Transportation Geography and Network Science/Topology

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Circuits and Trees[edit]

Circuits and Trees are two basic structures of planar networks. A circuit is a closed path, with no less than three links, that begins and ends at the same node. A tree is a set of connected lines that cannot form a complete circuit. [1]

At the individual trip level, the treeness is estimated as:

\phi_{tree} = \frac{l_{tb}}{l_{sb}}


l_{tb} = Length (km) of street segments belonging to a branch network within the buffer,

l_{sb} = Total length (km) of the street network within the buffer.


  1. Open source software developed by Feng Xie, Metropolitan Washington Council of Governments (MWCOG) can be used to identify tree and circuit links on planar networks. Code can be downloaded from [1]