Page 153 - Becoming Metric Wise

144 Becoming Metric-Wise

s
H 5 b; f ; g; d; e; h; i; j
2

s
H 5 f ; g; h; i; j
3

s
H 5 f ; h; i; j
4
s

H 5 h; i; j
5
There are now five generations, nodes h,i,j belong to the second,
third, fourth as well as the fifth generation, because they can be linked to
the target set in two, three, four, and five steps.
This illustrates the difference between overlapping and nonoverlapping
generations.
As multisets however we have:

G 0 5 fa; bg

m
G 5 c; f ; f ; g
1
m

G 5 d; e; h; i; j; h; i; j
2
Article f belongs twice to the first generation (as multisets) because it
is linked to the target set via a and also via b. Finally:
H 0 5 fa; bg

m
H 5 b; c; f ; f ; g
1
m

H 5 b; f ; f ; f ; g; d; e; h; i; j; h; i; j
2
m

H 5 h; i; j; f ; h; i; j; g; f ; h; i; j
3

m
H 5 h; i; j; f ; h; i; j
4
m
H 5 h; i; j
5