5.9 The Unsymmetric Szeged Matrix

The unsymmetric Szeged matrix, denoted by uSZ, is an unsymmetric V × V matrix defined as:

[uSZ]ij=
  Vi,(ij)                  if i ≠ j
  0                      otherwise                                    (100)      

where Vi,(ij)  is the number of vertices lying closer to the vertex i than to the vertex j [259,307,311].

Below we give the unsymmetric Szeged matrices for G1 (see structure A in Figure 2) and T2.
uSZ(G1)=
0
1
1
2
2
2
2
6
0
2
2
3
2
4
5
5
0
5
3
3
4
5
2
2
0
4
1
5
4
4
1
3
0
2
2
5
3
3
2
5
0
6
3
3
1
2
1
1
0

 

uSZ(T2)=
0
1
1
3
3
5
3
1
7
0
3
3
5
5
3
7
5
5
0
5
5
6
7
5
5
3
3
0
6
6
3
5
3
3
2
2
0
7
3
3
3
2
2
1
1
0
2
3
5
1
1
1
5
5
0
5
1
1
1
3
3
5
3
0

<< . . . >>