Geography Reference
In-Depth Information
Appendix: Measures of network structure
1
.
Density
Network density is dei ned as 'a measure of the proportion of possible lines that are actu-
ally present in a graph' (Wassermann and Faust, 1994, p. 101). It is calculated as follows:
the maximum possible number of lines in a graph is given by the sum of possible unor-
dered pairs of nodes:
n
(
n
− 1)/2 with
g
being the number of nodes in the network. The
density (
DN
) is calculated as the ratio of the number of lines present,
L
, to the maximum
possible:
DN
= (
L
/(
n
(
n
− 1)/2))
2
.
Actor coreness
Actor 'coreness' is dei ned as the degree of closeness of each node to a core of densely con-
nected nodes observable in the network, as described by Borgatti and Everett (1999).
3
.
Fragmentation
Fragmentation is a measure that counts the number of pairs of nodes that are discon-
nected from each other. The measure is found in Borgatti (2006) and is calculated as
follows: given a matrix
R
in which r
ij
= 1 if
i
can reach
j
and r
ij
= 0 otherwise, network
fragmentation is:
F
= 1 − (2∑∑ r
ij/n
(
n
− 1))
The indicator ranges from a minimum of 0 to a maximum of 1.
