ABSTRACT
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
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.
