Civil Engineering Reference
In-Depth Information
Response amplification
Person
Situation
Complexity attenuation
17.1
Complexity attenuation.
(data) for a decision-maker and a response amplifi er, since decisions made
for a specifi c cluster spread to all its constituents.
17.2.2 Network modelling
Graph theory provides a natural way of modelling networks (Brandes and
Erlebach, 2005; Bondy, 2008). A graph
G
(
V
,
E
) is an abstract data structure,
which consists of a set of nodes (vertices)
V
=
{
v
1
,
v
2
, . . . ,
v
n
} and a set of
connecting edges (also called links or arcs)
E
{
e
1
,
e
2
, . . . ,
e
m
} whose end-
points are elements of
V
. Vertices can represent any kind of elements (e.g.,
molecules, facilities, people), whereas links represent relationships between
them (e.g., attraction, distance/fl ow, or similarity/friendship).
The network structure (i.e., how elements are connected) is defi ned
either by the incidence matrix of a graph, or its adjacency matrix. The inci-
dence matrix
B
has
n
rows and
m
columns indicating relationships between
nodes and edges. Then, if nodes
i
and
j
are connected by link
k
, the elements
B
ik
and
B
jk
are taken as 1, or 0 otherwise. The adjacency matrix, on the other
hand, is a useful alternative to describe how vertices are connected, and is
denoted by a matrix
A
n
×
n
such that
a
ij
=
=
1 if nodes
v
i
and
v
j
are connected,
and
a
ij
0 otherwise.
A graph is said to be directed if
A
ij
and
A
ji
are different, i.e., the relation-
ship from
i
to
j
is different from that from
j
to
i
. Note that if
G
is an undi-
rected graph, its adjacency matrix is symmetrical. Weighted graphs can be
used to represent infrastructure networks, where edge values are other than
binary, capturing characteristics, such as cost and capacity between pairs of
nodes. Commonly, more than one attribute is necessary to describe a real-
world system; in this case, a multi-graph, with more than one link per pair
of nodes, is used.
=
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