Table. 1 Comparing different network representations of the same global shipping data.
Network
representation
No. of
edges
No. of
nodes
Network
density
Probability of
returning after two
steps
Probability of
returning after three
steps
Entropy
rate (bits)
Clustering
time (min)
Ranking
time (s)
Conventional first-
order
31,0282,6754.3 × 10−310.7%1.5%3.4441.3
Fixed second-
order
116,61119,1823.2 × 10−442.8%8.0%1.45737.7
HON, maximum
order of two
64,91417,2352.2 × 10−441.7%7.3%1.46454.8
HON, maximum
order of three
78,41526,5771.1 × 10−445.9%16.4%0.90636.2
HON, maximum
order of four
83,48030,6318.9 × 10−548.9%18.5%0.68677.0
HON, maximum
order of five
85,02531,8548.4 × 10−549.3%19.2%0.63687.6