  The efficient computation of shortest paths in complex networks is essential
to face new challenges related to critical infrastructures such as a near
real-time monitoring and control and the management of big size systems. In
particular, using information on the minimum paths in water distribution
networks (WDNs) allows to track the diffusion of contaminants and to quantify
the resilience and criticality of the system. This is, ultimately, approached
by considering dynamically changing path-weights that depend on the flow or on
other information available at run-time. These analyses tipically include all
the WDN assets but reducing the high degree of physical details with a minimum
lost of key information for their performance assessment. This paper proposes a
strategy to compute minimum paths that is based on a dimensionality-reduction
process. Specifically, the network is partitioned into communities and suitably
modified to obtain a reduced complexity representation (e.g., in terms of
number of nodes and links). The paper shows how this novel, reduced
representation is equivalent to the traditional network on computing the
shortest paths. The proposed approach is validated considering two utility
networks as case studies. The results show that the proposed method provides
the exact solution for the shortest path with a computational-time reduction
consistently over 50\% and up to 90\% for some cases. Furthermore, the
application of the proposal on WDNs partitioning shows both hydraulic and
economic advantages thanks to their monitoring and controlling at near
real-time.
