Spatial Network Generation Tool for Performance Analysis of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 71

The matrix created in the same way but with the IDs of available edges as elements is called
node-link matrix . For the graph in Figure 4.6, it will look as in Table 4.2.

Graph theory concepts are applicable in different fields such as communication, circuits,
mechanical systems, hydraulics, finance, transportation, etc. with different vertices, edges and
flow parameters, as illustrated in Table 4.3 (Ráez, 2003).

Table 4.3 Graph theory applications in various fields (Ráez, 2003)

Graph
(Network)

Vertexes
(Nodes)

Edges
(Arcs)

Flow

Communications Telephones exchanges, computers,

satellites

Cables, fiber optics,
microwave relays

Voice, video, packets

Circuits Gates, registers, processors Wires Current

Mechanical Joints Rods, beams, springs Heat, energy

Hydraulic Reservoirs, pumping stations,

lakes

Pipelines Fluid, oil

Financial Stocks, currency Transactions Money

Transportation Airports, rail yards, street

intersections

Highways, rail beds, airway
routes

Freight, vehicles,
passengers

Summarised, the graph theory terminology applied in the field of water distribution shall look
as given in Table 4.4.

Table 4.4 Graph theory terminology in water distribution

Graph theory Water distribution

Graph Network

Tree graph Branched network

Simple graph Network without parallel (and/or self-connected) pipes

Pseudo/degenerated graph Network with parallel (and/or self-connected) pipes

Planar graph Network without unconnected pipe crossings

Non-planar graph Network with unconnected pipe crossings

(Spanning) sub-graph Alternative network with the same set of nodes and arbitrary links

Induced (spanning) sub-graph Alternative network with the same set of nodes and common links

Vertex Reservoir, tank, (demand) node

Edge Links: pipe, pump, valve 1)

Degree/order of vertex Number of links connected to a reservoir/tank/(demand) node
Order of graph Total number of reservoirs/tanks/(demand) nodes
Size of graph Total number of links
1) Pumps and valves will be commonly presented as edges because of the change of head they inflict between the two
vertices. In newer computer software in water distribution, they can also be defined as vertices.