Geography Reference
In-Depth Information
Table 1 Main database characteristics
Users
Settlements
Number of nodes
4,058,505
2,562
Number of ties
785,841,313
1,372,540
Number of intracity ties (loops)
369,789,373
2,562
Number of intercity ties
415,653,749
1,369,978
0
1
@
A
w
ij
w
i
w
j
LLR
ij
¼
Log
ð
1
Þ
X
n
i
¼
1
,
j
¼
1
w
ij
in which LLR
ij
refers to the log-likelihood ratio between settlement i and j, w
i
and
w
j
are the sum of tie weights (total number of connections) of settlement i and j and
w
ij
is the raw weight of tie between settlement i and j. The higher positive LLR
refers to strong settlement-to-settlement ties, while negative LLR represents weak
intercity connections. In the following both raw weight ties and log-likelihood
ratios are applied to explore absolute and relative connectivity weight
characteristics.
Since raw weight ties are strongly biased by settlement size (cities with larger
population numbers have higher absolute number of connections) the histogram of
raw weight tie values show power-law distribution; the majority of settlements have
relatively small number of connections, while some have very large connection
numbers. The log-likelihood ratios of the overall 1,369,978 settlement connections
had on the other hand almost normal distribution with a skewness test 1.204 and
kurtosis result 2.244. LLR values range from
5.08 to 8.61 (Fig.
1
).
1.5 which means that the majority of
intercity connections are weak and strong connections are rare. This is also because
expected frequencies were calculated from the total number of connections of
cities, which also includes loops (intra-city ties) that are always higher than the
randomly expected. This pushes the distribution to the negative range.
The peak of the histogram is around
