Impacts of Node Connectivity on Reliability of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 130

6.1 INTRODUCTION

Graph theory is widely used to describe the degree of connectivity in networks of various
types: for transport of electricity, vehicles, or water. Node connectivity in those networks will
be presented in the form of matrices; the application of these in generation of water
distribution networks has been discussed in Chapter 4. In addition, the node connectivity
plays a role in network reliability. Obviously, having more pipes means more alternative
routes in the event of particular pipe failure. Next to sufficient head at the source(s) combined
with sufficient conveying capacity of the pipes, increased node connectivity helps to maintain
the guaranteed service levels during irregular supply conditions.
The research related to the node connectivity as an element of water distribution network
reliability is mostly dealing with the concepts of spanning trees and minimum cut-sets . Jain
and Gopal (1988) have proposed an algorithm for generation of mutually disjoint spanning
trees of the network graph, named as appended spanning trees (AST). Each AST represents a
probability term in the final global reliability expression. The algorithm calculates the global
reliability of the network directly, which can also be terminated at an appropriate stage for an
approximate value of global reliability.

Kansal et al. (1995) use the concept of AST to calculate the global network connectivity,
which is defined as the probability of the source node being connected with all the demand
nodes simultaneously. Since a water distribution network is a 'repairable system', a general
expression for pipeline availability using the failure/repair rate is considered. Furthermore,
the sensitivity of global reliability estimates due to likely error in the estimation of
failure/repair rates of various pipelines is also studied in this research.

More recently, an efficient algorithm for connectivity analysis of moderately sized
distribution networks has been suggested by Kansal and Devi (2007). This algorithm, based
on generation of all possible minimum system cut-sets, identifies the necessary and sufficient
conditions of system failure conditions and is demonstrated with the help of saturated and
unsaturated distribution networks. The computational efficiency of the algorithm is
compared to those of AST having the added advantage in generation of system inequalities,
which is useful in reliability estimation of capacitated networks.

Applications of graph theory and complex network principles in the analysis of vulnerability
and robustness of water distribution networks are also investigated by Yazdani and Jeffrey
(2010). Several benchmark water networks of different size and configuration, including their
vulnerability-related structural properties have been studied in this research. The metrics,
grouped as basic connectivity , spectral metrics and statistical measurements , are used to
correlate the network structure to the resilience against failures or targeted removal of the
nodes and links.

Network- i.e. graph structures are extensively studied by the researchers in other fields. For
example, Jamaković and Uhlig (2007) analyse in their work, serving predominantly electrical
networks, a relationship between the algebraic connectivity and graph's robustness to the
node and link failures. Furthermore, they have studied how the algebraic connectivity is
affected by topological changes caused by random node/link removal. The conclusion is that
the random node or link removal increases the value of the algebraic connectivity only if the