Civil Engineering Reference
In-Depth Information
The above considerations have led to a model that aggregates all con-
nectivity-related methods at the highest possible level, depending on the
network, and has a repeating template for the lower portion of each network,
so that in most cases, the same methods are present even though with
slightly different implementations for each particular system.
Figure 18.5 shows the class diagram of the
Network
class and sub-classes
in the current model. The
Network
class is an abstract one. From a computa-
tional standpoint, it is convenient to group these systems into
directed
(Fig. 18.4c) and
undirected
(Fig. 18.4d) ones, since most graph-theoretic
algorithms exist in specialised, optimised forms based on this distinction.
Typically utility networks are of the undirected type, i.e. they have a sym-
metrical adjacency matrix whereby the existence of an edge from node
i
to
node
j
implies the opposite, with the actual direction of fl ow in each edge
determined by the solution of the fl ow equations in the functional network
model (the fl ow model, as opposed to the structural model consisting
of a graph). Transportation systems, on the other hand, are typically
directed ones.
Examples of the main attributes and methods include, for instance, at the
Network
class level, the two lists of pointers to all
Nodes
and
Edges
in the
network, that store the network topology. A further important attribute is
States
. This variable is present in all classes in the object-oriented model and
is used to record the object state in each simulation run (see Section 18.7.3).
Among the methods, there are auxiliary methods, that include algorithms to
convert between alternative existing graph representations, such as from the
list of edges to the incidence or adjacency matrices, or search methods, that
include the search for a minimum path, given a set of generalised weights
on the edges, or for a sub-network satisfying given property requirements.
At the lower level of the
Directed
and
Undirected
abstract classes, there
are other methods that, as anticipated, exist in alternative forms depending
on the network type. An example is the method
isConnected
(which deter-
mines whether there is at least a path between any two nodes in the graph)
of the
Undirected
class, which has two counterparts in the
Directed
one,
since in this case the concept of connection is replaced by those of strong
and weak connections.
It should be underlined how all these methods are of great importance
beyond the basic integrity analysis of each system. Indeed, rapid knowledge
of the state of fragmentation of a network can avoid assembling and solving
fl ow equations for which a feasible solution does not exist. The common
connectivity model extends to the template for each concrete class at the
lower level. All are the composition of two classes, one for nodes and the
other for edges, both of the abstract type.
Classes describing nodes in each concrete network model store the geo-
graphical
position
(latitude, longitude and altitude) of the node and whether
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