Impacts of Node Connectivity on Reliability of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 131

resulting sub-graphs have approximately equal number of nodes and links. On the other hand,
random node or link removal will decrease the value of the algebraic connectivity if the
resulting sub-graphs have a larger number of nodes than links. In their further topological
analyses (2008), the authors compare the relationships among several topological measures
such as: the clustering coefficient , the assortativity coefficient and the rich-club coefficient ,
which is analysed in relation to the average node coreness , distance , eccentricity , degree and
betweenness . The results show various degree of correlation implying redundancy between
topological measures. Consequently, a significantly smaller set of topological measures has
been proposed to characterize real-world network's structures. The concepts elaborated in
this research look potentially applicable to water distribution networks, as well.

6.2 TOOLS FOR ANALYSIS OF NETWORK CONNECTIVITY

Several tools based on graph theory are available for generic analysis of network
connectivity, directly or indirectly. The interest for research in network connectivity has
significantly grown with the increase in numbers of web users and exponential growth in
memberships of various social networks on the Internet. While there are relatively few freely
available programs for graph-based analysis, these programs are of generally high quality,
and allow wide range of analyses and visualization tasks. In situations where such programs
are not sufficient, either because they cannot perform the required analysis or they are not fast
enough or user-friendly, there are freely available libraries for several common programming
languages. These libraries provide a wide range of graph-based data structures and algorithms
that can significantly reduce the coding process. Brief overview of a few tools coming out of
the Internet search is given in Table 6.1.

None of these tools has direct application in the field of water distribution. Yet, the
parameters they calculate aiming to assess the network connectivity can potentially be used in
the assessment of water distribution network reliability, too. The programmes developed for
social network analyses enable relatively easy processing of connectivity parameters and
visual representation of large networks, which makes them in any case initially attractive for
water distribution network analyses. The assumption of applicability is made in spite of the
fact that social networks have configurations that can substantially differ from physical
networks. For instance, they are predominantly branched and may possess loops formed by a
self-connected node.

NodeXL was selected for this study being easily accessible and transparent for use. This MS
Excel add-on, developed by Social Media Research Foundation with contributions from the
group of scientists is primarily a support to social network analyses; more information on that
can be found in Smith et al. (2009). The workbook template includes multiple worksheets
where all the information needed to represent a network/graph can be stored. Network
connections (i.e. graph edges) are represented as an 'edge list'. Other worksheets contain
information about each vertex (i.e. node) and cluster. MS Excel graphical interface is used to
represent network layouts with various map data attributes; this also includes filtering,
clustering, and customized mapping of vertex and edge-level data. The tool can easily handle
networks of several thousand vertices/edges. Figure 6.1 gives a screen snap-shot of it.