ESI 6417
Basic Graph Theory
1
Basic Graph Theory
Ref: AMO Sections 2.1 and 2.2
•
A graph or network is usually denoted as
G
(
N
,
A
) where
G
is short for ‘graph’ and
N
and
A
are names or labels for the sets that contains nodes and arcs in the network.
•
Elements of
A
are pairs of
distinct
nodes.
When the network is directed, then the
order of the nodes in the pair is important, for it indicates the direction. Otherwise
(for undirected networks), the order is irrelevant.
Example 1: Let
G
(
N
,
A
) be a
directed
network where
N
= {1, 2, 3, 4}
and
A
= {(1, 2), (1, 3), (2, 3), (3, 2), (2, 4), (3, 4)}.
Since the network is directed, the order of nodes in each element of
A
indicates
the direction of the arc.
Example 2: Let
G
(
N
,
A
) be an
undirected
network where
N
= {1, 2, 3, 4}
and
A
= {(1, 2), (1, 3), (3, 2), (2, 4), (4, 3)}.
Since the network is undirected, the order of nodes in each element of A is
not important
Note
:
In the above, elements of
A
are pairs of
distinct
nodes.
This is to disallow self-
loops or an arc that begins and ends on the same node.
For example, the arc (2,2)
in the following network is not allowed.
2
14
3
2
1
4
3
1
2