Spatial Network Generation Tool for Performance Analysis of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 76

Figure 4.10 Theoretical number of network layouts/maximum number of links for given number of nodes
One way to reduce the number of generated networks and shorten the process is to skip some
of the columns from Table 4.7 in the generation loop, which will eventually impact the
complexity of generated networks. For instance, selecting the columns 1 to 3 and skipping the
rest will result in pipe combinations {1,5,6}, {2,5,6}, and {3,5,6}, which depict branched
configurations, as shown in Figure 4.11. On the other hand, picking the columns 4, 5 and 7
gives pipe combinations {1,2,5,6}, {1,3,5,6} and {1,2,3,5,6},which create loops as shown in
Figure 4.12. Branched and looped networks are however not clearly distinguished by the
choice of columns in the process of generation; column 7 can also produce combination
{1,2,3} combining three rows where two are empty, which will again generate branched
layout. Nevertheless, the degree of complexity is generally ascending by selecting more
columns with two or three pipes.
Figure 4.11 Sub-graphs of branched configurations
Figure 4.12 Sub-graphs of looped configurations