Geography Reference
In-Depth Information
(the number of links that a node has), which is a commonly used measure in social-
network analysis (Freeman
1978
). The average nodal degree centrality < k > is
defined as follows:
N
X
v
1
h
k
i D
k
v
(15.6)
where N is the total number of nodes and
k
v
is the number of links (neighbors) that
node
v
has.
If node
v
has
k
v
neighbors and a total of
Ev
edges among these
k
v
nodes, the
degree of network clustering coefficient <
C
v
> can be defined as the density of
connection of the neighbors of node
v
(as shown in Eq.
15.8
). A larger value
indicates that a given set of neighbors are well connected with each other, which
means that a person with higher network clustering could have a higher probability
of infection if one of his or her neighbors were to be infected. This indicator can
measure transmission risk at a node in the network of space-time distances.
2E
v
k
v
.k
v
1/
N
X
v
1
2E
v
k
v
.k
v
1/
h
C
v
i
D
D
(15.7)
15.3
A Hypothetical Example
To explain how the proposed analytical method works in our study, we will give
a hypothetical example of how to use the spatiotemporal relationships of infected
cases to track the spread of an epidemic. Suppose the data
D
are obtained by
spatial-temporal data acquisition and that the data contain the identification (ID), the
residential location, and the onset time for each individual (as shown in Table
15.1
).
Figure
15.1
shows the spatial distribution of these cases and nodes. Darker colors
indicate onset of illness at an earlier stage of the epidemic.
Table 15.1
Residential
locations and illness onset
time of the hypothetical
epidemic
Residential locations
ID
X-coordinate
Y-coordinate
Illness onset time
1
1
2
6
2
2
1
7
3
3
4
1
4
3.5
3
0
5
4
4.5
2
6
4.5
3.5
1
7
6
5.5
2
8
5.5
1.5
5
9
6
2.5
3
10
7
1
4
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