Integrating “Hard” and “Soft” Infrastructural Resilience Assessment for Water Distribution Systems

Table 2

GT metrics used for the analysis of the technical dimension of resilience. The number of WDS nodes and links is denoted by and , respectively.

Resilience dimension

Metric

Formula

Description

Robustness

Density of bridges

A bridge is a link whose removal isolates part of the network. It relates the number of bridges () to the edges [44].

Central-point dominance

It is based on the betweenness centrality of each network node, , and of the most central node, . ranges from 0 (regular network) to 1 (star topology) [44, 45].

Spectral gap

Difference between the first and second eigenvalues of the adjacency matrix. A small spectral gap would probably indicate the presence of bridges [44, 45].

Algebraic connectivity

The second smallest eigenvalue of the normalized Laplacian matrix of the network. A larger value indicates enhanced fault tolerance against efforts to cut the network into isolated parts [44, 45].

Redundancy

Meshedness coefficient

Ratio between the total and the maximum number of independent loops in a planar graph. It ranges between 0 and 1 and is based on the existence of alternative supply paths [37, 38, 46].

Clustering coefficient

Based on the ratio of the number of triangular loops to the number of connected triples . It is usually smaller in grid-like structures while higher values indicate a more clustered network [44].

Rapidity

Network efficiency

It is the harmonic mean physical distance between nodes. It ranges between 0 for least-efficient and 100% for most-efficient networks and may be used as proxy for average water travel time [38].

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