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Table 1 List of Abbreviations & Symbols

From: A path-based approach to analyzing the global liner shipping network

Abbreviation

Meaning

IMR

Iterative Minimum Route

AIS

Automatic Identification System

TEU

Twenty-foot Equivalent Unit

\(G_{c}=(V_{c}, E_{c})\)

Directed co-route graph

R

Set of routes r∈R traversing ports \(p_{i}\), e.g. \(r=\langle p_{1}, p_{2}, \ldots , p_{\ell }\rangle \)

\(\ell _{r}\)

Length in edges of a route r∈R

Minimum-route paths between ports s and t with distance d

Minimum-route distance between ports s and t

\(D_{\max }\)

Maximum minimum-route distance among all pairs

\(\eta _{d}\)

# of pairs at minimum-route distance d

\(p_{d}\)

Max # of minimum-route paths between any pair at distance d

\(\textbf{A}_{i,j}\)

Adjacency matrix of the path graph (unless otherwise specified)

PG

Path graph

DCRG

Directed Co-route graph

UCRG

Undirected Co-route graph

∗-betw

Betweenness in ∗ representation

∗-deg

Degree in ∗ representation