4
(a) Characterize (with a short explanation) the following examples of networks into
the two following categories: "Random Network", "Scale Free Network"
• Network of highways
• Telephone system
• European airports connected by direct flights
• Protein-protein interaction networks
• World Wide Web
• Your own social network…
(b) Find a road map of Netherlands. Determine and plot the degree distribution P(k)
(probability of a node to have k connections) for the Dutch highway system. The
nodes are the intersections and the links are the roads connecting them.
Exercise 5
(a) For E. coli K-12 construct the stoichiometric matrix for the super-pathway of
ornithine degradation. To complete this task follow these steps:
• Locate the Web interface to the EcoCyc database (Google?)
• Find the browseable list of pathways and therein the „super-pathway of ornithine
degradation“
• Now you are set to actually construct the stoichiometric matrix
(b) How many reactions are listed in the database, in which ornithine takes place?
How many are listed for NADH and L-glutamate.
Hint: These compounds are directly accessible from the ornithine pathway.
(c) For which other species listed in the database does this super-pathway not exist?
Hint: Use the Cross-Species-Comparison