Impacts of Node Connectivity on Reliability of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 146

with fixed number of nodes will be reflected in the following trends of the indices shown in
Table 6.8:
1. Network grid index ( NGI ): growing for looped networks, and (forcefully) equal to 0 for
the branched/ serial networks.
2. Network connectivity factor ( NCFx ): growing for all the networks.
3. Network connectivity index ( NCIx ): equal to 1 for nearly all the networks except Net13 to
Net16; this gives distorted impression because the networks are too simple to be
diversified by this index.
4. Network shape index ( NSIx ): growing for looped networks, and (forcefully) equal to 0 for
the branched/ serial networks.

The results in Table 6.9 show the following trends for the increased number of links within a
cluster of fixed number of nodes, regardless the type of network configuration:
1. Average geodesic distance ( AGD ): reducing in the value.
2. Graph density ( GD ): increasing in the value.
3. Average node degree ( Deg avg ): increasing in the value.
4. Average betweeness centrality ( BC avg ): reducing in the value.
5. Average closeness centrality ( Cc avg ): increasing in the value.
6. Average clustering coefficient ( Cp avg ): no clear trend: equal to 0 for all the
branched/serial networks, but also for five looped networks.

6.6 SIMULATION RUNS, CASE 30 NETWORKS

The above set of networks could barely serve for more than to understand the concept behind
the indices and give the first indication of their trends. To get more insight, another set of
simulation runs has been executed, including the calculation of reliability indices, on a
sample of synthetic gravity networks all consisting of a reservoir and 76 discharge nodes,
connected in 30 random configurations ranging between 79 and 109 pipes (shown in Figure
6.10).

All the networks have configuration combined of loops and branches with variable degree of
connectivity. Some layouts are almost fully looped (such as SN8 or SN53 ) while the others
are having more branches (e.g. SN13 , or SN73 ). The connectivity to the source is provided
with one to four pipes (the latter done in SN34 ). Table 6.10 gives more information about the
geometry of each configuration and the connectivity factors and indices calculated by NDT.
The results for indices that have been obtained from NodeXL are shown in Table 6.11. The
order of results in both tables follows the order networks in Figure 6.10.

The correlation between the results in the tables and the number of links in each network is
shown in Figures 6.11 and 6.12, respectively. For the purpose of presenting all the NodeXL
results in one graph, the GD- and Cc-values have been multiplied by 100 and 1000,
respectively, while the BC-values are divided by 100. All the NodeXL results have been
calculated assuming undirected graphs i.e. networks. The connectivity calculations for
directed graph have been done after running the hydraulic simulations in EPANET, and
reversing the order of nodes for each link with negative flow/velocity. As a result, the
assumption of directed graph has only influenced the BC-values; the correlation with the
number of pipes has improved slightly, with the R 2 -value increasing from 0.6429 to 0.6754.