Impacts of Node Connectivity on Reliability of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 153

That is not quite a surprise in view of the fact that pipe resistance has not been considered in
this analysis. The Pearson correlation test gives the results shown in Tables 6.13 and 6.14,
with shaded figures showing better correlation than the rest. The low values of I n reflecting
low-resilient layouts, may have contributed to the low correlation of this index.

Table 6.13 Pearson correlation - case 30 nets (undirected, fixed D, variable Q)

Measures NGI NCF3 NCF avg NCI3 NSI3 AGD GD Deg avg BC avg Cc avg
ADFavg 0.94 0.47 0.75 0.01 0.54 -0.81 0.75 0.75 -0.81 0.74

NBI 0.91 0.43 0.71 0.00 0.51 -0.79 0.71 0.71 -0.79 0.72

In -0.33 -0.20 -0.25 -0.05 -0.22 0.52 -0.25 -0.25 0.52 -0.49

Table 6.14 Pearson correlation - case 30 nets (undirected, optimised D, fixed Q)

Measures NGI NCF3 NCF avg NCI3 NSI3 AGD GD Deg avg BC avg Cc avg
ADFavg 0.61 0.22 0.68 -0.18 0.19 -0.70 0.68 0.68 -0.70 0.70

NBI 0.53 0.21 0.60 -0.15 0.17 -0.60 0.60 0.60 -0.60 0.61

In 0.29 0.06 0.11 -0.01 0.16 -0.10 0.11 0.11 -0.10 0.03

A few remarks specific to the NDT results: these evaluate a couple of networks against the
impression obtained from visual observation. For instance, SN53 ranks as the 4 th with the
value of NSI3 (0.77), the 5 th with the value of NCI3 (0.81) and only the 13 th for the value of
NCF avg (2.62). On the other hand, while looking as less connected network configuration,
SN79 has the highest value of NSI3 (0.83) and NCI3 (0.88) but ranks only 22 for the value of
NCF avg (2.49). A few reasons possibly explaining this situation are:
- Unlike is the case with the measures of NodeXL, NCI and NSI both attempt to describe
any network, regardless its size, with the connectivity factor that can never be greater than
1, i.e. in relative terms.
- With variable number of links, networks with fewer loops can still be well connected i.e.
with fewer branches; this causes the higher value of NCI .
- The length of pipes gives visual impression of higher or lower connectivity. The total
pipe length of SN79 is 13,231 m, while SN53 is 17,510 m long.
- Few configurations having non-adjacent basic loops, such as SN17 or SN69 have been
evaluated unrealistically high due to too high value of L n . This results in higher values of
NGI (and consequently NSI ).
- In networks with larger number of pipes, the selection of (only) two major connectivity
categories for determination of NCF may yield too low values; hereby the highly
connected nodes have been cut-off being in low numbers.

6.7 SIMULATION RUNS, CASE THREE CLUSTERS OF 10 NETWORKS

To further investigate the correlations, the 30 networks have been recreated into three groups
of 10 networks with fixed number of pipes 79, 99, and 109, respectively. This has been
achieved by adding/removing/reconnecting pipes in the networks of the previous batch. The
layout of the new networks is shown in Figure 6.17. The rational for this analysis has been
twofold: (a) to investigate the sensitivity of connectivity measures with fixed number of
nodes and pipes and (b) to check the correlations in case of more radical differences in
number of pipes/loops of the three groups.