Environmental Engineering Reference
In-Depth Information
that V(G) = (R, n1, n2, n3, n4, n5, n6) and E(G) = (1, 2, 3, 4, 5, 6, 7, 8) . The magnitude of
graph G is characterized by the number of vertices | V |, which is seven (called the
order
of
G) and number of edges | E |, which is eight (the
size
of G). The content of the adjacency
matrix is shown in Table 4.1.
Figure 4.6
Water distribution network as a graph
Table 4.1
Adjacency matrix for the graph shown in Figure 4.6
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
A =
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
The matrix will show only the vertex connectivity. For simple graphs, all diagonal elements
are zero, while all other elements can be zero or one. The sum of elements in the
i
th
row (or in
the
i
th
column) gives the
degree
(or the
order
) of vertex
i
i.e. the number of edges connected
to the vertex.
Table 4.2
Node-Link matrix for the graph shown in Figure 4.6
From node
To node
R
n1
n2
n3
n4
n5
n6
R
0
1
0
0
0
0
0
n1
1
0
2
0
4
0
0
n2
0
2
0
3
0
5
0
n3
0
0
3
0
0
0
6
n4
0
4
0
0
0
7
0
n5
0
0
5
0
7
0
8
n6
0
0
0
6
0
8
0
Search WWH ::
Custom Search