Risk assessment and management of civil infrastructure networks: a systems approach - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 432

The purpose of a network can be described by a multi-attribute function
g . In most cases, g is described in terms of form or fl ow. Models that focus
on the form of the network concentrate on changes in its topological struc-
ture (i.e., the way in which elements are connected) and address connectiv-
ity of the system. Models that focus on fl ow deal with cost and effi ciency of
the system. Flow in a general sense describes commodity transport through
a network, such as traffi c in transportation systems. Although form and fl ow
are linked concepts, their relationship might be diffi cult to generalize and
assess explicitly.
Performance measures are used to assess the state of individual links and
nodes in a network (i.e., local indices) or the state of the whole network
(i.e., global indices). A list and description of basic indicator is presented
next (Brandes and Erlebach, 2005), whilst other widely used indices in the
context of infrastructure can be found elsewhere (Garrison and Marble,
1962; Dueñas-Osorio et al. , 2007).

￿ Local indices: Local network measures are concerned with network

links or nodes, emphasizing their relative topological characteristics and
focusing on indicators of individual nodes, set of nodes or pre-specifi ed
paths. For instance:
￿ Distance: shortest-path between two nodes, i.e., the sum of attributes
in the links of the path (e.g., cost).
￿ Degree: number of neighbours of a node (links going inside and/or
outside a node).
￿ Betweenness: nodes/links that occur on many shortest-paths have
higher betweenness than those that do not.

￿ Global indices: Global measures provide a single metric that summa-

rizes the characteristics of the entire network and can be used to compare
different networks. Such indices are conceptually straightforward but
computationally demanding (e.g., the maximum number of network
cycles of different lengths). For instance, the clustering coeffi cient
accounts for the probability that nodes a and b are connected, given
that they share a common neighbour c . Most local indices can be taken
to a global level by taking the average, maximum, and/or minimum
(depending on the type of measure) over all nodes/links, paths, or pairs
of nodes (e.g., average shortest-path).

These measures are neutral in nature but decision makers can introduce
their attitudes towards risk by specifying acceptable thresholds with respect
to the probability of an index exceeding a certain level. Moreover, statistical
analyses can be made about the distribution of metrics such as distance, or
degree, throughout the network to determine the frequency with which
different values occur. For instance, a common measure is the degree dis-
tribution of a network, which indicates the probability that a randomly